How to Calculate Slope and Grade for Drainage (5 Steps)

Slope is the one site measurement that decides where water goes, and water going the wrong way is the most expensive slow problem a property can have. The arithmetic behind it is simple enough to do on a scrap of paper: a vertical fall, a horizontal run, one division. What makes it awkward in practice is that the answer gets written four different ways depending on who is asking, that the measurement is easy to take badly, and that the target you are aiming for is decided by your building department rather than by any number printed on a website.

This manual separates those three things deliberately. The arithmetic gets covered in full, because it is the part that is reliably true everywhere: converting between percent, ratio, degrees, and inches of fall per foot, in both directions, with the derivation rather than a lookup table. The measuring gets covered in full, because a string line and a spirit level will get you a trustworthy number for the cost of an afternoon. The targets get treated honestly as commonly cited starting points, with a pointer to who actually decides. Our estimator handles the running arithmetic while you read.

Slope, grade, pitch and fall are one number with four names

Walk a site with three trades and you will hear the same measurement called four things. A landscaper says grade. A drainage contractor says fall. A carpenter says pitch. A drawing says slope, usually with a percentage next to it. They are describing one relationship: how far a surface drops vertically over a given horizontal distance.

The word choices carry faint habits with them. Fall usually means the total vertical drop across a specific run, quoted in inches, as in “we have four inches of fall to the street.” Grade usually refers to the surface itself and its elevation, as in “the grade falls away from the house.” Slope is the ratio, most often quoted as a percentage. Pitch, on a site rather than a roof, tends to mean the slope of a pipe.

None of that changes the arithmetic. If somebody tells you a run has four inches of fall and somebody else tells you the same run is at 1.4 percent, they have not disagreed with each other, they have used different units. The one habit worth building is asking for both the fall and the run whenever a number arrives without them, because a percentage on its own cannot be checked and an inch figure on its own is meaningless.

The one formula, and the four ways to write its answer

Everything in this article comes out of a right triangle. The vertical leg is the fall, sometimes called the rise. The horizontal leg is the run. The surface itself is the hypotenuse. The slope is the relationship between those two legs, and the formula is:

Slope, as a decimal = fall ÷ run

with fall and run in the same unit. Multiply by 100 and you have percent. That is the whole thing. Every other form is a restatement of that same ratio.

Percent slope = (fall ÷ run) × 100. The common form on drawings and in conversation. A 6 inch fall over 120 inches of run is 6 ÷ 120 × 100, which is 5 percent.

Ratio, written 1 in n = run ÷ fall. Common in plumbing and in older drainage practice. That same 6 in 120 is 1 in 20.

Degrees = arctan(fall ÷ run). Needed when an angle finder or a phone is doing the reading. 6 ÷ 120 is 0.05, and arctan(0.05) is about 2.86 degrees.

Inches of fall per foot = (fall ÷ run) × 12 when the run is in feet, or percent ÷ 100 × 12. That 5 percent is 0.60 inches per foot.

Four expressions, one measurement. Pick whichever your reader thinks in and convert without ceremony.

Before you start: what to settle before a single stake goes in

Three questions decide whether the measuring you are about to do will be worth anything, and all three are cheaper to answer standing still than halfway through a trench.

Where is the water supposed to end up? Slope only means something relative to a destination. A back yard at a healthy 2 percent that runs straight at a neighbour’s fence line has solved nothing and created a dispute. Identify the outlet first: a street, a swale, a drywell, a daylight point on a bank, an existing storm connection. If you cannot name the outlet, you are not ready to measure slope, you are ready to ask your building department where water from your property is permitted to go.

What is buried along the route? Call the utility locating service before any stake goes deeper than a few inches, and give them the lead time they ask for. This is free, it is standard practice, and it is not optional.

What is the run, roughly? Pace it out. A 20 foot run and a 200 foot run are different jobs, needing different tools and different levels of care about string sag. Knowing which one you have before you pick up a tool saves a wasted setup.

Write the answers down. The rest of this article assumes you have them.

Step 1: Find the high point, the low point and the run

Start at the ends, not in the middle. Walk the area and identify the point that has to be highest, which is usually the point closest to whatever you are protecting, and the point that has to be lowest, which is the outlet you named a moment ago. Drive a stake at each.

The high point is rarely a matter of choice. Against a house it is fixed by the existing grade at the foundation. On a patio it is fixed by the door threshold or the slab edge. On a driveway it is fixed by the garage floor. These are the elevations you have to work with rather than elevations you get to set, which is why they are the natural place to start.

Now measure the run between the two stakes, and measure it horizontally. On near-level ground the tape can lie on the ground and the error is negligible. On ground that already falls noticeably, hold the tape level and plumb down to the low stake, or step the measurement in shorter level sections and add them.

Write down the run in feet and, immediately, in inches. Most of the slope arithmetic wants inches, and converting once at the start prevents the single most common calculation error in the whole exercise. A 24 foot run is 288 inches. Put both numbers on the paper.

Step 2: Establish a true level line and measure the fall

The fall is the difference in ground elevation between the two stakes, and you cannot measure a difference in elevation without a reference that is genuinely horizontal. That reference is the entire skill in this step.

Tie a mason line to the high stake a few inches above the ground and run it to the low stake. Wrap it once around the low stake so it can slide up and down but stays put when you let go, and pull it tight enough that it stops sagging visibly. Hang a line level at the midpoint of the string, or hold a spirit level against it, and slide the string at the low stake until the bubble sits dead centre. The line is now level.

Measure from the string straight down to the ground at the high stake and write it down. Do the same at the low stake. Both measurements must be plumb, not square to a sloping surface, so let the tape hang or use a torpedo level against it.

Fall = the low stake reading minus the high stake reading. If the string sits 2 inches above the ground at the high stake and 4.5 inches above it at the low stake, the ground has dropped 2.5 inches across the run. That is the fall.

Take the whole set of readings twice, and re-centre the line level between them. Agreement is what tells you the number is real.

Step 3: Convert the fall into percent, ratio, degrees and inches per foot

Now the arithmetic, and this is the part that behaves the same on every site on earth.

Take the fall of 2.5 inches and the run of 288 inches from the last step. Divide fall by run: 2.5 ÷ 288 = 0.00868. That decimal is the slope, and everything else is a presentation of it.

Percent: 0.00868 × 100 = 0.87 percent.

Inches per foot: 0.00868 × 12 = 0.104 inches per foot, or with the run already in feet, 2.5 ÷ 24, which is the same thing. Just over three thirty-seconds of an inch, a shade under an eighth.

Ratio: 288 ÷ 2.5 = 115.2, so 1 in 115. One unit of drop for every 115 units of travel.

Degrees: arctan(0.00868) = 0.497, so about half a degree. Set the calculator to degree mode before you trust that, because in radian mode the same keystrokes return 0.00868, which looks like the input and is easy to mistake for a mis-key.

Four numbers, one measurement, no judgment involved yet. Write all four down, because the next conversation you have about this run will use whichever one you did not calculate.

Step 4: Compare what you measured against the target you want

Only now does the number get judged, and judging it needs two things: a target, and the total fall that target implies across your specific run.

Converting a target percentage into inches of fall is the same formula run backward:

Required fall = target percent ÷ 100 × run in inches

At a target of 2 percent across the 288 inch run, that is 0.02 × 288 = 5.76 inches. The measurement in Step 2 gave 2.5 inches. The run is short by 5.76 minus 2.5, which is 3.26 inches.

That subtraction is the whole output of this step, and it is worth stating in both directions. You have 0.87 percent and you want 2 percent. You have 2.5 inches of fall and you need 5.76. The inch figure is the one to carry forward, because inches are what you dig, haul and rake, while percentages are what you write on paper.

Where the target comes from is a separate question and this article cannot answer it for you. Common conventions exist and the next few sections describe them honestly as conventions. The number that governs your project comes from your building department, from whoever engineered the structure if a structure is involved, and from the specific product instructions if you are laying a manufactured surface.

Step 5: Stake the finished grade and check it as you cut and fill

A calculated slope becomes a real one when it is marked on the ground in a form a shovel can follow.

Set intermediate stakes along the run at even spacing, 8 feet apart is comfortable for a back yard. Restring the level line and mark it on every stake with a pencil or a wrap of tape, so you now have a horizontal datum running the length of the job.

Then compute the drop below that datum at each stake. Your target slope times the distance from the high stake gives it directly. On the 24 foot run at a 2 percent target, the drop below the level line grows by 0.24 inches per foot: 1.92 inches at 8 feet, 3.84 inches at 16 feet, 5.76 inches at 24 feet, added to whatever the string height was at the high stake. Measure down from the string and put a mark on each stake at that depth. Those marks are the finished grade.

Now cut and fill to the marks. Check as you go rather than at the end, because soil moves in bulk and a raked surface that looks flat can be an inch out over 10 feet. When the surface is close, restring the line and re-measure at every stake.

The final check is water. Run a hose at the high end and watch. Water is a perfect level and an unforgiving one, and a puddle that forms where you expected flow is telling you something the tape did not.

The string line method, set up properly

The string line is the workhorse for anything up to about 50 feet, and its accuracy is entirely a function of how it is set up.

Use a proper mason line rather than household twine. Braided mason line stretches predictably and stays taut, while twine sags, absorbs moisture and lies to you. Pull it tight enough that plucking it gives a low note rather than a dull thud.

Sag is the enemy and it is worst at midspan. A line level hung at the midpoint reads the average of the string’s own geometry, which is why the level goes in the middle rather than near an end, and why on longer runs it pays to check with a spirit level held against the string at two or three points along it.

Wind matters more than people expect. A steady breeze on a 40 foot string bows it sideways and lifts it, and the reading drifts while you watch. Measure on a still morning if you can.

Stake height matters too. Keep the string low, a few inches above the ground at the high end, so the numbers you are subtracting stay small. A string set 3 feet up because the stakes were long turns every reading into a large number, and subtracting two large numbers to find a small difference multiplies whatever error each one carries.

The level and tape method, and the two errors it invites

The other classic approach uses the level itself as the horizontal reference: rest one end of a long spirit level on the high ground, raise the free end until the bubble centres, and measure the gap from the level’s underside down to the ground. Slope is that gap divided by the level’s length.

It is quick and it is fine for short distances. A 4 foot level with a 1 inch gap under the free end is 1 ÷ 48, which is 2.08 percent. A 2 foot level with a half inch gap is 0.5 ÷ 24, the same 2.08 percent.

Two errors follow it around. The first is measuring the gap somewhere other than the level’s true end, which makes the run something other than the level’s length. Measure at the very end of the tool, and remember that the run is the level’s length whatever the ground under it is doing.

The second is that the method samples a short piece of ground and reports it as the whole run. A 4 foot level bridging a mound reads steep, and bridging a dip reads flat, and neither describes the 30 feet the water actually has to cross. Take several readings along the run and use the string line for the overall figure. The level is a spot check, not a survey.

Laser levels, water levels and phone inclinometers

Rotary and line lasers turn a one person job into a fast one. A self levelling laser on a tripod projects a horizontal reference, and a detector on a graduated rod reads the height of that plane above the ground at any point. Slope is the difference between two rod readings divided by the distance between them, which is the string line method with the string replaced by light that never sags. Check the calibration on a known level surface before trusting a borrowed one.

A water level is a length of clear tubing filled with water, and it is the cheapest genuinely accurate tool in this whole article. Water finds its own level, so the surface in one end is always at the same elevation as the surface in the other, no matter how the tube snakes between them. That makes it the right tool for measuring around a corner or across an obstacle where nothing has line of sight. Bleed every air bubble out first, because a trapped bubble breaks the continuous column and the readings become fiction.

Phone inclinometers and digital levels read the angle directly in degrees, which converts with the tangent relationship. They are convenient for a quick sanity check and less convincing for a final number, because a shallow site slope of half a degree sits inside the drift these sensors show. Calibrate on a surface you have independently confirmed is flat, take several readings, and treat a disagreement with the string line as the string line winning.

Inches of fall per foot, and the fractions people call out on site

Nobody standing in a trench says zero point two four inches. They say a quarter inch per foot, and the conversation continues in fractions from there. Being fluent in both directions is worth the two minutes it takes.

Going from percent to inches per foot, multiply the percentage by 0.12. The whole conversion is that one constant, because 12 inches divided by 100 percent is 0.12. So 1 percent is 0.12 inches, 2 percent is 0.24, 3 percent is 0.36, and 5 percent is 0.60.

Going the other way, multiply inches per foot by 8.333. An eighth of an inch per foot is 0.125 × 8.333, which is 1.042 percent. A quarter inch is 2.083 percent. Half an inch is 4.167 percent. A full inch per foot is 8.333 percent.

The fractions and the round percentages are near neighbours rather than twins, and the gap only matters over distance. An eighth per foot and 1 percent differ by 0.005 inches per foot, which is a fifth of an inch over 40 feet. On a patio that is nothing. On a long pipe run where the outlet depth is already tight, it is the difference between the trench working and not.

The conversion table, and how to rebuild any row of it

Tables get rounded, photocopied and misremembered, so it is worth being able to regenerate any line of that one from scratch. Every column comes from the same decimal.

Start with the slope as a decimal, which is percent divided by 100. Take 3 percent, so 0.03.

The fall per foot column is that decimal times 12: 0.03 × 12 = 0.36 inches.

The ratio column is 1 divided by that decimal: 1 ÷ 0.03 = 33.3, so 1 in 33.

The degrees column is the arctangent of the decimal: arctan(0.03) = 1.72 degrees.

Two checks confirm you are doing it right. The first is that 8.333 percent must give exactly 1.00 inches per foot and exactly 1 in 12, because a 1 inch drop over a 12 inch run is 1 ÷ 12, which is 0.08333. The second is that at these shallow angles the degrees column runs at almost exactly 0.5729 times the percentage, because the tangent of a small angle is close to the angle itself in radians. If your degrees figure is not close to percent times 0.573, something has gone wrong in the keystrokes. Above about 20 percent that proportionality drifts away and only the true arctangent will do.

Commonly cited targets, and why they are starting points

Here is the honest position of this manual. The arithmetic above is universal. The target numbers below are not, and presenting them as though they were would be the most useful looking and least useful thing on the page.

Minimum grades away from foundations, across paved surfaces, along swales and inside drain pipes are set by the building code adopted where you live, and adopted codes vary between jurisdictions and are amended locally. They also interact with soil type, frost depth, rainfall intensity, the presence of a basement, and what the neighbouring properties are doing. Some situations attract conditions that no general figure anticipates.

So the sections that follow describe the conventions that circulate widely, explain the mechanism behind each one, and stop there. They will help you plan, sanity check a contractor’s number, and ask a better question. They are not a specification, and no code section numbers appear here because quoting a section that has been amended locally is worse than quoting nothing.

Two calls settle it: your building department for what is required, and a licensed engineer for anything that touches a foundation, a retaining wall, a slope that could fail, or water being directed off your property. Both calls are cheaper than being wrong.

Grade away from a foundation

The figure that circulates most widely is roughly 6 inches of fall in the first 10 feet away from the foundation, which is 5 percent. Treat it as a commonly cited starting point rather than a requirement, because the requirement is your building department’s to state.

The mechanism behind it is worth more than the number. Water that reaches the soil against a foundation wall soaks in, saturates the backfill, and applies pressure to the wall from outside while looking for any route through it. Backfill is disturbed soil and it settles for years after construction, which is why a grade that was correct at handover can be flat or reversed a decade later. Getting water away from the wall in the first few feet is what the steep zone is for.

Several details travel with it. The soil should not be brought up against untreated siding or across a weep course, so the grade has to fall away without raising the ground level at the wall. Downspouts discharging into that steep zone will overwhelm it, which is why extensions or buried leaders exist. Hard surfaces that abut the wall need their own fall rather than relying on the soil beside them.

Anything that suggests a structural problem, a foundation crack, a bowed wall, a persistently wet basement, is not a grading question. That is an engineer’s call.

Patios, walkways and other hard surfaces

A hard surface sheds essentially all the water that lands on it, which makes its slope more consequential than lawn. The range most commonly cited for patios, walkways and slabs is something like 1 to 2 percent away from the building, an eighth to a quarter inch per foot. Again, commonly cited, not code, and your building department decides.

The tension is between drainage and comfort. Too flat and water sits in the low spots, which on a paved surface means staining, moss, ice in winter, and joint material washing out. Too steep and furniture wobbles, a table rocks, and the tilt becomes noticeable underfoot, which people do register somewhere above about 3 percent.

Direction matters as much as magnitude. The fall should carry water away from the house and toward somewhere it can go, which means the slope is planned alongside the outlet rather than after it. A patio sloped correctly into a corner with no outlet has moved the puddle rather than removed it.

Setting the slope happens at the base, not the surface. Our paver patio manual covers screeding a base to a planned fall, and our gravel depth reference covers what sits underneath it. The arithmetic in Step 5 is what puts the marks on the stakes.

Driveways: the cross slope and the running slope

A driveway has two slopes at once and they are calculated separately from the same formula.

The cross slope runs across the width and its job is shedding water sideways, off the surface and into whatever runs alongside. Commonly cited figures for cross slope sit in the same 1 to 2 percent territory as patios. On a 12 foot wide drive at 2 percent, the low edge is 0.02 × 144, or 2.88 inches, below the high edge. A crowned drive splits that: high down the centreline, falling both ways, so each half carries half the width.

The running slope goes along the length and is usually decided by the site rather than chosen, since it has to connect a garage floor to a street. Where it does become a design question, the constraints are traction in wet or icy conditions, vehicle ground clearance at the transitions, and the drainage that a long slope concentrates at the bottom. Maximum running slopes are set locally and vary considerably, so ask rather than assume.

Transitions deserve a mention because they cause more damage than gradients do. Where a steep slope meets a flat apron, the change in angle can bottom out a low vehicle even when neither slope alone is a problem. Easing that change over a few feet is the fix. Our gravel driveway manual covers the base work the slope sits on.

Drain pipe pitch is a different problem from ground grade

Pipe pitch uses the same formula and behaves differently, because a pipe carries water in a confined channel rather than across an open surface.

Two failure modes bracket it. With too little pitch, flow slows, and anything the water is carrying, silt, sand, fines washed off a roof, drops out and stays where it lands. Over years that builds into a blockage. With too much pitch in a pipe carrying solids, water can run ahead of the solids and leave them stranded, which is the same outcome by a different route. Between those bounds is a range where flow stays fast enough to keep the pipe scouring itself clean.

The specific figure for your pipe depends on what it carries, its diameter, its material, and the code enforced where you live, so it is not something an article can hand you. Ask your building department, and follow whatever your drawings specify.

What the arithmetic does give you is the consequence. Pitch times length is total drop, and total drop plus starting depth is how deep the outlet has to be. A 40 foot run at 1 percent drops 0.01 × 480, or 4.8 inches. The same run at an eighth of an inch per foot drops 40 × 0.125, which is 5.0 inches. Starting 10 inches deep at the inlet, the outlet invert lands about 14.8 inches down. If the point where the pipe must daylight is shallower than that, the design has to change before the digging starts. Our french drain cost reference covers what the rest of that trench involves.

Swales: a shallow channel with a slope of its own

A swale is a broad shallow depression that collects surface water and moves it somewhere, and it has two slopes that both need calculating.

The side slopes run down into the channel from either side and control whether the swale is mowable, walkable and stable. They are usually quoted as a ratio of horizontal to vertical, and gentler is more forgiving of erosion and easier to maintain. Steep sides on loose soil scour and slump.

The longitudinal slope runs along the swale toward the outlet, and it is the number this article’s arithmetic supplies. Too flat and the swale becomes a linear puddle that stays wet and kills the grass. Too steep and the flow starts moving fast enough to cut into the channel and carry soil away, which is when armouring with stone starts to be discussed. Commonly cited longitudinal slopes for grassed residential swales sit in the low single digit percentages, and as with everything in this section, the applicable figure comes from whoever regulates drainage where you live.

Sizing a swale to a rainfall event is hydrology, not arithmetic, and it belongs to an engineer. So does any swale that carries water toward a property line, a structure, or a slope that could fail. What you can do yourself is measure the fall along the route with a string line and find out whether the elevation you need actually exists.

Worked example: checking a 24 foot back yard run

A back yard slopes gently from the house toward a low corner where an existing drain sits. The homeowner wants to know whether the existing grade will carry water there, and if not, by how much it falls short. All figures here are illustrative and exist to demonstrate the method.

The measurement. Stake at the patio edge against the house, stake at the low corner, tape held level between them reads 24 feet, so the run is 288 inches. Mason line tied at the high stake, wrapped at the low stake, line level centred at midspan. Reading down to the ground at the high stake: 2 inches. At the low stake: 4.5 inches. Fall = 4.5 minus 2 = 2.5 inches.

The conversions. 2.5 ÷ 288 = 0.00868. That is 0.87 percent. In inches per foot, 2.5 ÷ 24 = 0.104, just under an eighth. As a ratio, 288 ÷ 2.5 = 1 in 115. In degrees, arctan(0.00868) = 0.50.

The comparison. The homeowner is planning for 2 percent, a figure they have been given as a starting point and intend to confirm with the building department. Required fall = 0.02 × 288 = 5.76 inches. They have 2.5. The shortfall is 3.26 inches.

Reading the shortfall. Over the first 10 feet, the existing grade delivers 0.00868 × 120, which is 1.04 inches, against the roughly 6 inches commonly cited for the zone against a foundation. That is a bigger relative gap than the whole run shows, and it points at where the work matters most.

The options. Raise the high end 3.26 inches and taper to zero at the outlet. Or cut the low end down, if there is depth to cut into and the drain can take it. Or shorten the run by bringing the outlet closer. Or move the water in a pipe instead of across the surface. Take the same numbers through our estimator with your own run and fall.

Turning a slope correction into a volume of soil

A shortfall in inches becomes an order in cubic yards, and the shape it becomes is a wedge: full depth at one end, zero at the other.

The volume of that wedge is half the maximum depth times the length times the width. Continuing the worked example, the correction is 3.26 inches at the house tapering to nothing at 24 feet, across a regraded area 16 feet wide.

Convert the depth to feet first: 3.26 ÷ 12 = 0.2717 feet. Then 0.5 × 0.2717 × 24 × 16 = 52.2 cubic feet. Divide by 27 and that is 1.93 cubic yards, call it 2 yards.

Two adjustments follow. Fill compacts, and soil placed loose and then compacted occupies meaningfully less space than it did on the truck, so order above the calculated figure rather than exactly at it. And a regrade rarely stops at a neat rectangle, because the new surface has to tie into the existing ground at the edges without leaving a lip.

Our cubic yard manual covers the volume arithmetic in full and our topsoil manual covers ordering and spreading. If the regrade is going under new lawn, our sod manual picks up from there.

Cross slope, compound slope and draining in two directions

Real surfaces often fall in two directions at once, and the two components are calculated separately and then combined.

A patio might fall 2 percent away from the house along its depth and 1 percent along its width toward a side yard. Each component is its own fall over its own run, and each gets staked independently: the marks on the stakes account for both, because a corner that is far along both axes carries both drops.

The resulting steepest path down the surface is steeper than either component. For a surface falling at 2 percent one way and 1 percent the other, the combined slope is the square root of 2 squared plus 1 squared, which is the square root of 5, about 2.24 percent, running diagonally across the surface. That is the direction water will actually take, and it is worth knowing because it is where a long puddle will form if the surface is out anywhere along it.

The practical consequence is a warning about single axis thinking. A patio staked carefully for its 2 percent away from the house and never checked across its width can be dead flat one way and hold a line of water along its edge. String the line in both directions before you call the grade finished.

Common mistakes that produce a wrong slope

Measuring the run along the ground. The formula wants horizontal distance. A tape lying on sloping ground reads the hypotenuse, which is longer than the run, and a longer denominator reports a flatter slope than you have. On a gentle site the difference is tiny. On a bank it is not.

Mixing units in the division. Fall in inches divided by run in feet gives a number twelve times too large. Convert the run to inches at the start of Step 1 and the error becomes impossible.

Trusting a sagging string. A line that droops at midspan puts the level on a curve rather than a straight, and the readings at the ends inherit whatever that curve did. Pull it tight, check it at more than one point on long runs, and pick a still day.

Reading the tape square to the slope. The fall is a vertical distance. A tape held perpendicular to a sloping surface reads short. Let it hang plumb.

Taking one reading and building on it. Ground is uneven and stakes move. Every reading in this article should be taken twice, and any disagreement resolved before the shovel comes out.

Solving for slope and forgetting the outlet. A perfectly graded run that discharges against a fence, a foundation or a neighbour has created a problem rather than solved one. The outlet is decided first.

Troubleshooting: what to do when the fall is not there

The numbers say there is not enough drop. Re-measure before you believe it, using a different method if you can, because a water level and a string line disagreeing by an inch usually means one of them was set up badly. If the shortage survives a second measurement, it is real.

There is fall, but water still sits. The overall slope can be fine while a local dip holds water anyway. Set intermediate stakes at 8 foot spacing and read the ground at each against a level line. The dip will show up as a reading larger than the two either side of it.

The low end has nowhere to go. This is the hardest case and the one where do-it-yourself options run out fastest. Possibilities include a drywell if soil percolation and the local rules allow it, a pumped system, or a connection to an existing storm outlet if you are permitted to make one. All three are questions for your building department before they are questions of technique.

The run is long and flat and the outlet is fixed. A pipe can hold a consistent shallow pitch that a raked surface cannot, so moving the water in a pipe is often the answer when surface grade has run out.

Anything involving a wall, a bank or a structure. Stop. Changing where water goes changes the loads on a retaining wall and the stability of a slope. Our retaining wall manual explains why drainage behind a wall is a structural matter, and the engineering belongs to an engineer.

The field checklist

Run through this before the tools go back in the truck.

• Outlet identified and confirmed as somewhere water is permitted to go.
• Utility locate requested and marks on the ground.
• High stake and low stake driven, run measured horizontally, written in both feet and inches.
• Mason line strung, line level centred at midspan, checked at a second point on runs over 30 feet.
• String to ground read at both stakes, plumb, twice, and the two sets agree.
• Fall calculated as low reading minus high reading.
• Slope converted to percent, ratio, degrees and inches per foot, and all four written down.
• Target confirmed with the building department rather than assumed from a chart.
• Required fall computed as target ÷ 100 × run in inches, and the shortfall or surplus stated in inches.
• Intermediate stakes set and marked with the finished grade depth below the level line.
• Volume of cut or fill estimated and ordered with a compaction allowance.
• Hose test run on the finished surface, and any puddle traced back to a stake reading.

Where this sits beside the rest of the site math

Slope is usually the first calculation on a site and rarely the last one. Once the grade is settled, the rest of the numbers follow from it.

Area comes next, because a regrade, a patio or a drive all get ordered by the square foot. Our square footage manual covers the shapes that real yards come in. Depth turns area into volume, and our cubic yard manual handles the conversion that trips up most first orders.

Materials follow from volume. Our gravel manual covers the aggregate a drainage trench or a base course needs, and our coverage reference collects the yield figures for the rest of the order in one place.

And the whole sequence works better written down in the same order every time, which is what our estimating checklist is for. Slope belongs at the top of that list, because a slope discovered late changes every quantity below it.

The bottom line

Slope is fall divided by run, times 100 for percent, with both figures in the same unit. That single line generates everything else: inches of fall per foot is the decimal times 12, the ratio is 1 divided by the decimal, and the angle is the arctangent of it. A 2.5 inch fall over a 24 foot run is 0.87 percent, 0.104 inches per foot, 1 in 115, and half a degree, and you can rebuild every one of those from the two measurements.

The measuring is worth more care than the arithmetic. Two stakes, a taut mason line, a line level centred at midspan, and a tape hanging plumb will give you a number good to a quarter inch, which is finer than soil holds anyway. Read the run horizontally, convert it to inches immediately, take everything twice, and the calculation cannot go wrong afterward.

What the number then has to meet is not yours to decide from a chart. Grades away from foundations, across patios and driveways, along swales and inside pipes are set by the building department where you live, and anything touching a foundation, a retaining wall or an unstable slope is an engineer’s work rather than a weekend’s. Measure it properly, name the outlet before you dig, take the arithmetic through our estimator, and make the phone call that turns a commonly cited figure into the one that actually applies to your property.

What you have just read is measurement and estimating education from the bench, not a drainage design, a grading plan, or a substitute for advice from your local building department. Every slope target described above, whether for the ground beside a foundation, a patio, a driveway, a swale or a drain pipe, is presented as a figure that circulates commonly and is offered for orientation only: the requirement that governs your property is set by the authority that enforces the code where you live, and it can differ from any convention repeated here. All dimensions, falls and volumes in the worked example are illustrative numbers chosen to show the method. Where a project touches a foundation, a retaining structure, a slope that could move, or water directed toward another property, that is work for a licensed engineer or a qualified drainage contractor rather than for a formula.