Rise Over Run Calculator
Enter any one format and get every equivalent back: percent, degrees, ratio, x in 12 and inches per foot. Add a run and it gives you the actual rise too.
Working from two coordinate points instead? That is the algebra version of the same division, and the slope calculator takes x and y pairs and returns the equation of the line with it.
Is it rise over run or run over rise?
Rise over run. The height goes on top. Divide how far it climbs by how far it travels flat.
Most people arriving here are not learning that, they are checking it, so here is how to catch yourself if you have flipped it. Anything you would walk on, drive on or drain water down divides out to less than 1, because 1 is already a 45 degree slope. A 2 in 12 roof is 0.167. A wheelchair ramp is 0.083. A steep driveway is 0.2. Only a roof steeper than 12 in 12 passes 1, and nobody walks up one of those without staging. If your answer came out as 6, or 12, or 50, you divided the wrong way round.
Turn the flipped number into a percent and it gets obvious. That same 2 in 12 roof, divided run over rise, gives 6, which reads as a 600% grade. A 100% grade is already 45 degrees, so 600% is a face at 80 degrees. Spires and steeples do get that steep. A shallow 2 in 12 does not.
The thing nobody mentions is that the flipped number is not junk. Run over rise is the length you need for each unit of height, and that is the number you actually want when you are laying something out. Run over rise of 12 on a 1:12 ramp is telling you 12 feet of ramp for every foot you climb. So if you did it backwards, you did not get a wrong answer. You got a different useful one.
Which number goes first in a ratio
This one catches professionals, not just students. A ramp written 1:12 means one of rise to twelve of run. An earthworks batter written 3:1 means three of run to one of rise. Same colon, opposite order, and both are standard in their own trade.
Check which order the specification uses before you rely on either reading. Accessibility ramps are normally written rise first, earthworks batters are often written run first, and the drawing may not say which it is using.
Where you cannot check, the smaller number is usually the rise, because almost nothing gets built steeper than 1:1. That reading gets you 1:12 and 3:1 both right. It stops working the moment a slope is steeper than 45 degrees, so treat anything near or above 1:1 as ambiguous and ask.
How to use the rise over run calculator
Six tabs, because there are six ways people arrive here. Pick whichever number you already have.
- Rise & Run. You measured both. The straightforward direction.
- Percent. A drawing says 2% and you need to know what to cut.
- Angle. You have degrees off a phone or a digital level.
- Ratio 1:n. A spec says 1:12 or 1:48.
- Pitch (x in 12). The roofer’s unit.
- Inches per Foot. The plumber’s and the concrete finisher’s unit.
The last five all have an optional run box. Leave it alone and you get the conversions. Fill it in and you also get the actual rise, in your units, for the run you have. That is the part most calculators skip: they will tell you 2% is 1.15 degrees, but not that it is a quarter inch over the four foot level in your hand.
You can type fractions. 3 1/2, or 3 1/2″, or 6′ 3 1/2″ all work. Most calculators for this use a number-only field, which makes a fraction impossible to enter on a page aimed at people who work in sixteenths.
What you get back
- Percent, the headline, because that is what most drawings use.
- Degrees, for a phone level or a mitre saw.
- Ratio written 1:n.
- Inches per foot, which is how the fall on a drain or a slab gets called out.
- Pitch as x in 12, the roofing convention.
- The decimal and the reduced fraction, which is rise over run in its plainest form.
- Rise, run and slope length in your own units.
There is no pass or fail box here on purpose. This page tells you what your slope is. Whether it is allowed depends on what you are building, and that belongs on the page for the thing you are building.
About units
Rise and run only have to match each other, because slope is a ratio and the units cancel. Inches over inches gives the same answer as metres over metres.
Two outputs are exceptions and are always the same regardless of what you picked. Inches per foot is inches per foot everywhere, and pitch is always rise per twelve. Both are conventions rather than measurements.
The rise over run formula
One division, written six ways.
- slope = rise ÷ run
- percent = (rise ÷ run) × 100
- degrees = arctan(rise ÷ run)
- ratio = 1 : (run ÷ rise)
- inches per foot = (rise ÷ run) × 12
- slope length = √(rise² + run²)
Rise over run conversion table
Every row is the same slope written five ways. Find the one you have and read across. The last column is there to help you recognise a number, not to tell you what is allowed, and most of those entries are rules of thumb rather than rules.
Two rows are the exception, and both come from the same place. Under the ADA Standards a walking surface steeper than 1:20 is a ramp rather than a walkway, and 405.2 caps a ramp run at 1:12. Those are definitions, not conventions. Everything else in that column is there for recognition, and the real limit for whatever you are building lives on its own page.
| Ratio | Percent | Degrees | Inches per foot | x in 12 | Often seen as |
|---|---|---|---|---|---|
| 1:100 | 1.00% | 0.57° | 0.12 in | 0.12 / 12 | About as flat as surface drainage is usually taken |
| 1:96 | 1.04% | 0.60° | 1/8 in | 0.13 / 12 | Fall on a larger drain line |
| 1:50 | 2.00% | 1.15° | 0.24 in | 0.24 / 12 | Common target for water off a slab |
| 1:48 | 2.08% | 1.19° | 1/4 in | 0.25 / 12 | The quarter inch per foot commonly quoted for drains |
| 1:20 | 5.00% | 2.86° | 0.60 in | 0.60 / 12 | Where a walking surface starts counting as a ramp |
| 1:12 | 8.33% | 4.76° | 1.00 in | 1 / 12 | Commonly cited as the accessibility maximum |
| 1:10 | 10.00% | 5.71° | 1.20 in | 1.2 / 12 | Hard work on foot with a load |
| 1:8 | 12.50% | 7.13° | 1.50 in | 1.5 / 12 | Well past ramp limits, easy in a vehicle |
| 1:6 | 16.67% | 9.46° | 2.00 in | 2 / 12 | Around the shallowest ordinary shingle roof |
| 1:4 | 25.00% | 14.04° | 3.00 in | 3 / 12 | A loading ramp rule of thumb |
| 1:3 | 33.33% | 18.43° | 4.00 in | 4 / 12 | A common cut or fill batter |
| 1:2 | 50.00% | 26.57° | 6.00 in | 6 / 12 | A 6 in 12 roof, the common one |
| 1:1 | 100.00% | 45.00° | 12.00 in | 12 / 12 | 100% is 45 degrees, not vertical |
Read the last row twice, because it is the one that surprises people. A 100% grade is 45 degrees. Percent is not a share of vertical, it is rise divided by run, so at 45 degrees the rise and the run are equal and the answer is 1, which is 100%. Past that it keeps climbing: a 200% grade is 63.4 degrees, and true vertical has no percent at all, because the run is zero and you cannot divide by it.
The other half of that mistake is assuming a 45 degree slope is 50%. It is not. 50% is 26.57 degrees, which is an ordinary 6 in 12 roof.
The table above stops at the slopes people actually meet. If your figures are for a roof, the roof pitch calculator works in the x-in-12 form the trade actually uses.
Which unit your trade actually uses
The maths never changes. The vocabulary changes at every trade boundary, which is why a plumber handed a drawing in degrees and a roofer handed one in percent both end up here.
| Trade | Says it as | Example |
|---|---|---|
| Roofing and framing | x in 12 | a 6 in 12 roof |
| Plumbing and drainage | inches per foot | a quarter inch per foot |
| Civil, site plans, roads | percent | a 6% grade |
| Accessibility and ramps | ratio | 1:12 |
| Surveying and machine control | degrees or percent | 2.86° |
| Earthworks and batters | ratio, run first | 3:1 |
Three of those are the same number wearing different clothes. 1:12, 8.33% and one inch per foot are one slope, and a spec sheet will happily use all three in the same set of drawings.
How to calculate rise over run by hand
A patio that drops 1 3/4 inches across a 7 foot slab, and you want to know whether that is enough fall.
- One unit. 7 ft is 84 inches. The rise is 1.75 inches.
- Divide. 1.75 ÷ 84 = 0.02083.
- Percent. 0.02083 × 100 = 2.08%.
- Inches per foot. 0.02083 × 12 = 0.25, a quarter inch per foot.
- Degrees. arctan(0.02083) = 1.19°.
- Ratio. 84 ÷ 1.75 = 48, so 1:48.
Look at step 2. The answer is 0.02, comfortably under 1, which is the check from the top of this page working in practice. Had it come out at 48 you would have divided the wrong way.
Four reasons rise over run comes out wrong
- The run was measured along the surface. The one in the diagram. Run is flat distance. Pull the tape up the slope and you have measured the slope length, which is longer, so the answer comes out too gentle. On a 6 in 12 roof the error is about 12%.
- The units did not match. Rise in inches over run in feet is twelve times too steep, and it looks plausible enough to survive a sanity check. Put both in one unit before dividing.
- It got divided the wrong way. Run over rise. Covered at the top, and the giveaway is an answer bigger than 1.
- A percent got read as an angle. They are never the same number. A 15% grade is 8.53 degrees, and a 15 degree slope is 26.79%. The percent figure is always the larger of the two, and the gap widens as the slope steepens: at 45 degrees the percent has reached 100.
Once you have the number, what counts as acceptable depends entirely on what you are building, and those thresholds live on the page for the thing being built rather than here. They are not properties of the arithmetic.
One more source of a wrong answer worth naming, because it does not look like a measuring mistake at all. If your figures came from a column of readings rather than from a tape, the method changes: finding the slope from a table of values means picking a pair of rows and subtracting, and picking rows that are not evenly spaced is where it goes wrong.
Frequently asked questions
Is it rise over run or run over rise?
Rise over run. The height goes on top, the flat distance underneath. The quickest way to check yourself is the size of the answer: anything you would walk on, drive on or drain water down divides out to less than 1. A 2 in 12 roof is 0.167 and a wheelchair ramp is 0.083. If your answer is 6 or 12 or 48, you divided run by rise. That number is still useful though, because it tells you how much length you need for each unit of height.
How many inches per foot is a 2% slope?
Just under a quarter inch. 2% is 0.24 inches per foot, and the quarter inch per foot that gets quoted everywhere is actually 2.08%, or 1:48. They are close but they are not the same number, so build to whichever one your specification actually names rather than swapping them. To convert exactly, multiply the percent by 0.12: 1% is 0.12 in per foot, 2% is 0.24, 5% is 0.60.
Why is a 100% grade only 45 degrees?
Because percent is rise divided by run, not a share of vertical. At 45 degrees the rise and the run are the same length, so the division gives 1, which is 100%. It does not stop there: 200% is 63.4 degrees. True vertical has no percentage at all, because the run is zero and dividing by zero has no answer. The same confusion runs the other way, with people assuming 45 degrees is 50%. It is not. 50% is 26.57 degrees, an ordinary 6 in 12 roof.
How do you convert rise over run to degrees?
Take the arctangent. Divide rise by run, then hit the inverse tan key, sometimes labelled tan⁻¹ or atan. A 6 in 12 roof is 6 ÷ 12 = 0.5, and arctan(0.5) is 26.57 degrees. Going the other way, multiply the tangent of the angle by your run to get the rise. The calculator above does both, and it will accept degrees as a starting value rather than only as an answer.
Do I measure the run flat or along the slope?
Flat. Run is the horizontal distance, the shadow the slope would cast at noon. The distance along the sloping surface is the slope length, and on any real slope it is the longer of the two. Only on dead level ground are they equal. Measuring along the surface and calling it the run is the most common source of a wrong answer here, and the error is always in the same direction: it makes the slope look gentler than it is. On a 6 in 12 roof the two differ by about 12%.
What does 1:12 mean, and which number is the rise?
One unit of rise for every twelve of horizontal run, so one inch up per foot of run, or one foot up per twelve feet of run. Measured flat, not along the ramp surface. The smaller number is usually the rise. That rule holds across trades even when the order flips: an earthworks batter written 3:1 is three of run to one of rise, because nobody builds anything that climbs three for every one across. Where a ratio is close to 1:1 and genuinely ambiguous, ask rather than guess.
Is rise over run the same as slope?
Effectively, yes, though the words are not perfect synonyms. Slope, gradient, grade and fall all describe the same steepness and differ mainly in the format each trade reports it in: a plumber says fall and means inches per foot, a civil drawing says grade and means percent, an accessibility spec uses a ratio. Pitch is the one to watch, because in roofing it sometimes means rise over the whole span rather than over the run, which halves the number. Everything else here is rise divided by run.
What is the rise over run of a flat or a vertical line?
A flat line has a rise of zero, so the slope is zero: 0 divided by anything is 0. A vertical line is the awkward one. Its run is zero, and dividing by zero has no answer, so the slope is undefined rather than infinite. This is why a vertical face has no percent grade and no ratio, only an angle of 90 degrees.