Slope Percentage Calculator

Rise over run — and run means horizontal

The whole calculation is one division, and the only thing that can go wrong is measuring the wrong bottom line. The run is the horizontal distance covered — the shadow the slope casts on level ground — and not the distance walked along its surface. On a shallow slope the two are nearly identical: at 8.3333% the sloping face is only 0.3466% longer than the run. On a steep one they diverge fast, and using the slope length as the denominator quietly reports a gentler grade than the one you have built.

Because both quantities are lengths in the same unit, the unit cancels: 8.3333% means the same thing in metres, feet, or millimetres, which is why a grade travels between drawings and trades without conversion. It also means a grade is not a percentage of anything in the usual sense. It compares two different directions rather than a part against a whole, and that is why it can pass 100% — a 45° slope rises exactly as much as it travels forward, and beyond that it rises more.

A 100% grade is 45 degrees, and that surprises almost everyone

The intuition that trips people up is treating percent as a share of a right angle, so that 100% ought to mean vertical and 50% ought to mean 45°. Neither is true. The percentage is a tangent, not a fraction of a turn: 100% is a rise equal to the run, which is 45°, and 45° converts back to exactly 100%. Vertical is not 100% but infinite — the run has gone to zero and there is nothing left to divide by.

Near the bottom of the range the two measures track each other closely enough to be confused: a 1% grade is 0.5729° and a 5% grade is 2.8624°, both within a few per cent of one-half the number of degrees. That approximation breaks well before it matters on a roof. A 4-in-12 roof is a 33.3333% grade and 18.4349°; a 6-in-12 is 50% and 26.5651°; a 12-in-12 is 100% and 45°. The grade doubles each time and the angle does not go anywhere near doubling.

Which measure you want depends on the instrument. Inclinometers, digital levels, and machine-control displays read degrees; highway signs, drainage schedules, treadmills, and site drawings use percent; accessibility standards and railways use ratios. The calculator above reports all four at once so a figure taken from one can be handed to another without a second visit.

Reading 1:12, and why bigger n means gentler

A ratio written 1:n means one unit of rise for every n units of run, so the second number is a run and not a total. 1:12 is 8.3333%; 1:20 is 5%; 1:48 is 2.0833%. The relationship runs backwards from the percentage — a larger n is a gentler slope, because the same rise is being spread over more distance — which is the single most common misreading of the notation.

Converting either way is one division: n = 100 ÷ grade, and grade = 100 ÷ n. That makes some of the standard figures easier to recognise once you have seen them: 1:12 and 8.3333% are the same slope, 1:20 and 5% are the same slope, and 1:1 is 100% and 45°.

One warning about notation. In some European drawings and older texts the same slope appears as 12:1 with the run first, and in a few contexts a ratio is written as a fraction of a different quantity entirely. If a drawing gives a ratio without units and the number is large, it is almost always 1:n with a horizontal n — but where it governs a build, confirm it against the notes on the same sheet rather than assuming.

Setting out a fall: the number you actually mark

On site the question is rarely “what is this grade” and usually “how far down is the far end”. That is the third mode, and it is a multiplication rather than a division: fall = run × grade ÷ 100. A 2% fall across a 30 m run drops 0.6 m — 600 mm — and sets out at 1.1458°, which is what a digital level clamped to the string line should read.

Two habits keep this accurate over a long run. Work from a single datum rather than accumulating short measurements, because a fall of 20 mm per metre is small enough that each transfer’s error is a meaningful share of it. And take the run horizontally, with the tape level, not laid on the ground you are grading — on the falling surface itself the horizontal distance is shorter than the tape reads, so the fall you set out comes up short.

The length along the slope matters separately when ordering: at this grade the face is 30.006 m against a 30 m run, and materials that follow the surface — membrane, pipe, edging, sheet — follow the longer figure. That gap widens quickly with pitch, which is why a roof takes noticeably more covering than its plan area suggests.

The recognisable slopes, and which document actually governs

The reference table beside the calculator lists slopes worth knowing on sight, each converted by the same engine. Two of them are genuine published limits and the rest are trade conventions, and the difference matters:

• 1:12 — 8.3333%, 4.7636°. The steepest running slope the ADA Standards allow for a ramp run, with a cross slope no steeper than 1:48. Those figures are published by the US Access Board and are linked below. They come with conditions this page does not cover — maximum rise per run, landings, handrails — so read the standard rather than the row.
• 1:20 — 5%. The boundary below which a walking surface is treated as a route rather than a ramp under the same standards, which is why 5% appears so often on site drawings as a target to stay under.
• ¼ inch per foot — 2.0833%. The minimum fall commonly required for small drain pipes, and 1.0417% for larger ones. These come from the adopted plumbing code in your jurisdiction, which is revised on its own cycle and is not the same document everywhere. Treat the row as a memory aid and take the figure from your code.
• Roof pitches — 4 in 12 is 33.3333%. Trade convention, and the usual lower limit for standard asphalt shingle installation; below it manufacturers generally require an underlayment specification of their own. That requirement belongs to the product, so it is in the installation instructions.

Nothing on this page is a compliance check. It converts the number you have into the other three forms exactly, which is the part that is arithmetic; whether that number is the permitted one is a question for the standard, the adopted code, or the authority having jurisdiction.

Measuring a slope you have not been given

The cheapest reliable method needs a spirit level and a tape. Rest the level on the surface, raise one end until the bubble centres, and measure the vertical gap at that end and the horizontal length of the level: those are your rise and run, and a level is a convenient run because it is a known length. A 1.2 m level lifted 24 mm gives a 2% grade.

A phone’s inclinometer reads degrees, and degrees are what the arctangent column is for — enter the reading into the convert mode and take the grade from it. Accuracy is limited by how flat the phone sits on an uneven surface, so rest it on a straightedge rather than on the ground, and take the reading in both directions along the same line: averaging the two cancels a constant sensor offset, which is the largest error in practice.

For a long run, a laser level or a dumpy level is measuring the same two quantities with better instruments. The arithmetic does not change — every method here produces a rise and a run, and the grade is their quotient.

In a spreadsheet, watch the radians

With the rise in A1 and the run in B1, the conversions are short formulas. The trap is trigonometry: both Excel and Google Sheets work in radians, so an angle needs converting on the way in or out or the answer is silently wrong by a factor of about 57:

• Percentage grade: =A1/B1 with the cell formatted as Percentage, or =A1/B1*100 for the raw number.
• Angle in degrees: =DEGREES(ATAN(A1/B1)). Leaving off DEGREES returns radians, which look like a plausible small number and are not degrees.
• Grade from an angle in A1 measured in degrees: =TAN(RADIANS(A1))*100.
• The n in a 1:n ratio from a grade in A1 held as a plain number: =100/A1.
• Length along the slope: =SQRT(A1^2+B1^2).

There is nothing to download for any of this and no account to create: the calculator above is a free web page that runs entirely in your browser, on desktop or mobile, and the numbers you type are never sent anywhere.

Sources and methodology

The trigonometry cites no authority because none exists to cite — it is written out in full above rather than asserted. What is cited below is the part that is somebody else’s document: the accessible-ramp slopes named in the standards section, and what a spreadsheet does with the formulas above. The plumbing figures are deliberately not cited to a standard, because the model code text is not freely readable and the adopted version differs by jurisdiction — they are named as common practice and pointed back at your own code, which is the honest way to state them.

• US Access Board — ADA Accessibility Standards (ramps, §405)
• ADA.gov — 2010 ADA Standards for Accessible Design
• Microsoft Support — the ATAN function in Excel
• Microsoft Support — the DEGREES function in Excel
• How we calculate — methodology

Method. Every figure here — the calculator, the step-by-step working, the reference table of recognisable slopes, and the worked examples in the prose — is produced in your browser by one engine, src/lib/slope-percentage.ts, so nothing on the page can disagree with the tool above it. Each reference row’s gradient is written in the source as the division it comes from — 1 ÷ 12, 0.25 ÷ 12 — rather than as a decimal, so the figure it names stays checkable. That engine is verified on every change against 87 hand-written assertions, including that a 100% grade is exactly 45°, that every form of one slope round-trips back to itself, that 90° and a zero run are refused rather than answered with a very large number, that the sloping face is never shorter than the run, and that the fall mode and the rise-and-run mode agree on the same slope. The count and the per-case breakdown are published on the formula verification page.

Read the guide

The section on the length along the slope is where this page stops and a roof begins. How to Calculate Roofing Squares (Not Just Footprint Area) takes the same geometry into ordering: a pitched roof’s real surface is larger than the footprint it covers, by exactly the factor this calculator reports, and the guide works a 40 × 30 ft example through to the number of squares. Convert the pitch here; size the material there.

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