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Stair Angle Calculator

Find a stair's angle in degrees from one step or from the overall rise and run, or work backwards from the angle you want to the run you need.

What you know

Units
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Angle 32.5 degrees, grade 63.6 percent. Drawing and details

Worked example: edit any value

Angle

Angle32.5°from horizontal
Grade63.6 %
Rise : run1 : 1.57
Run11 in
Stair angle triangleRight triangle with a rise of 7 in over a run of 11 in, giving an angle of 32.5 degrees from horizontal.32.5°run 11 inrise 7 in
Angle scaleScale from 0 to 90 degrees showing published angle ranges, with the current angle of 32.5 degrees marked.rampsstairsship stairsladders0°30°45°60°90°IBC 32.5°IRC 37.8°32.5°
The scale shows the angle ranges in OSHA's general-industry figure (29 CFR 1910.25: ramps to 30°, standard stairs 30–50°, ship and alternating-tread stairs 50–70°, ladders 60–90°) and the steepest geometry the IRC and IBC riser and tread limits allow. They are references for comparison, not rules for your project.
How this result was calculated
  1. Angle from rise and runθ = atan(rise ÷ run) = atan(7 ÷ 11) = atan(0.6364) = 32.47°
All values (table)
ValueResultMeaning
Angle from horizontal32.47°atan(rise ÷ run)
Grade (slope %)63.64 %rise ÷ run × 100
Rise : run1 : 1.571run per unit of rise
Rise per 12 of run7.64 in 12roof-pitch style
Rise7 in
Run11 in
Sloped length1 ft 1 1/16 in√(rise² + run²)
IRC steepest geometry37.8°7 3/4 in riser on 10 in tread (derived)
IBC / ADA steepest geometry32.5°7 in riser on 11 in tread (derived)

Which angle do you mean?

A stair's angle is the slope of its pitch line, the line touching the front edge of every tread. For a uniform stair it is the same as the angle of a single step: atan(riser ÷ going). That is the number to use for comfort, for handrail and baluster cuts, and for comparing with published ranges.

Dividing total rise by total run gives a slightly steeper figure whenever the upper floor is the top step, because the total rise contains one more riser than the total run contains goings. In the 9 ft example on the stair calculator, 14 risers of 7.714 in with 13 goings of 10.5 in have a pitch of 36.3°, while atan(108 ÷ 136.5) gives 38.4°. The "total rise and total run" mode warns about this and fits a real step layout to your totals.

The formulas

  • Angle: θ = atan(rise ÷ run). Example: atan(7 ÷ 11) = 32.47°.
  • Grade: rise ÷ run × 100. Example: 7 ÷ 11 = 63.6 %. A 45° stair is a 100 % grade.
  • Run for an angle: run = rise ÷ tan θ. Example: 108 in at 35° needs 108 ÷ 0.7002 = 154.2 in of run.
  • Rise per 12: rise ÷ run × 12, the way roof pitch is quoted. 7 on 11 is 7.64 in 12.

These examples are automated test fixtures (A1 on the methodology page).

Published angle ranges, and what they are not

Residential codes in the US do not set a stair angle. They limit riser height and tread depth, which caps the angle indirectly. The IRC's 7 3/4 in maximum riser on its 10 in minimum tread works out to about 37.8°; the IBC's and the ADA Standards' 7 in riser on an 11 in tread works out to about 32.5°. Those are derived from the dimensional limits, not stated in the codes.

OSHA's general-industry rule for workplace stairs (29 CFR 1910.25) does state angles: standard stairs between 30° and 50°, with ship stairs and alternating-tread devices steeper. Its construction rule (29 CFR 1926.1052) uses the same 30° to 50° range for stairways on construction sites. Neither is a rule for the stair in your house. See how stair codes apply for which rulebook covers what.

How angle feels on a stair

Angle alone does not describe comfort. Two stairs at 35° can feel different if one has 6 in risers on 8.6 in goings and the other 8 in risers on 11.4 in goings. The second has bigger steps. Designers often look at riser and going together, for example with the old 2 × riser + going rule of thumb, which the stair calculator shows for each layout.

Questions people ask

These are questions Google showed under "People also ask" for related searches (checked 2026-10-24), answered here with the same tested formulas the calculators use.

How do you calculate the angle of stairs?

Angle = atan(riser ÷ going). For 7 in risers on 11 in goings: atan(0.636) = 32.5°. For 7.714 in on 10.5 in: 36.3°. Use one step's riser and going. Total rise ÷ total run overstates the angle when the upper floor is the top step, because there is one more riser than goings.

What is the standard angle of stairs?

There isn't one. US residential codes limit riser height and tread depth rather than the angle. The IRC's limits (7 3/4 in on 10 in) allow up to about 37.8°; the IBC's and ADA's (7 in on 11 in) about 32.5°. OSHA's workplace rule for general industry sets standard stairs between 30° and 50°, but that is not a house rule.

Why is 37 degrees the best angle for stairs?

It isn't a code value or a proven optimum. Figures around 37° circulate because they sit close to the steepest stair the IRC allows (about 37.8°), which saves floor space. Comfort depends on riser and going together: the 7-11 stair is 32.5° and most people find it easier, especially carrying things. Compare layouts in the stair calculator to see what each angle costs in floor space.

How to cut a handrail for stairs?

The rail runs parallel to the stair's pitch line. Under the IRC its top sits 34 to 38 in above the nosings, measured vertically (2024 R320.2). Where it meets a vertical post, the end cut is plumb: set a miter saw to the stair angle (for example 36.3° for the 9 ft example) and test on scrap first. Rail returns, extensions and grip size have their own rules; check your local code.