Use this Stair Angle Calculator to convert stair rise and run into degrees, percent slope, rise-to-run ratio and sloped length. Calculate from one step or from the total rise and run of an entire stair flight.
Choose the measurements you know
Calculate from one step's riser/run or from the total rise and total run of a flight.
Your stair angle
See the slope as degrees, percent, ratio and a proportional right triangle.
Transparent calculation
How stair angle is calculated
Rise and run form the legs of a right triangle. The angle is the arctangent of rise divided by run.
atan(rise ÷ run)(rise ÷ run) × 100rise ÷ run : 1√(rise² + run²)Important: the result is geometric. Do not use angle alone as a code, accessibility or structural approval check.
Step by step
How to use the Stair Angle Calculator
Choose One step when you know a riser height and tread run, or choose Whole flight when you know the total vertical rise and total horizontal run. The two modes answer different questions: One step uses a riser and tread, while Whole flight uses the total rise/run envelope. In a floor-to-floor stair where the upper floor acts as the final walking surface, the two angles can differ slightly.
- Select the measurement system.
- Choose One step or Whole flight.
- Enter the matching rise and run dimensions.
- Calculate to see degrees, percent slope, ratio and sloped length.
- Use a dedicated stair-layout calculator if you also need riser count, tread count or stringer planning.
Read your result
What the stair angle results mean
Angle in degrees
The inclination of the rise/run triangle above horizontal for the mode you selected.
Percent slope
Vertical rise divided by horizontal run, multiplied by 100. It is another way to describe the same geometry.
Rise : run ratio
The vertical rise expressed relative to one unit of horizontal run.
Sloped length
The diagonal side of the right triangle created by the entered rise and run.
Worked example
Example: 7¾ in rise and 10 in run
For one step with a 7.75 in rise and 10 in run, the calculator uses the rise/run ratio to determine the stair angle.
7.75 ÷ 10 = 0.775atan(0.775) ≈ 37.8°0.775 × 100 = 77.5%√(7.75² + 10²) ≈ 12.65 inThe angle is a mathematical description of the step geometry. It should be considered alongside actual riser/tread dimensions and all other project requirements.
Measure the same geometry
Stair angle measurement tips
- For one-step mode, use the vertical riser and horizontal tread run from the same step geometry.
- For whole-flight mode, use total vertical rise and total horizontal run for the same flight.
- Do not mix sloped stringer length into the horizontal-run field.
- Use finished dimensions when evaluating a finished stair layout.
- Recalculate if you change either riser height or tread run.
Know the limits
Assumptions and limitations
The calculator treats the entered rise and run as a right triangle. It does not calculate stair count, landings, nosings, headroom, guard/handrail requirements, accessibility conditions or structural capacity. Whole-flight mode assumes the total rise and total run describe one consistent straight flight.
A stair can have the same approximate angle while still differing in individual riser/tread dimensions, so do not use angle as a substitute for checking those dimensions directly.
Planning context
Why angle is not a stand-alone code check
Residential stair provisions are commonly expressed using dimensions such as riser height and tread depth rather than a single universal stair-angle limit. BuildCalcForge therefore reports the calculated angle while keeping the underlying rise and run visible.
For model-code context, the 2021 IRC includes stair riser and tread provisions in R311.7.5.1 and R311.7.5.2. Local adoption and amendments can differ.
International Code Council — 2021 IRC, Chapter 3 ↗Common questions
Stair Angle Calculator FAQ
How do you calculate stair angle from rise and run?
Divide rise by run, then take the arctangent of that ratio. The calculator converts the result to degrees.
Can I calculate angle from total rise and total run?
Yes. Whole-flight mode uses the total vertical rise and total horizontal run to calculate the overall flight angle.
Is percent slope the same as angle?
They describe the same rise/run relationship in different forms. Percent slope is rise divided by run times 100; angle is the arctangent of rise divided by run.
What is a good stair angle?
This calculator intentionally does not prescribe one universal angle. Stair suitability depends on actual riser/tread dimensions, stair type and the requirements applicable to the project.
Can I enter fractions?
Yes. US one-step fields accept fractional inches such as 7 3/4 and 10 1/2.
Does this calculator check local code?
No. It provides geometry and planning context only. Verify the requirements adopted where the stair will be built.
Sources & methodology
How this calculator is checked
The calculation uses standard right-triangle trigonometry and preserves the entered dimensions so users can see the basis of the result.