Stair geometry

Stair Calculator

Estimate equal risers, treads, horizontal run, and stair angle from floor height and preferred step dimensions.

Rise and tread

Enter stair dimensions

Stairs
Layout summary

Stair estimate

Side view of stairs showing total rise, individual riser, tread depth, run, and angle
Equal risers divide the floor height; one fewer tread is used for a stair ending at the upper floor.

Your stair layout will appear here

Enter the total rise and preferred riser and tread sizes.

Table of Contents

1

What is Stair?

The stair calculator turns a floor-to-floor rise, a preferred riser height and a tread depth into a basic straight-flight layout. It estimates the number of risers, the adjusted uniform riser height, number of treads, horizontal run and stair angle. Inputs can use the offered metric or imperial units; results are shown in inches.

This is an early layout aid rather than a construction approval. Stair rules vary by location, occupancy and use. Landings, headroom, nosings, handrails, guards, structural support and maximum flight dimensions are outside this calculation and must be checked separately.

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How to Use This Calculator

  1. Measure the finished vertical distance from the lower finished floor to the upper finished floor.
  2. Enter a preferred riser height and its unit. This is a target used to choose a whole number of equal risers.
  3. Enter the horizontal tread depth and its unit.
  4. Select Calculate.
  5. Review the adjusted riser, riser and tread counts, total run and angle against the rules for the actual project.

A typical straight flight that ends at an upper floor has one fewer tread than risers because the upper floor serves as the final walking surface. The calculation therefore uses risers minus one for the tread count. A landing or different arrangement can change how runs are divided.

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Formula Used

Risers = nearest whole number to total rise ÷ target riser. Actual riser = total rise ÷ risers. Treads = risers − 1. Total run = treads × tread depth. Angle = arctan(actual riser ÷ tread depth).

All lengths are converted to inches before these operations. Rounding the riser count creates equal actual risers that exactly span the entered floor-to-floor height. The nearest whole count is a layout choice, not proof that the resulting dimensions comply locally.

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Variables Explained

Input or resultMeaning
Total riseFinished-floor to finished-floor vertical height.
Target riserPreferred step height used to choose a whole count.
Actual riserEqual height after dividing total rise by the final riser count.
Tread depthEntered horizontal depth used for this simplified run.
Total runHorizontal tread count multiplied by tread depth.
AngleInclination above horizontal based on actual rise and entered tread depth.
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Worked Example

Use a floor-to-floor height of 9 ft, a target riser of 7 in and a tread depth of 11 in. Nine feet is 108 inches. Dividing 108 by 7 gives 15.43, which rounds to 15 risers. The adjusted riser is 108 ÷ 15 = 7.2 inches.

A single flight to the upper floor has 14 treads, so the run is 14 × 11 = 154 inches. The angle is arctan(7.2 ÷ 11) = 33.2°. The endpoint displays 15 risers, 14 treads, a 7.2-inch riser, 11-inch tread, 154-inch run and 33.2° angle.

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Why Use This Calculator?

Check the actual riser rather than the preferred entry because the whole-number count changes it. Uniformity matters: OSHA rules for covered workplace stairs require uniform riser heights and tread depths between landings. OSHA’s general-industry standard also sets dimensions and a 30° to 50° angle for its covered standard stairs, but residential and local building provisions may differ.

Total run is only the horizontal sequence of treads in this simplified flight. It excludes landing depth, wall clearances and projections. The entered tread depth may also differ from a local rule’s exact measurement definition, especially where nosings are present. Before cutting stringers, confirm finished surfaces, local requirements and field dimensions with the responsible building professional or authority.

Field layout should preserve the full unrounded rise when marking equal risers. For example, rounding 7.2 inches is harmless in the worked example because it is exact there, but a value such as 7.258 inches repeated across many risers can accumulate a noticeable mismatch if every mark uses 7.26. Layout methods often distribute from a common datum or retain more precision until the final mark. Finished tread and floor thickness also affect the first and last risers, which is why checking only the rough stringer dimensions can create uneven finished steps.

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Common Mistakes

  • Measuring rough framing rather than finished-floor height.
  • Calling every riser a tread and adding one extra tread to the run.
  • Using the target riser after the count has adjusted it.
  • Mixing centimetres and inches under the wrong selectors.
  • Ignoring landings, headroom, nosings and handrails.
  • Assuming one jurisdiction’s limits apply everywhere.
  • Rounding several intermediate values before laying out the full rise.
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Frequently Asked Questions

Why are there fewer treads than risers?

In a straight flight ending at an upper floor, that floor is the final walking surface, so the usual count is one fewer tread.

Why does the calculated riser differ from my entry?

The entry is a target. Total rise is divided evenly by a whole number of risers to avoid an odd final step.

Are results shown in my input unit?

No. The current results are displayed in inches, while the angle is in degrees.

Does total run include a landing?

No. It covers only the calculated tread sequence.

Can I use the result to cut stringers immediately?

Check finished dimensions, local rules and all omitted design details before fabrication.

What if my stairs turn at a landing?

Calculate and lay out each flight as part of a complete design; this page models one simplified straight sequence.

Is a 30-to-50-degree angle always required?

That range applies to standard stairs covered by the cited OSHA rule. Other building types and jurisdictions can use different provisions.

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Sources & References