Stair Calculator Guide: Risers, Treads, Blondel Rule and Stair Geometry
Stair preliminary sizing starts with floor-to-floor height, but the riser count must be a whole number. The actual riser height is recalculated from that count, then tread depth, total run, stair angle, landings and headroom are checked together. CivilCalc helps compare these geometric relationships in one workflow.
Content and method reviewed: September 19, 2026
1. From floor height to riser count
Define the total vertical floor-to-floor height H. Estimate the riser count from a target riser height, choose a suitable whole number, and recalculate the actual riser.
R = H / n
R is actual riser height and n is the number of risers.
2. Blondel relationship
A common ergonomic check evaluates riser height and tread depth together using the Blondel relationship. A value around 60–65 cm (about 23.6–25.6 in) is often used as a preliminary comfort check; mandatory dimensions depend on occupancy and the applicable building code.
2R + T ≈ 60–65 cm
Comparing alternatives for a 300 cm floor height
| Risers | Actual R | T for 2R+T = 63 cm | Geometry effect |
|---|
| 17 | 17.65 cm | 27.71 cm | Higher riser, shorter tread |
| 18 | 16.67 cm | 29.67 cm | Balanced comparison case |
| 19 | 15.79 cm | 31.42 cm | Lower riser, longer tread |
This table illustrates geometric trade-offs; it does not certify code compliance.
Worked example
Floor height: 300 cm
Risers: 18
Tread: 29 cm
R = 300 / 18 = 16.67 cm
2R+T = 2×16.67+29 = 62.33 cm
The Blondel result is reasonable as a preliminary ergonomic check, but final stair compliance requires additional code and geometry checks.
Why can tread count differ from riser count?
In a typical floor-to-floor stair, the upper floor can act as the final walking surface, so the number of treads in a straight flight is often one less than the number of risers. Split flights and special layouts should be checked flight by flight.
Typical straight flight: treads ≈ n − 1
Total run and stair angle
For m treads of depth T, approximate horizontal run is L=m×T. The stair angle can be estimated from the riser-to-tread ratio.
L = m × T • θ = arctan(R / T)
For R=16.67 cm and T=29 cm, the step geometry gives an angle of about 29.9°.
Landings and split flights
For a two-flight stair, distribute the total risers between flights and check each flight, landing length and total plan footprint. Riser consistency is important; do not allow small elevation errors to accumulate into a different first or last riser.
Use finished floor elevations
Where possible, check stair geometry from finished floor to finished floor. Different finish thicknesses at the bottom and top can change the first or last riser even when the structural concrete geometry appears regular.
6 checks before design sign-off
1. Floor height
Use the actual vertical distance between finished floor elevations.
2. Equal risers
Verify consistent riser geometry throughout the stair.
3. Available footprint
Confirm the total horizontal run fits the stair opening.
4. Landing and headroom
Check conflicts with slabs, beams and landings separately.
5. Occupancy and egress
Verify clear width, guards and fire/egress requirements under the applicable code.
6. Accessibility
Review accessibility provisions applicable to the building and use.
Frequently asked questions
How many risers are needed for a 300 cm floor height?
There is no single universal answer. With 18 risers, the actual riser is 16.67 cm. The final count must also suit tread depth, available footprint, occupancy and applicable code requirements.
What does the 2R+T rule check?
It evaluates riser height and tread depth together as an ergonomic walking-rhythm check. It does not replace building-code requirements.
Are the number of risers and treads the same?
Not always. In a typical floor-to-floor straight flight, the upper floor serves as the final walking surface, so tread count is often one less than riser count.
How is stair angle calculated?
For a straight flight, the approximate angle is θ = arctan(R/T), using the same units for R and T.
Do floor finishes affect stair calculations?
Yes. Different finish thicknesses at the bottom and top can create an inconsistent first or last riser, so final geometry should be checked using finished elevations.
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