Your stair measurements
Every length in decimal inches and as it reads on a tape measure, to the nearest 1/16 in.
| Measurement | Inches | On a tape |
|---|---|---|
| Total rise | 108.00 | 9 ft |
| Riser height | 7.71 | 7 11/16 in |
| Tread depth | 10.00 | 10 in |
| Total run | 130.00 | 10 ft 10 in |
| Stringer length | 164.19 | 13 ft 8 3/16 in |
What are risers, treads and stringers?
A riser is the height of one step and a tread is the part you stand on, each measured between the front edges of the treads. The stringers are the sloping boards that hold the treads; the length here runs along the step corners, from the top of the first riser to the edge of the top floor.
Source City of Boise · IRC Code Handout #437, Section R311.7.5 Stair treads and risers ↗
How to calculate stairs
Here it is with your numbers:
- Divide the rise by the highest riser: 108 ÷ 7.75 = 13.9355. Round up to 14 risers.
- Each riser: 108 ÷ 14 = 7.7143 in.
- Treads are one fewer than risers, because the top floor is the last step: 13 treads.
- Total run: 13 × 10 = 130 in.
- Stringer, along the step corners: 13 × √(7.7143² + 10²) = 164.19 in.
- Stair angle: arctan(7.7143 ÷ 10) = 37.6°.
It means 14 risers of 7 11/16 in and 13 treads 10 in deep, with stringers 13 ft 8 3/16 in along the step corners. That is within the code limits.
Make every riser the same: the code allows at most 3/8 in between the tallest and shortest in a flight. There is one tread fewer than risers, because the top floor is the last step.
Source Town of Timnath · 2018 Residential Stair Guide, Section R311.7 Stairways ↗Common Core State Standards · Grade 8, the Pythagorean Theorem (8.G.B.7) ↗Common Core State Standards · High School Geometry, solving right triangles (G-SRT.C.8) ↗
Stair code limits
The International Residential Code (IRC) section R311.7.5 sets risers no more than 7.75 in and treads at least 10 in deep, measured without carpet or rugs. States and cities can amend it, so ask your building department what applies before you build.
Steps for common floor heights
With risers up to 7.75 in, the code limit.
| Total rise | Risers | Riser height | Treads |
|---|---|---|---|
| 96 in | 13 | 7.38 in | 12 |
| 102 in | 14 | 7.29 in | 13 |
| 105 in | 14 | 7.50 in | 13 |
| 108 in | 14 | 7.71 in | 13 |
| 114 in | 15 | 7.60 in | 14 |
| 120 in | 16 | 7.50 in | 15 |
FAQs
How many steps are in a flight of stairs?
It depends on the height from floor to floor. Divide it by 7.75 in, the tallest riser the code allows, and round up: a 9 ft (108 in) rise needs 14 risers and 13 treads. There is one tread fewer because the top floor is the last step.
Source City of Boise · IRC Code Handout #437, Section R311.7.5 Stair treads and risers ↗
How do you calculate stair stringers?
Each step is a right triangle, so stringer = treads × √(riser² + tread²). With 13 treads of 10 in and 7.71 in risers, that is 164.19 in. Cut it from a longer board, to leave room for the cuts at each end.
Source Common Core State Standards · Grade 8, the Pythagorean Theorem (8.G.B.7) ↗
What is a stair riser?
The height of one step, measured vertically between the front edges of two treads. In one flight, the tallest riser may be at most 3/8 in taller than the shortest.
Source City of Boise · IRC Code Handout #437, Section R311.7.5 Stair treads and risers ↗
How do you calculate stair rise and run?
Rise ÷ risers gives each riser and treads × tread depth gives the run. The code wants a floor or landing at the top and bottom, so there is one tread fewer than risers.
Source Town of Timnath · 2018 Residential Stair Guide, Section R311.7 Stairways ↗
What is the maximum height of a stair riser?
7.75 in under the International Residential Code (R311.7.5.1). States and cities can change it, so check with your building department.
Source City of Boise · IRC Code Handout #437, Section R311.7.5 Stair treads and risers ↗
How far should a stair tread overhang the riser?
The code asks for a nosing (the overhang) of 0.75 – 1.25 in. None is needed when the tread is at least 11 in deep.
Sources
- City of Boise: IRC Code Handout #437, Section R311.7.5 Stair treads and risers
- Town of Timnath: 2018 Residential Stair Guide, Section R311.7 Stairways
- Common Core State Standards: Grade 8, the Pythagorean Theorem (8.G.B.7)
- Common Core State Standards: High School Geometry, solving right triangles (G-SRT.C.8)
- NIST Handbook 44 (2026): Appendix C, General Tables of Units of Measurement