How stair dimensions are calculated
Start with the total rise — the finished floor-to-floor height — and divide by a comfortable target riser to get a whole number of steps:
Steps = round(Total rise ÷ target riser)
Actual riser = Total rise ÷ steps | Total run = (steps − 1) × tread
For a 44-inch rise with a 7-inch target, that's 6 steps, a 7.33-inch actual riser, a 50-inch run over 5 treads, and a stringer of √(44² + 50²) ≈ 66.6 inches at about 41°.
Comfort and code
- Riser: about 7 in is comfortable; codes often cap it near 7.75 in.
- Tread: 10–11 in is typical; codes usually require at least 10 in.
- Rule of thumb: 2 × riser + tread ≈ 25 in, or riser + tread ≈ 17–18 in.
The stringer
The stringer is the diagonal support, found with the Pythagorean theorem on the total rise and total run. Always buy the board a little longer than the calculated length to allow for the cuts at each end.
Frequently asked questions
How do I calculate stairs?
Divide the total rise (floor-to-floor height) by a target riser height of about 7 inches and round to a whole number of steps. The actual riser is the total rise divided by that step count. The total run is the number of treads times the tread depth, and the stringer length is the diagonal found with the Pythagorean theorem.
What is a comfortable riser height and tread depth?
A common comfort guideline is a riser of about 7 inches and a tread of 10–11 inches. The "rule of thumb" is that riser + tread ≈ 17–18 inches, or 2 × riser + tread ≈ 25 inches. Most building codes cap risers near 7.75 inches and require treads of at least 10 inches.
What is the difference between rise/run, riser, and tread?
The riser is the vertical height of one step; the tread is the horizontal depth you step on. Total rise is the full vertical height of the staircase, and total run is the full horizontal distance it covers. The stringer is the diagonal board that supports the steps.
How long should the stringer be?
The stringer length is the straight-line diagonal of the staircase: √(total rise² + total run²). For 44 inches of rise and 50 inches of run, that is √(1936 + 2500) ≈ 66.6 inches. Buy stringer stock a bit longer to allow for cuts.
Disclaimer: Stair geometry is regulated by building codes that vary by location. Verify riser, tread, headroom, and handrail requirements with your local code before building.