Steps Needed
14
14
steps needed
7.71"
10.00"
130.0"
169.0"
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Inputs
Result
Steps = round(108 / 7.5) = round(14.4) = 14. Actual riser = 108 / 14 = 7.71". Total run = 10 × (14 - 1) = 130". Stringer = sqrt(108² + 130²) = sqrt(11,664 + 16,900) = sqrt(28,564) = 169.0". Angle = atan(108/130) = 39.7°.
Inputs
Result
Steps = round(36 / 7) = round(5.14) = 5. Actual riser = 36 / 5 = 7.20". Total run = 11 × (5 - 1) = 44". Stringer = sqrt(36² + 44²) = sqrt(1,296 + 1,936) = sqrt(3,232) = 56.9". Angle = atan(36/44) = 39.3°.
Inputs
Result
Steps = round(120 / 7.5) = round(16.0) = 16. Actual riser = 120 / 16 = 7.50". Total run = 11 × (16 - 1) = 165". Stringer = sqrt(120² + 165²) = sqrt(14,400 + 27,225) = sqrt(41,625) = 204.0". Angle = atan(120/165) = 36.0°.
Building codes typically require riser heights of 7-7.75 inches and tread depths of 10-11 inches. The "rule of 17" suggests rise + run should equal about 17-18 inches for comfortable stairs.
Divide total rise (floor-to-floor height) by ideal riser height (7-7.75 inches), then round. An 8-foot ceiling needs 13 steps, a 9-foot ceiling needs 14 steps, and a 10-foot ceiling needs 16 steps (with 7.5" ideal riser and 10" tread).
| Ceiling Height | Total Rise | Steps (7.5" riser) | Actual Riser | Total Run (10" tread) | Stringer Length |
|---|---|---|---|---|---|
| 8 ft | 96" | 13 steps | 7.38" | 120" | 153.7" |
| 9 ft | 108" | 14 steps | 7.71" | 130" | 169.0" |
| 10 ft | 120" | 16 steps | 7.50" | 150" | 192.1" |
| 12 ft | 144" | 19 steps | 7.58" | 180" | 230.5" |
Total rise is the vertical height from floor to floor. Total run is the horizontal distance the stairs cover. Total run = tread depth × (number of steps - 1).
Stringer length = √(total rise² + total run²). Use the Pythagorean theorem. For 108" rise and 130" run: √(108² + 130²) = √28,564 = 169" or about 14 feet.
| Total Rise | Total Run | Stringer Length | Common Lumber |
|---|---|---|---|
| 36" (deck) | 44" | 56.9" (4.7 ft) | 2×12 × 6 ft |
| 96" (8 ft ceiling) | 120" | 153.7" (12.8 ft) | 2×12 × 14 ft |
| 108" (9 ft ceiling) | 130" | 169.0" (14.1 ft) | 2×12 × 16 ft |
| 120" (10 ft ceiling) | 150" | 192.1" (16.0 ft) | 2×12 × 16 ft |
Building codes limit stair angle to approximately 42 degrees (max 7.75" riser, min 10" tread). Comfortable stairs are typically 30-37 degrees. Steeper than 42 degrees requires a ladder or ship ladder design.
Horizontal space = tread depth × (steps - 1) + landing. A typical 9-foot ceiling with 14 steps at 10" treads needs 130" (10.8 ft) of horizontal run, plus 36" for a landing at top and bottom.
| Ceiling Height | Steps | Run (10" tread) | Run (11" tread) | With Landing |
|---|---|---|---|---|
| 8 ft | 13 | 10.0 ft | 11.0 ft | 13.0-14.0 ft |
| 9 ft | 14 | 10.8 ft | 11.9 ft | 13.8-14.9 ft |
| 10 ft | 16 | 12.5 ft | 13.8 ft | 15.5-16.8 ft |
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Last Updated: Mar 26, 2026
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