CalculateY
How to calculate stair rise and run
The two numbers that define every staircase are rise (the vertical height of each step) and run (the horizontal depth of each step). For a comfortable, code-compliant staircase, rise should be 7 to 7.75 inches and run should be at least 10 inches. Total rise (the floor-to-floor height) divided by individual rise gives the step count. A 108-inch total rise with 7.5-inch steps needs 14.4 steps, rounded to 14 risers and 13 treads.
\[\text{Number of Risers} = \frac{\text{Total Rise (in)}}{\text{Target Rise per Step (in)}}\]The number of treads is always one less than the number of risers because the top floor counts as the final landing.
Building code limits (IRC)
The International Residential Code (IRC) sets these limits for residential stairs:
| Dimension | Minimum | Maximum |
|---|---|---|
| Riser height | 4 in | 7.75 in |
| Tread depth (run) | 10 in | (no max, but 11+ uncommon) |
| Stair width | 36 in (clear) | (no max) |
| Headroom | 6 ft 8 in | (no max) |
| Variation between steps | 0 in | 0.375 in |
The variation rule is strict: any two risers in the same staircase cannot differ by more than 3/8 inch. The same applies to tread depths. Inconsistent steps cause trips because the body learns the cadence from the first few steps.
Commercial buildings have stricter rules (typically max 7 in rise, min 11 in run). Local jurisdictions can amend the code; check before building.
Calculating from total rise
Total rise is the vertical distance from the lower floor surface to the upper floor surface. For interior stairs, measure from finished floor to finished floor (including any subfloor and finish materials at the destination level).
For a 9-foot ceiling with 1-inch joist depth and 0.75-inch finished floor above, total rise from the lower finished floor to the upper finished floor is approximately:
\[\text{Total Rise} = 108 + 11.25 + 0.75 = 120 \text{ in}\]Where 108 is the 9-foot ceiling height, 11.25 is the floor system depth (joists plus subfloor), and 0.75 is the upper finished floor.
For an 8-foot ceiling with the same floor system: 96 + 11.25 + 0.75 = 108 in.
Worked example: deck stairs from a 36-inch deck
A backyard deck with its surface 36 inches above grade needs stairs to ground level.
Step 1: Total rise
\[\text{Total Rise} = 36 \text{ in}\]Step 2: Number of risers
Target rise per step: 7 inches (comfortable for outdoor use).
\[\text{Risers} = \frac{36}{7} = 5.14\]Round to 5 risers (closer to the target than 6 would be).
Step 3: Actual rise per step
\[\text{Actual Rise} = \frac{36}{5} = 7.2 \text{ in}\]This falls within the IRC limit of 7.75 in maximum. All five steps will have an identical 7.2-inch rise.
Step 4: Number of treads
\[\text{Treads} = \text{Risers} - 1 = 4\]The fifth riser carries you onto the deck itself, which serves as the final landing.
Step 5: Tread depth (run)
A standard tread depth of 11 inches with a 1-inch nosing overhang gives a run dimension of 10 inches between risers.
Step 6: Total run
\[\text{Total Run} = \text{Treads} \times \text{Run per Step} = 4 \times 10 = 40 \text{ in}\]The stairs project 40 inches horizontally from the deck.
Step 7: Stringer length
The stringer is the diagonal board that supports the steps. Length is found with the Pythagorean theorem:
\[\text{Stringer} = \sqrt{\text{Total Rise}^2 + \text{Total Run}^2} = \sqrt{36^2 + 40^2} = \sqrt{1296 + 1600} = \sqrt{2896} \approx 53.8 \text{ in}\]Add 12-18 inches for cuts and bottom plate fitting; order a 6-foot 2 × 12.
Interior stairs to a second floor
For a typical 2-story house with 9-ft ceilings:
Total rise: 120 in (calculated above)
Target rise per step: 7.5 in (interior comfort standard)
Risers: 120 / 7.5 = 16 (exactly)
Actual rise: 7.5 in (matches target)
Treads: 15
Run per step: 10 in (IRC minimum)
Total run: 150 in (12.5 ft)
A 16-step staircase requires 12.5 feet of horizontal floor space. Reducing run to fit a smaller space requires using fewer steps with a higher rise, which makes the stairs steeper and less comfortable.
The “rise + run” rule
A rule of thumb for comfortable stairs:
\[\text{Rise} + \text{Run} = 17 \text{ to } 18 \text{ inches}\]This produces stairs that match a natural walking stride. Some examples:
| Rise | Run | Sum | Comfort |
|---|---|---|---|
| 6.5 | 11.5 | 18 | Comfortable, gentle |
| 7 | 11 | 18 | Comfortable, standard |
| 7.5 | 10.5 | 18 | Standard |
| 7.5 | 10 | 17.5 | Standard, slightly steep |
| 8 | 9 | 17 | Steep (only allowed for utility/basement stairs) |
Outdoor or main entry stairs often use a lower rise (6.5-7 in) and deeper tread (11-12 in) for easier use. Basement or attic stairs are sometimes built closer to the maximum rise to save floor space, sometimes with reduced tread depth that does not meet code for new construction.
Common mistakes
Forgetting the floor thickness in total rise. Measuring from subfloor to subfloor is wrong. The finished floor at the top adds 0.75-1.5 inches; ignoring it makes the top step too shallow.
Mismatched riser heights. The bottom step ends up shorter or taller than the others because of misalignment with the floor or framing. The 3/8-inch limit is strict; even 1/2-inch variation is a trip hazard.
Cutting the stringer wrong. The first riser cut at the bottom must be reduced by the tread thickness (typically 1 in), or the first step ends up taller than the others. The top tread cut is usually omitted because the upper floor surface forms that tread.
Ignoring nosing. Most stairs have a 0.75 to 1.25 inch tread overhang (nosing) that extends past the riser below. The run dimension in code is the horizontal distance from one nosing to the next, not the full tread board width.
Picking total run before total rise. Total rise is fixed (you can’t change the ceiling height). Run flexes to fit the space. Designing run-first leads to non-compliant rise heights.
Quick reference
| Total rise (in) | Risers | Actual rise (in) | Total run (in) |
|---|---|---|---|
| 24 | 3 | 8.0 | 20 |
| 36 | 5 | 7.2 | 40 |
| 48 | 7 | 6.86 | 60 |
| 72 | 10 | 7.2 | 90 |
| 96 | 13 | 7.38 | 120 |
| 108 | 14 | 7.71 | 130 |
| 120 | 16 | 7.5 | 150 |
| 144 | 19 | 7.58 | 180 |
(Run assumes 10 in per tread; treads = risers - 1)
The stair calculator handles total rise, target rise, and run inputs and produces the actual rise per step, number of treads, total run, and stringer length.