Stair Calculator: Rise, Run, Risers and Stringer Length
Enter the height between finished floors. You get the number of risers and treads, the riser height, the total run and the angle, drawn to scale with every formula shown.
Worked example: edit any value
Result
Angle 36.3° Going 10 1/2 in Tread depth 11 1/2 in Pitch-line length 15 ft 2 7/16 in
Informational checks
Geometry compared with the published values you selected. This is not a code-compliance decision: adoption, amendments and exceptions vary. How stair codes apply.
- Within referenceRiser height. 7 11/16 in against a reference of at most 7 3/4 in. IRC 2024 R318.7.5.1 (2021: R311.7.5.1)
- Within referenceTread depth (going, nosing to nosing). 10 1/2 in against a reference minimum of 10 in. IRC 2024 R318.7.5.2 (2021: R311.7.5.2)
- Within referenceNosing projection. 1 in against a reference of 3/4 in to 1 1/4 in. Stairs with open risers may have larger projections under this reference. IRC 2024 R318.7.5.3 (2021: R311.7.5.3)
- Within referenceRise of a single flight. 108 in is within the 151 in reference for one flight between floors or landings. IRC 2024 R318.7.3 (2021: R311.7.3)
- CheckHandrail. 14 risers: this reference calls for a handrail on at least one side of flights with 4 or more risers. Handrail height and grip rules also apply. IRC 2024 R318.7.8 (2021: R311.7.8)
- CheckHeadroom. Not calculated here. Check the clear height above the line of the nosings along the whole flight, especially under the floor opening at the top. IRC 2024 R318.7.2 (2021: R311.7.2)
- CheckUniformity as built. This plan assumes every riser and tread is identical. Finished floors added later change the first and last risers, so plan for the final flooring before cutting. This reference allows at most 3/8 in (9.5 mm) between the largest and smallest riser, and between the largest and smallest tread, in a flight (IRC 2024 R318.7.5.1–.2).
Other riser counts
Each extra riser makes every step lower and the stair one going longer. There is rarely only one right answer.
| Risers | Riser | Treads | Total run | Angle | Note | Action |
|---|---|---|---|---|---|---|
| 13 | ≈ 8 5/16 in | 12 | 10 ft 6 in | 38.4° | Riser over your 7 3/4 in max | |
| 14 | ≈ 7 11/16 in | 13 | 11 ft 4 1/2 in | 36.3° | Current plan | |
| 15 | ≈ 7 3/16 in | 14 | 12 ft 3 in | 34.4° | ||
| 16 | 6 3/4 in | 15 | 13 ft 1 1/2 in | 32.7° | ||
| 17 | ≈ 6 3/8 in | 16 | 14 ft 0 in | 31.2° |
How this result was calculated
- Number of risers: round up so no riser is taller than your maximum
R = ⌈total rise ÷ max riser⌉ = ⌈108 ÷ 7.75⌉ = ⌈13.935⌉ = 14 - Riser height: every riser is equal
h = total rise ÷ R = 108 ÷ 14 = 7.7143 inNearest 1/16 in: 7 11/16 in. - Number of treads
T = R − 1 = 14 − 1 = 13The upper floor works as the last step, so there is one fewer tread than risers. - Total run: treads × going
run = T × g = 13 × 10.5 = 136.5 in = 11 ft 4 1/2 inMeasured from the face of the bottom riser to the face of the top riser. The bottom tread's nosing projects a further 1 in. - Pitch angle: the slope of the line through the nosings
θ = atan(h ÷ g) = atan(7.7143 ÷ 10.5) = 36.30° - Why not atan(total rise ÷ total run)?
atan(108 ÷ 136.5) = 38.35°That rectangle has 14 rises but only 13 goings, so it overstates the slope a person walks. Use the riser/going angle (36.3°). - Pitch-line length: a geometric reference, not a cut length
R × √(h² + g²) = 14 × √(7.7143² + 10.5²) = 14 × 13.0292 = 182.4089 inA real stringer board must be longer: it also needs material for the bottom and top cuts and the connection. The stringer calculator works out the shortest board. - Comfort check (rule of thumb, not a code rule)
2h + g = 2 × 7.7143 + 10.5 = 25.9286 inSteps of similar 2h + g feel similar to walk. Compare layouts with it rather than aiming for one number.
All dimensions (table)
| Dimension | Value | Meaning |
|---|---|---|
| Total rise | 9 ft 0 in | Finished floor to finished floor |
| Risers | 14 | Minimum for your maximum riser |
| Riser height (each) | ≈ 7 11/16 in | 7.7143 in exact |
| Treads | 13 | Risers − 1 (upper floor is the top step) |
| Going (nosing to nosing) | 10 1/2 in | Horizontal step-to-step distance |
| Nosing projection | 1 in | Overhang past the riser below |
| Tread depth incl. nosing | 11 1/2 in | Front-to-back size of a tread board |
| Tread thickness | 1 in | Used for stringer cuts |
| Total run | 11 ft 4 1/2 in | Bottom riser face to top riser face |
| Run incl. bottom nosing | 11 ft 5 1/2 in | Plan length at tread level |
| Pitch angle | 36.30° | atan(riser ÷ going) |
| Slope | 73.5 % | Riser ÷ going × 100 |
| Pitch-line length | 15 ft 2 7/16 in | Geometric reference, not a cut length |
| 2 × riser + going | 25 15/16 in | Comfort heuristic |
How to use the stair calculator
- Measure the total rise: the vertical distance from the lower finished floor to the upper finished floor, taken where the bottom of the stair will land. Use finished surfaces (or allow for flooring that is not down yet). How to measure total rise accurately.
- Set the tallest riser you will accept. The calculator uses the fewest risers that keep every riser at or below it. Lower risers make a gentler stair that needs more floor space.
- Set the going, the horizontal distance from one nosing to the next. Choose how the top of the stair meets the upper floor; that decides how many treads you build.
- Read the result, compare it with the other riser counts, and open the stringer calculator when you are ready to lay out the boards.
Fractions such as 7 3/4, 7-3/4 or ¾ work, and so do feet and inches like
9' 1 1/2". In metric mode, plain numbers are millimetres; add cm or m if
you prefer.
Risers, treads and goings: the terms that cause mistakes
- Total rise
- Finished floor to finished floor. It is not the floor-to-ceiling height, and it is not the height of the framing if flooring will be added later.
- Riser and riser height
- A riser is one vertical step up. Riser height is the total rise divided by the number of risers, so every step is identical. Codes measure it between the leading edges of adjacent treads.
- Tread and going
- A tread is a surface you stand on. The going (also called run per step or unit run) is the horizontal distance from one nosing to the next. It is shorter than the tread board when the tread has a nosing.
- Nosing
- The front edge of a tread that overhangs the riser below. It adds foot room without adding run, which is why tread depth = going + nosing.
- Total run
- Number of treads × going. It is the horizontal length of the stepping part of the stair, from the face of the bottom riser to the face of the top riser. Landings and the bottom nosing are extra.
Why there is usually one fewer tread than risers
On most stairs the upper floor is the last step: you take the final riser and land on the floor, not on a tread. So a stair with 14 risers normally has 13 treads. Count the steps on any staircase in your house and you will find the same thing.
Some stairs, often deck stairs with flush-mounted stringers, put a full tread level with the upper surface. Then treads equal risers, and the stair is one going longer. Other calculators sometimes assume this without saying so, which is the most common reason two calculators disagree on the run. Pick the option that matches how you will attach the top of the stair.
Worked example: a 9-foot floor-to-floor stair
A basement stair has a total rise of 108 in (9 ft 0 in). The builder will accept risers up to 7 3/4 in and wants a 10 1/2 in going with a 1 in nosing. The upper floor is the top step.
- Risers: 108 ÷ 7.75 = 13.94, rounded up to 14. Rounding down would make risers too tall.
- Riser height: 108 ÷ 14 = 7.714 in, about 7 11/16 in. Every riser is the same.
- Treads: 14 − 1 = 13.
- Total run: 13 × 10.5 = 136.5 in = 11 ft 4 1/2 in.
- Angle: atan(7.714 ÷ 10.5) = 36.3°.
What one extra riser does. With 15 risers instead, each riser drops to 7.2 in (about 7 3/16 in), the angle eases to 34.4°, and the run grows by one going to 147 in (12 ft 3 in). If you have the space, the gentler stair is often worth it; if you do not, the 14-riser version is the steepest layout your maximum allows. These figures are checked in the site's automated tests (fixtures F1 and F8 on the methodology page).
Common stair-planning mistakes
- Measuring to the subfloor and forgetting the flooring. If 3/4 in hardwood goes on the upper floor after the stair is built, the top riser grows by 3/4 in. If tile goes down at the bottom, the first riser shrinks. Include finishes in the total rise, or plan the stringer cuts around them.
- Measuring at the wrong spot. Floors are rarely perfectly level. Measure where the bottom riser will actually land, not straight down from the upper floor edge.
- Using the tread board depth as the going. An 11 1/4 in board with a 1 in nosing gives a 10 1/4 in going. Use the going for the run.
- Rounding the riser count down. Fewer risers means taller ones. Always round up, then check whether one more riser fits.
- Treating the pitch-line length as the board length. The diagonal is a geometric reference. A cut stringer needs extra length for the top and bottom cuts; the stringer calculator finds the shortest board.
- Forgetting headroom. A layout can be perfect on paper and still hit the floor framing above. Check the clear height over the nosings along the whole flight.
A note on building codes
The checks panel compares your geometry with published values, for example the IRC limit of 7 3/4 in risers and 10 in treads for houses. In the 2024 IRC these rules are in section R318.7; in the 2021 edition the same values are in R311.7. Which edition applies, and with what amendments, depends on where you build. Commercial buildings, accessible routes and workplaces follow different rules entirely. Read how stair codes really apply before relying on any single number.
Related tools and guides
- Stair Stringer Calculator Notch layout, bottom drop, throat depth and minimum board length for a cut stringer.
- Deck Stair Calculator Deck height, sloping ground, landing pad and board treads, with landing distance.
- Stair Angle Calculator Angle, grade and pitch from rise and run, or the run needed for a target angle.
- Rise and run formulas Every formula with substituted numbers, in inches and millimetres.
Questions people ask
How many stairs are in 9 feet height?
For a finished rise of 9 ft (108 in) and risers no taller than 7 3/4 in, the US residential (IRC) maximum: 108 ÷ 7.75 = 13.9, rounded up to 14 risers of about 7 11/16 in, with 13 treads because the upper floor is the top step. With a 10 1/2 in going the stair runs 11 ft 4 1/2 in.
If you would rather keep risers at 7 in or less, it takes 16 risers of 6 3/4 in and 15 treads. Measure your real finished floor-to-floor height first; it is rarely exactly 9 ft.
How many stairs do you need for a 10 foot ceiling?
The stair climbs from floor to floor, not floor to ceiling, so add the floor structure above the ceiling. For example, a 10 ft ceiling plus 2x10 joists (9 1/4 in), 3/4 in subfloor and 3/4 in flooring is a 130 3/4 in rise: 130.75 ÷ 7.75 = 16.9, so 17 risers of about 7 11/16 in and 16 treads.
If the floor-to-floor height really were 120 in, you would need 16 risers of 7 1/2 in. Measure the rise rather than guessing the floor depth.
What is the 7-11 rule for stairs?
It is a rule of thumb for a comfortable stair: risers about 7 in high and treads about 11 in deep, which gives an angle of about 32.5°. Those numbers match the commercial limits in the 2024 IBC (section 1011.5.2: risers at most 7 in, treads at least 11 in) and the 2010 ADA Standards (504.2).
Houses built under the IRC may be steeper: risers up to 7 3/4 in and treads down to 10 in. So 7-11 is a good target, not the residential limit. Try both in the calculator above and compare the run each one needs.
How to calculate staircase length?
The horizontal length, called the total run, is number of treads × going. Treads are usually risers − 1. In the 9 ft example: 13 × 10 1/2 in = 136 1/2 in (11 ft 4 1/2 in).
Then add what sits outside that length: the nosing of the bottom tread, and a landing at the bottom, which the IRC sets at least 36 in deep on a straight run (2024 R318.7.6). The sloped length along the nosings, risers × √(riser² + going²), is 182.4 in in the example. It is a geometric reference, not a board length.
What are the parts of a staircase called?
- Tread: the surface you step on. Going: the horizontal distance from one nosing to the next.
- Riser: the vertical step between treads (or the board that closes it).
- Nosing: the front edge of a tread that overhangs the riser below.
- Stringer: the inclined board that carries the treads, cut (notched) or solid.
- Landing: a level platform at the top, bottom or a turn.
- Handrail: the rail you hold. Guard: the barrier on an open side. Balusters: the vertical members in a guard. Newel: the main post at the end of a rail.