Stair Calculator
How do I calculate stairs?
A stair calculator converts the total rise into the number of risers, the riser height, the number of treads, the total run, the stringer length and the stair angle. Measure the total rise from the finished floor below to the finished floor above, and enter it in inches. The calculator divides the total rise by the maximum riser height of 7 3/4 in and rounds up, so you get the fewest risers the code allows, then it divides the rise exactly so every riser is the same height. The upper floor is the last step, so there is one tread fewer than risers. The result also checks the comfort rule, twice the riser plus the tread between 24 in and 25 in, and the IRC limits, so you know before you cut whether the stair will pass inspection. No price is published on this page. Enter your own price per stair for a cost.
Calculate stairs
Enter a total rise greater than 0.
Enter a target riser height from 4 to 7.75 in.
Enter a tread depth from 9 to 12 in.
Enter a tread thickness from 0 to 2 in.
Enter a stair width from 24 to 60 in.
Enter a price of 0 or more, or leave it blank.
Enter your dimensions and click Calculate.
No result yet. Enter your dimensions and click Calculate.
Prices vary by supplier and location. Confirm with your local supplier before ordering.
The calculator takes the total rise, a target riser height, the tread depth, the tread thickness and the stair width. The target riser height defaults to 7 3/4 in, the code maximum, and you can lower it from 4 to 7 3/4 in to get more risers at a lower height. The tread depth defaults to 10 in, the code minimum, and you can change it from 9 to 12 in. The tread thickness is used for the first step height only, because the first riser is shorter than the rest by the thickness of the tread. The stair width defaults to 36 in, the code minimum, and you can change it from 24 to 60 in. A 36 in wide stair typically has three stringers. Price per stair is optional: leave it blank and no cost is shown. The formula used is shown directly under the result, so you can check the number.
What is a stair calculator?
A stair calculator works out the layout of a straight flight of stairs from the total rise, which is the vertical distance from the finished floor below to the finished floor above. It gives the number of risers, the exact riser height, the number of treads, the total run, the stringer length and the stair angle, so you can cut the stringers and order the material.
The parts of a stair are the riser, the vertical face between two treads; the tread, the horizontal step you walk on; the stringer, the diagonal board that carries the treads, usually a notched 2×12; the nosing, the front edge of the tread that sticks out past the riser below it; and the landing, a flat platform between two flights.
The limits that matter come from IRC R311.7, the residential stair code. The maximum riser height is 7 3/4 in (R311.7.5.1). The minimum tread depth is 10 in (R311.7.5.2). Nosing must be 3/4 to 1 1/4 in where the tread is under 11 in (R311.7.5.3). Headroom must be at least 6 ft 8 in (R311.7.2). One flight must not rise more than 12 ft 7 in, or 151 in, between floors or landings (R311.7.3). Riser and tread sizes in one flight must not vary by more than 3/8 in (R311.7.5.1 and R311.7.5.2). The IRC is a model code, and jurisdictions adopt different editions and amendments, so check local building codes before you build.
One number needs a clear definition, because calculators disagree about it. The stair angle on this page is the angle along the nosing line, the line through the nosing of each tread, found as arctan(riser height / tread depth). The tip-to-tip diagonal angle, arctan(total rise / total run), is a different number, because there is one more riser than tread. For the worked example below, the nosing-line angle is 36.87 deg and the diagonal angle is 38.93 deg. This page shows the nosing-line angle everywhere, and labels it as such.
The stringer length is the tip-to-tip length of the cut stringer, and it is also the minimum length of 2×12 material needed to lay it out. The first step is shorter than the rest: its height is the riser height minus the tread thickness, because the tread sits on top of the first riser.
How to calculate stairs
- Measure the total rise. Measure from the finished floor below to the finished floor above, in inches. Include the finished flooring on both levels, because a floor finish changes the rise.
- Work out the number of risers. Divide the total rise by 7 3/4 in and round up. That gives the fewest risers the code allows. A lower target riser height gives more risers.
- Divide the rise exactly. Divide the total rise by the number of risers to get the exact riser height. Every riser must be the same height, within 3/8 in.
- Count the treads. Subtract one from the number of risers. The upper floor is the last step, so there is one tread fewer than risers.
- Work out the total run. Multiply the number of treads by the tread depth. A tread of 10 in is the minimum, and 10 to 11 in is the usual target.
- Check the comfort rule and the angle. Work out 2 x riser + tread. It should fall between 24 in and 25 in. Work out the stair angle as arctan(riser / tread). Most residential stairs fall between 30 deg and 37 deg.
Design targets, as a starting point only:
| Design target | Target value |
|---|---|
| Riser height | 6.5 to 7 in, aim for about 7 in |
| Tread depth | 10 to 11 in, at least 10 in |
| 2R + T | 24 to 25 in, a rule of thumb, not code |
| Stair angle | 30 to 37 deg, along the nosing line |
| Headroom | At least 6 ft 8 in |
| Stair width | At least 36 in |
These are typical values, not a specification. The size your stair needs depends on the total rise, the space available and local code, so confirm it before you order.
Stair formula and worked example
Risers: Risers = ceil(Total rise / Target riser height), with the target defaulting to 7.75 in.
Riser height: Riser height = Total rise / Risers.
Treads: Treads = Risers – 1.
Total run: Total run = Treads x Tread depth.
Stringer length: Stringer length = sqrt(Total rise squared + Total run squared).
Stair angle (along the nosing line): Stair angle = arctan(Riser height / Tread depth).
2R + T: 2R + T = 2 x Riser height + Tread depth.
First step height: First step height = Riser height – Tread thickness.
Cost: Cost = Risers x Price per stair (only if a price was entered).
Worked Example
A 105 in total rise (8 ft 9 in), tread depth 10 in, tread thickness 1 in, stair width 36 in:
Risers = ceil(105 / 7.75) = ceil(13.55) = 14 risers
Riser height = 105 / 14 = 7.5 in
Treads = 14 – 1 = 13 treads
Total run = 13 x 10 = 130 in, or 10 ft 10 in
Stringer length = sqrt(105 squared + 130 squared) = sqrt(27,925) = 167.11 in, or 13 ft 11.11 in
Stair angle = arctan(7.5 / 10) = 36.87 deg
Comfort rule: 2 x 7.5 + 10 = 25.0 in, at the top of the 24 to 25 in range, within it.
First step height = 7.5 – 1 = 6.5 in.
Code checks: riser 7.5 in is at most 7 3/4 in, tread 10 in is at least 10 in, total rise 105 in is at most 151 in, so all checks pass.
Check by the alternative layout: dividing by a target riser of 7 in and rounding to the nearest whole number gives 15 risers of 7.0 in, 14 treads of 10.5 in, a total run of 147 in, or 12 ft 3 in, and an angle of 33.69 deg.
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Frequently asked questions
How do you calculate stair rise and run?
Divide the total rise by the maximum riser height of 7 3/4 in and round up to get the number of risers. Divide the total rise by the number of risers to get the exact riser height. Subtract one from the riser count to get the number of treads, because the upper floor is the last step. Multiply the treads by the tread depth to get the total run. For example, a total rise of 105 in needs 14 risers of 7.5 in, 13 treads of 10 in, and a total run of 130 in. The calculator on this page does the same sum.
What is the maximum riser height and minimum tread depth?
Under IRC R311.7, the maximum riser height is 7 3/4 in (R311.7.5.1) and the minimum tread depth is 10 in (R311.7.5.2). Nosing must be 3/4 to 1 1/4 in where the tread is under 11 in (R311.7.5.3). Riser and tread sizes in one flight must not vary by more than 3/8 in. Check local building codes, because the IRC is a model code and jurisdictions adopt different editions and amendments.
How do you find the stringer length?
The stringer length is the tip-to-tip diagonal of the stair, found with the Pythagorean theorem: Stringer length = square root of (total rise squared + total run squared). For example, a stair with a total rise of 105 in and a total run of 130 in has a stringer length of 167.11 in, or 13 ft 11.11 in. That is the minimum length of 2×12 material needed to lay out the stringer.
What is the 2R + T rule for stairs?
The 2R + T rule says twice the riser height plus the tread depth should fall between 24 in and 25 in for a comfortable stair. For example, a riser of 7.5 in and a tread of 10 in gives 2 x 7.5 + 10 = 25.0 in, which is at the top of the range. The rule is a rule of thumb, not a building code. A stair can meet the code and still fall outside the comfort range, so check both.
What is a good angle for stairs?
Most residential stairs fall between about 30 deg and 37 deg, measured along the nosing line, which is the line through the nosing of each tread. The calculator on this page shows the nosing-line angle, found as arctan(riser height / tread depth). A stair with a 7.5 in riser and a 10 in tread has an angle of 36.87 deg. The tip-to-tip diagonal angle is a different number, so always check which angle a calculator shows.
Why is there one fewer tread than risers?
Because the upper floor is the last step. Each riser lifts you one step, and the last riser lifts you onto the upper floor, so you need one tread fewer than the number of risers. A stair with 14 risers has 13 treads. The tread above the last riser is the upper floor itself, so it is not counted in the total run.