How the Stair Calculator Works
Good stairs are comfortable to climb because every step is the same. If one step is even a little higher than the others, people trip, especially in the dark. To plan a staircase, you need to divide the total height into equal steps, and to know how much floor length they need. The Stair Calculator does this from the height between the two floors.
The words used for stairs
- Total rise: the height from the finished bottom floor to the finished top floor.
- Riser: the vertical part of a step. The number of risers is the number of steps up.
- Tread: the flat part of a step that you stand on. The depth of the tread is how far it goes back.
- Run: the total horizontal length of the stairs.
- Stringer: the sloping board on each side that holds the steps.
What you enter
- The total rise, in inches or centimeters.
- The depth of a tread. A common tread is 10 to 11 inches (25 to 28 cm).
How the results are worked out
risers = total rise / 7 inches, rounded to a whole number riser height = total rise / risers treads = risers - 1 total run = treads x tread depth stringer = square root of (rise^2 + run^2) angle = arctangent (riser height / tread depth) comfort number = 2 x riser height + tread depth
A riser height of about 7 inches is a good target, so the calculator divides the total rise by 7 and rounds to the nearest whole number. Then it divides the rise by this number, so that all the risers are exactly the same height. There is always one tread fewer than risers, because the top floor works as the last step.
A worked example
The total rise is 100 inches, which is 8 feet 4 inches. The tread is 10 inches.
| Step | Result |
|---|---|
| Risers (100 / 7 = 14.29, rounded) | 14 |
| Riser height (100 / 14) | 7.14 in (181 mm) |
| Treads (14 - 1) | 13 |
| Total run (13 x 10) | 130 in, which is 10 ft 10 in |
| Stringer (square root of 100 x 100 + 130 x 130) | 164 in, which is 13 ft 8 in |
| Angle (arctangent of 7.14 / 10) | 35.5 degrees |
| Comfort number (2 x 7.14 + 10) | 24.29 in |
The stairs need about 11 feet of floor length, and the board for the stringer must be about 13 feet 8 inches long, plus what you need to cut off.
How many risers for common heights?
With a 10-inch tread:
| Total rise | Risers | Riser height | Run needed |
|---|---|---|---|
| 96 in (8 ft) | 14 | 6.86 in | 10.8 ft |
| 105 in | 15 | 7.00 in | 11.7 ft |
| 108 in (9 ft) | 15 | 7.20 in | 11.7 ft |
| 110 in | 16 | 6.88 in | 12.5 ft |
| 120 in (10 ft) | 17 | 7.06 in | 13.3 ft |
Notice that the ceiling height alone does not give you the total rise. You must add the thickness of the floor between the two levels.
Chart: the floor length that the stairs need
For a 10-inch tread. Green is a short run, and amber and red are longer runs.
100 in rise ███████████████████████████████ 10.8 ft 108 in rise █████████████████████████████████ 11.7 ft 120 in rise ██████████████████████████████████████ 13.3 ft 126 in rise ████████████████████████████████████████ 14.2 ft
One step more, or one fewer
If the result does not fit your space, you can use one riser more or fewer. Take the total rise of 100 inches, with a 10-inch tread:
| Risers | Riser height | Angle | Comfort number |
|---|---|---|---|
| 13 | 7.69 in | 37.6 degrees | 25.38 in |
| 14 | 7.14 in | 35.5 degrees | 24.29 in |
| 15 | 6.67 in | 33.7 degrees | 23.33 in |
13 risers ██████████████████████████████████████ 37.6 degrees 14 risers ████████████████████████████████████ 35.5 degrees 15 risers ██████████████████████████████████ 33.7 degrees
Fewer risers give steeper stairs, and more risers give a gentler slope, but they need more floor length.
The comfort rules
For many years, builders have used simple rules to make stairs feel natural:
- 2 x riser + tread = 24 to 25 inches. This matches the length of a normal step. In the example, it is 24.29 inches.
- Riser + tread = 17 to 18 inches. Another way to say the same thing.
- An angle between 30 and 37 degrees. Stairs that are steeper feel unsafe, and stairs that are shallower use a lot of room.
Building code limits
The calculator checks the result against two limits that appear in the US model code for stairs in a house. A riser must not be higher than 7 3/4 inches, and a tread must be at least 10 inches deep. Every riser in one flight must be the same, with a difference of no more than 3/8 inch. The code has more rules, for example for headroom, handrails, guards, landings, and the width of the stairs. The rules differ between countries and cities, and they change. Always check the code that applies to your building, and ask the local building office.
Tips
- Measure from finished floor to finished floor. If a new floor covering will be added, include its thickness.
- Make the bottom and top step the same as the others. The bottom riser is shorter by the thickness of the tread, and the top riser is often adjusted. Ask your builder about this.
- Check the headroom. There must be enough height above the stairs. In many places the minimum is 6 feet 8 inches.
- Check the space at the top and bottom. There must be room to walk on and off the stairs.
- Use a stair gauge or a level and a template to mark the stringer, and test it before you cut all the boards.
What this calculator does not include
- The thickness of the treads and the nosing, which changes the height of the first and the last riser.
- Landings, turns and winding stairs.
- Headroom, handrails, guards, and the width of the stairs.
- The rules of your local building code, which may be different from those used for the checks.
This tool gives an estimate for general information only. It is not a construction plan. Check the design with a qualified builder or your building office before you build.