What Is the Stair Calculator?
The Stair Calculator works out the layout of a straight flight of stairs. From the total height between two floors, it finds how many risers are needed, the exact height of each one, the number of treads, the horizontal space the stair occupies and the length of the stringers that support it.
Stairs are one of the most tightly regulated parts of a house, with good reason. People climb stairs without looking at their feet, relying on every step being the same. A variation of even three-eighths of an inch between risers is enough to cause a trip. Accurate layout is a safety matter first and a carpentry matter second.
How the Calculator Works
The calculator divides the total rise by your maximum riser height and rounds up to a whole number of risers. Rounding up guarantees that the actual riser height is at or below the maximum you set.
It then divides the total rise by that number of risers to get the exact riser height. A straight stair has one fewer tread than risers, because the upper floor acts as the final step. The total run is the number of treads multiplied by the tread depth.
The stringer length is the hypotenuse of the triangle formed by the total rise and the total run. The calculator also reports the stair angle and a comfort check based on a long-established rule that twice the riser plus the tread should be between 24 and 25 inches.
The Stair Formula
Number of risers = Total rise ÷ Maximum riser height, rounded up
Actual riser height = Total rise ÷ Number of risers
Number of treads = Number of risers − 1
Total run = Number of treads × Tread depth
Stringer length = √(Total rise² + Total run²)
The comfort rule
2 × Riser + Tread = 24 to 25 inches
This rule reflects the length of an average stride. A low riser pairs with a deep tread, and a high riser with a shallow one. Stairs that satisfy it feel natural to climb.
Step-by-Step Explanation
- Measure the total rise from the finished surface of the lower floor to the finished surface of the upper floor.
- Divide the total rise by 7.5 inches, or your chosen maximum riser.
- Round the result up to the next whole number. This is the number of risers.
- Divide the total rise by the number of risers to get the exact riser height.
- Subtract one from the number of risers to get the number of treads.
- Multiply the number of treads by the tread depth for the total run.
- Use the Pythagorean theorem with the total rise and total run to find the stringer length.
Worked Example
A basement stair must climb 108 inches from the slab to the finished floor above. You want risers no taller than 7.5 inches and treads 10 inches deep.
- Risers: 108 ÷ 7.5 = 14.4, rounded up to 15.
- Actual riser height: 108 ÷ 15 = 7.2 inches.
- Treads: 15 − 1 = 14.
- Total run: 14 × 10 = 140 inches, or 11 feet 8 inches.
- Stringer: √(108² + 140²) = √(11,664 + 19,600) = 176.8 inches, or about 14 feet 9 inches.
- Comfort check: 2 × 7.2 + 10 = 24.4 inches, within the guideline.
You would buy 16 foot 2×12 boards for the stringers. If only 10 feet of floor length is available, the stair will not fit as a straight run, and you would consider a landing with a turn.
How to Use the Calculator
- Enter the total rise. Include the thickness of finished flooring on both levels.
- Enter your maximum riser height. Check your local code for the limit.
- Enter the tread depth, measured from the front of one tread to the front of the next.
- Press Calculate.
- Check that the total run fits the space and that the comfort check is in range.
- Adjust the tread depth and recalculate if needed.
Stringers and treads are usually cut from dimensional lumber, and the Lumber Calculator converts your cut list to board feet for pricing. Exterior stairs to a deck go with the Decking Calculator, and their landing pad can be sized with the Concrete Calculator. If the stair will be carpeted, the Carpet Calculator helps estimate the material, and the geometry used here is the same as in the Roof Pitch Calculator.
Practical Tips
- Measure total rise at the point where the stair will land, not somewhere convenient. Floors are often out of level.
- Account for finished floor thickness. If tile or hardwood will be added later, the first and last risers change.
- Use at least three stringers for stairs 36 inches wide, and add one for each additional 16 to 18 inches.
- Choose straight, dry 2×12 lumber with few knots. After notching, at least 3.5 inches of solid wood should remain.
- Lay out with a framing square and stair gauges so every step is identical.
- Cut one stringer, test it in place, then use it as the pattern for the others.
- Check headroom. Most codes require at least 6 feet 8 inches measured vertically from the nosing line.
Common Mistakes
Measuring to the subfloor. The rise must be finished floor to finished floor. Otherwise the top or bottom step ends up a different height.
Forgetting to drop the stringer. The bottom of the stringer must be trimmed by the thickness of one tread so the first step is the same height as the rest.
Rounding the riser height. If the exact riser is 7.2 inches, lay out 7.2 inches. Rounding to 7.25 accumulates to three-quarters of an inch over 15 steps.
Counting treads equal to risers. A stair has one fewer tread than risers unless the top tread is level with the upper floor.
Ignoring the nosing. Tread depth in codes is measured nose to nose. The board itself is usually an inch or so deeper because of the overhang.
Not checking code. Limits for riser height, tread depth, width, headroom and handrails vary by jurisdiction.
Typical Code Limits
Under the International Residential Code, the maximum riser height is 7.75 inches and the minimum tread depth is 10 inches. The largest riser or tread may not exceed the smallest by more than 3/8 inch. Minimum stair width is 36 inches and minimum headroom is 80 inches. A handrail is required on at least one side when there are four or more risers. Local amendments are common, so confirm with your building department.
Landings and Turns
When a straight run does not fit, split the stair with a landing. Treat each flight separately. The landing counts as a tread and must be at least as deep as the stair is wide. Divide the total risers between the two flights so the riser height stays the same throughout.
Stair Angle
Comfortable residential stairs fall between about 30 and 37 degrees. Below 30 degrees the stair takes a lot of floor space. Above 40 degrees it starts to feel like a ladder. The angle is set entirely by the riser and tread you choose.
Deck and Exterior Stairs
Outdoor stairs follow the same rules, with a few additions. Use pressure-treated or naturally durable lumber, and corrosion-resistant fasteners and hangers. Leave a small gap between tread boards for drainage. The bottom of the stringers should rest on a concrete pad or paver base, not directly on soil. Measure the total rise to the top of that pad, because the ground often slopes away from the deck and the rise can be several inches more than it appears at the deck edge.