ToolwickStair Stringer Calculator
Use this free stair calculator to work out unit rise, tread run, cut angles, throat and stringer length for deck, basement and interior stairs. It also checks your layout against common IRC limits and gives a cut schedule you can mark on the board.
Schematic, not to scale. Labels update with your numbers. θ is the slope of the nosing line from horizontal.
Estimates only. By using this calculator you agree to our Terms.
All results are shown in inches. Planning estimate only, not an engineering, permit or inspection approval.
How to Use This Stair Calculator
Enter the total rise (the vertical distance from the lower finished floor to the upper finished floor), the number of risers, and the tread depth you want. Add your tread thickness and stringer board width, then press Calculate. You get the unit rise, total run, cut angles, throat, stringer length, a cut schedule, and a comparison of nearby riser counts. Warnings flag anything outside common IRC limits.
Why This Matters
Stairs are one of the few places in a house where a quarter inch matters. People learn step height in their legs, so a riser 3/8″ taller than its neighbours is a classic trip point. That is why the IRC limits the variation between the tallest and shortest riser in a flight to 3/8″.
Take a deck 49″ above grade. Seven risers give exactly 7″ each, which is comfortable and compliant. Six risers give 8.17″ each, over the 7¾″ residential maximum. Eight give 6.125″ each, legal but with more run and more lumber. A calculator compares those options in seconds, before you buy a single 2×12. The same numbers set your lumber order, saw angles, ground footprint, and whether enough solid wood remains under each notch.
How It's Calculated
A flight with N risers has N − 1 treads, because the top riser meets the upper floor or deck. All formulas use inches.
Total run = Tread depth × (N − 1)
Stringer length = √(Total rise² + Total run²)
Seat cut angle (to board edge) θ = arctan(Unit rise ÷ Tread depth)
Plumb cut angle (to board edge) = 90° − θ
Throat = Board width − (Unit rise × Tread depth) ÷ √(Unit rise² + Tread depth²)
Bottom riser cut = Unit rise − Tread thickness
The board edge tilts θ from horizontal. When the stringer is installed, the seat cut is level and the plumb cut is vertical. Measured against the board's edge, the seat cut makes θ and the plumb cut makes 90° − θ. The throat is the perpendicular distance from a notch's inside corner to the board's lower edge, the thinnest wood carrying the load. The bottom riser is cut shorter by one tread thickness so the first finished step matches the rest.
Stock length adds at least 12″ (or one board width, if larger) to the stringer length, then rounds up to the next standard length (8, 10, 12, 14, 16, 18, 20 or 24 ft). Length rounds up and throat rounds down, so the displayed numbers err on the safe side.
Checks follow IRC 2021 R311.7 for one- and two-family homes: maximum riser 7¾″ (R311.7.5.1), minimum tread 10″ (R311.7.5.2), nosing on solid-riser stairs when treads are under 11″ (R311.7.5.3), and maximum 151″ (12 ft 7 in) of rise between floors or landings (R311.7.3). The IBC for commercial stairs is stricter: 4″ to 7″ risers, 11″ treads, and 144″ between landings. The 3½″ minimum throat is a common rule of thumb, not a code number. Local codes vary.
Worked Example
A deck is 49″ above a concrete pad. We want 7 risers, 11″ treads, 1.5″ thick treads, and 2×12 stringers (11.25″).
- Unit rise = 49 ÷ 7 = 7.000″.
- Treads = 7 − 1 = 6, so total run = 6 × 11 = 66″.
- Stringer length = √(49² + 66²) = √6,757 = 82.201″. The tool rounds up and shows 82.21″.
- θ = arctan(7 ÷ 11) = 32.5°. The seat cut makes 32.5° with the board edge, and the plumb cut makes 90° − 32.5° = 57.5° with the board edge.
- Step diagonal = √(7² + 11²) = 13.04″. Throat = 11.25 − (77 ÷ 13.04) = 11.25 − 5.91 = 5.34″, well above 3½″.
- Bottom riser cut = 7.0 − 1.5 = 5.5″.
- Stock needed = 82.20 + 12 = 94.20″ = 7.85 ft, so buy 8 ft boards.
- Checks: 7″ ≤ 7¾″, 11″ ≥ 10″, and rise + run = 18″. No warnings.
Tips & Common Mistakes
- Do not round the unit rise and step it off. A 7.714″ rise marked at 7 11/16″ is 0.027″ short per step, over 1/4″ across 10 steps. Use the cumulative heights in the cut schedule.
- Measure total rise to finished surfaces. Include upper decking or flooring and the landing pad. Measuring to the framing is off by a full tread thickness.
- Apply the bottom riser adjustment. Without it the first step is one tread thickness taller than the others.
- Check the throat before you cut. A tall rise with a short tread leaves little wood under the notch. Use wider stock, an engineered stringer, or add a riser.
- Mind span and spacing. Long runs often need a landing or support post. Stringers are usually 16″ on center or closer under 5/4 decking, and a 36″ stair normally gets three. Check span tables for your species and grade.
- Keep wood out of the soil. Land the bottom on a concrete pad or approved footing, and treat cut ends of pressure-treated lumber.
Frequently Asked Questions
How many stringers do I need for a staircase?
For a 36″ wide stair, three stringers (two outside, one in the middle) is usual practice. Space them no more than 16″ on center with 5/4 decking, and closer for thinner treads or heavy loads. Your local code or span tables have the final word.
What is the ideal rise and run for comfortable stairs?
Most people find stairs comfortable when rise plus run is 17 to 18 inches, or when twice the rise plus the run is 24 to 25 inches. A 7″ rise with an 11″ run fits both rules. Steeper stairs save floor space but are harder to climb and descend.
Why is total run one tread less than the number of risers?
The top riser lands on the upper floor or deck, so it has no tread of its own. A stair with 7 risers has 6 treads, and total run is 6 times the tread depth. Counting 7 treads would make the stair and stringer too long.
What is a stringer throat, and how much do I need?
The throat is the thinnest section of wood left under a notch, measured perpendicular to the board's edge. Many builders want at least 3½″ on a 2×12. That is a rule of thumb rather than a code figure, and it depends on lumber grade, spacing and span.
Why is the bottom riser cut shorter than the others?
The stringer rests directly on the pad, but the first tread sits one tread thickness above the bottom notch. Cutting the bottom riser shorter by that thickness makes the first finished step equal the others. At the top there is no tread to subtract, because the deck or floor surface is the last step. The top is cut to suit how the stringer attaches to the header or framing, so dry-fit it before final cuts.
What angle do I set on my saw or framing square?
Against the board's edge, the seat cut makes the θ angle shown in the results and the plumb cut makes 90° minus θ. On a framing square, put the unit rise on one leg and the tread depth on the other, both touching the board's edge. The rise leg marks the plumb cut and the run leg marks the seat cut.