Stair Stringer Calculator
Use this free stair stringer calculator to lay out a staircase before you cut a single board. Enter your total rise, riser count and tread depth to get the exact stringer length, the stair angle, the tread count, how many stringers your width needs, and the 2×12 boards to buy. Results update instantly as you type.
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Enter your stair dimensions to see the stringer layout.
How to use this calculator
Measure the total rise — the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor, in inches. Include finished flooring on both levels. Then enter your number of risers: a stair always has one more riser than treads, because the upper floor or landing counts as the final step.
Enter your tread depth (11″ is the common default) and the stair width, which sets how many stringers to cut. The stringer length is the full hypotenuse along the angled face of the board — the results round it up to the next even-foot 2×12 so you buy stock that covers it.
Check the stair angle and the cut diagram before you mark the board. Angles between roughly 30° and 37° make the most comfortable stairs; if yours lands outside that band, change the tread depth or riser count first.
How it works
The calculator treats the staircase as a right triangle. The total run is the horizontal leg — one fewer tread than risers, times the tread depth:
total run = (risers − 1) × tread depth
riser height = total rise ÷ risers
The stringer is the hypotenuse of that triangle, and the stair angle — the angle each step cut makes, set with a framing square — comes from the arctangent of one riser over one tread:
stringer length = √(total rise² + total run²)
angle = atan(riser height ÷ tread depth)
Worked example: a 105″ total rise with 15 risers gives 7″ risers. With 14 treads × 11″, the total run is 154″. The stringer length is √(105² + 154²) = √34,741 = 186.39″ (15 ft 6.4 in), and the angle is atan(7 ÷ 11) = 32.47°. Rounding up to stock, that stair needs a 16 ft 2×12 per stringer.
The number of stringers follows a carpentry rule of thumb — at least two, spaced roughly every 16″ on center: stringers = max(2, floor(width ÷ 16) + 1). A 36″-wide stair gets 3 stringers; a 48″-wide stair gets 4.
These are planning estimates based on standard geometry and common carpentry practice, not building-code advice. Stair codes vary by jurisdiction (riser limits, tread minimums, handrail and headroom rules), so confirm your design with your local building code and inspector before you cut or build.
Frequently asked questions
How do you calculate stair stringer length?
Square the total rise and the total run, add them together, and take the square root: stringer length = sqrt(total rise squared + total run squared). The total run is (risers - 1) x tread depth, since the upper landing counts as the final step. Example: a 105 in rise with 14 treads of 11 in (154 in run) gives sqrt(105^2 + 154^2) = sqrt(34,741) = about 186.4 in, or 15 ft 6.4 in.
What angle should a stair stringer be cut at?
The stringer angle comes from atan(riser height / tread depth). A 7 in riser with an 11 in tread gives atan(7 / 11) = about 32.5 degrees. Most comfortable residential stairs sit between about 30 and 37 degrees. If your angle falls outside that band, adjust the tread depth or riser height before you cut.
How many stringers does a stair need?
Use at least two, spaced roughly every 16 in on center: stringers = max(2, floor(width / 16) + 1). So a 30 in wide stair gets 2 stringers, a 36 in wide stair gets 3, and a 48 in wide stair gets 4. If your treads are a single 2x board (under 1.5 in thick), consider adding one more stringer to prevent bounce. This is general guidance, not code advice.
What size board do I need for a stair stringer?
Cut stringers from 2x12 lumber - its 11.25 in face leaves enough wood for the stair notches after the cuts are made. Buy stock at least as long as the stringer length: the calculator rounds up to the next even-foot board length. A 186.4 in (15 ft 6.4 in) stringer needs 16 ft 2x12s, and the shopping list in the results shows how many boards to buy for your stair width.
Why is the stringer longer than the total run?
Because the stringer is the hypotenuse of the rise-and-run right triangle, so it is always longer than either leg. A stair with 105 in of total rise and 154 in of total run needs a 186.4 in stringer - about 32 in longer than the run alone. Measure and mark along the angled face of the board, not along the flat run.