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What a stair stringer is
A stringer is the long diagonal board that carries a staircase. It is cut like a sawtooth, with one notch for each step, and it runs from the lower floor to the upper floor. Two or three stringers usually support the whole staircase, and their length decides what size of lumber you must buy. If you buy boards too short, you cannot fix it by joining pieces: a stringer must be one solid board.
This calculator finds the stringer length from the total rise and total run of your staircase. The math is the old right-triangle rule: the stringer is the diagonal of a triangle whose vertical side is the total rise and whose horizontal side is the total run. Square both sides, add them, and take the square root. That diagonal is the straight length of the board before any notches are cut.
You can enter the total rise and total run directly if you already know them, or let the calculator work from your tread depth. When you give a tread depth, it estimates the number of risers and the riser height too, so you can check that the staircase is comfortable before you buy anything.
A worked example
Take a staircase with a total rise of 60 inches and a total run of 80 inches. The stringer length is the square root of 3,600 plus 6,400, which is the square root of 10,000, or exactly 100 inches. That is a clean 3-4-5 triangle, and it is a good way to check your own numbers: if your rise and run form a 3-4-5 ratio, the diagonal is five parts.
Real staircases rarely land on round numbers. A rise of 105 inches and a run of 130 inches gives a stringer of about 167 inches, or just under 14 feet. The calculator adds a cutting allowance on top of that, because you need extra board at the top and bottom for the cuts where the stringer meets the floors. Buy the next standard board length above the result, not the exact result.
How to use the result
First, confirm the total rise and total run with real measurements. The total rise is finished floor to finished floor, and the total run is the horizontal distance from the face of the first riser to the face of the last riser, or to the upper floor edge. Measure both on site, not just from a drawing, because real floors and walls are never perfectly true.
Next, check the stair angle the calculator shows. A comfortable staircase usually sits between 30 and 37 degrees. Below 30 degrees the staircase eats a lot of floor space, and above 40 degrees it starts to feel like a ladder. If your angle is outside the comfortable range, change the tread depth or the number of steps rather than forcing a steep staircase into a small space.
Then buy boards at least as long as the suggested purchase length. Lumber comes in standard lengths, so round up to the next available size. It is far better to trim a foot off a long board than to discover your board is six inches short after you have cut the notches.
Cutting tips
Mark the stringer with a framing square and a pair of stair gauges, which clamp onto the square at the riser and tread measurements. Mark every step before you cut any of them, and check the marks against your total rise and run. One misplaced mark early in the layout shifts every step after it.
Cut a test stringer from cheap lumber first. Set it in place and check that the top lands level with the upper floor and the bottom sits flat on the lower floor. If the test stringer fits, use it as a template for the rest. If it does not fit, you have learned the lesson on a cheap board, not on the expensive one.
Safety and building codes
This tool is an educational estimator only, never professional advice. Stair results are estimates, so check your local building codes and consult a licensed builder or carpenter before building. Stringer spacing, lumber size, and support rules all matter: a stringer that is too thin or spaced too far apart will flex and feel unsafe, even if its length is right.
Frequently asked questions
Why is the buy length longer than the stringer length? The diagonal is the length between the two ends, but the top and bottom cuts are plumb and level cuts, not square cuts, and you need material to make them cleanly. The allowance covers that waste plus a small margin for error.
How many stringers do I need? A narrow staircase may need only two, but wider staircases need a centre stringer as well. Check local rules and the span tables for your lumber: the wider the staircase, the more support it needs.
Can I use engineered lumber for stringers? Yes, and it is often straighter than sawn lumber, but it must be rated for the job and installed to the maker’s instructions. Ask your supplier which product suits stair stringers.
Measure the real rise and run, run the numbers, and cut a test piece first. A stringer cut right the first time saves lumber, time, and the frustration of a staircase that never quite sits level.
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