Stair stringer calculator

How the steps are worked out

1. Number of risers. Divide the total rise by your target riser height and round to the nearest whole step. If that leaves the riser over the code maximum, add a step until it is legal.
2. Riser height. Divide the total rise by the number of risers. Every riser is the same height; the code allows only 3/8 in of variation in a flight.
3. Treads. One fewer than the risers, because the upper floor is the last step. Total run is treads times tread depth.

For 108 in of rise at a 7.5 in target: 108 / 7.5 = 14.4, so 14 risers of 7.714 in, just under 7-3/4. That gives 13 treads, and at 10 in each a total run of 130 in.

Stringer length and the uncut depth

The board has to be long enough to hold every notch plus the cuts at each end. The calculator finds the shortest straight board that contains the whole stringer outline and rounds up to the next lumber length.

Each notch cuts into the board by riser x tread / √(riser² + tread²), measured square to the edge. What is left is the uncut depth, or throat, and it is what carries the load. DCA 6, the American Wood Council's deck guide, asks for at least 5 in. A 2x12 at 7-3/4 by 10 in leaves 5.12 in, which is why 2x12 is the minimum and why a 2x10 cut stringer fails at almost any normal pitch.

Laying it out

1. Clamp stair gauges to a framing square: the riser height on the tongue, the tread depth on the blade.
2. Mark each notch along the board, sliding the square so the gauges stay on the edge. Use the cumulative heights in the layout table to check you have not drifted.
3. Cut the bottom riser short by the tread thickness, so the first step comes out the same height as the rest once the tread is on.
4. Cut one stringer, test it in place, then use it as the pattern for the others.