Stair stringer calculator: risers, treads, stringer length and stairwell opening

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Stair stringer calculator

Type the total rise from finished floor to finished floor. You get equal risers, the tread run, the cut for the shorter first riser, the board left under the notch, the stringer length and count, the tread boards, and the shortest stairwell opening for 6 ft 8 in of headroom. Nothing leaves your browser.

The method

Risers. Total rise divided by 7-3/4 in, rounded up. Divide the rise by that count: every riser is equal (the code allows 3/8 in between the tallest and shortest).

Treads. One fewer than risers; the top step is the floor. Each at least 10 in deep.

Notch. The pitch line joins the nose points. The board left under the inside corner of the notch is the board depth minus R×T/√(R²+T²); the usual minimum is 3-1/2 in.

First riser. Cut one tread thickness short at the bottom so the finished first step matches the rest.

Headroom. The opening must run (80 in + floor thickness) × tread ÷ riser along the stair.

Questions

What is the formula for a stair stringer?

Divide the total rise (finished floor to finished floor) by the largest riser you may use, 7-3/4 in under the model residential code, and round up to get the number of risers. Divide the total rise by that number for the riser height. There is one fewer tread than risers, and each tread is at least 10 in. The pitch line along the nose points is the hypotenuse of the riser and tread.

How many stringers does a stair need?

It depends on the width and the tread board. It depends on the width and the stringer spacing you choose. The calculator defaults to 11-1/2 in between stringers (4 on a 36 in stair) and notes when the gap is more than a tread board of that thickness usually spans (12 in under 1-1/4 in thick, 16 in under 1-1/2 in, 24 in for 2x). Your local code and the tread board decide.

Why is the first riser cut shorter?

The first step's riser is cut one tread thickness short at the bottom stringer so that once the tread board is on top, the first finished step is the same height as all the others.

How much stairwell opening do I need for headroom?

About (80 in + floor thickness) x tread / riser, so for a 9 ft rise with 10 in treads and a 12-1/2 in floor, at least 9 ft 11-15/16 in. The calculator solves it for your numbers.