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Work out the stringers for a straight flight of stairs or steps. Enter the total rise and the width, choose the timber, and press Calculate to see the number of steps, the rise and going to mark out, the stringer length to buy, the throat left after cutting and how many stringers you need.
| Risers | Rise × Going | Pitch | Stringer |
|---|
The same total rise with a different number of steps. Rows marked ✗ fall outside the limits for your stair.
You get the number of risers and treads, the rise and going to mark out, the pitch and run, the stringer length and the timber to buy, the throat left after cutting and the number of stringers. A drawing shows the cut stringer, a table compares one step more or fewer, and you can copy the result or save it as a PDF.
Stringers are the sloping boards that carry the treads of a stair, one at each side and often more in between. A cut stringer, or open stringer, has a sawtooth of notches cut into its top edge, and the treads and risers sit on the notches. It is the usual choice for deck steps, garden steps and simple stairs. A closed stringer stays whole, with the treads and risers housed into grooves routed in its face, as in most joiner-made staircases. This calculator sets out cut stringers; the rise and going are the same for a closed string, and our staircase calculator also covers headroom and the stairwell opening.
Rise = total rise ÷ risers · run = treads × going · pitch = tan⁻¹(rise ÷ going)
Stairs inside a home in England must meet Approved Document K. For a private stair, the one serving a single dwelling:
| Item | Limit |
|---|---|
| Rise of each step | 150 to 220 mm |
| Going of each step | 220 to 300 mm |
| Pitch | 42° maximum |
| 2 × rise + going | 550 to 700 mm |
| Headroom above the pitch line | 2 m clear |
All the rises and goings in a flight must be equal. For garden steps and deck stairs, Part K does not normally apply, but the same comfort rules make steps safer, and a little lower and deeper is easier outdoors. The calculator uses the Part K figures as a guide for outdoor steps, with goings up to 450 mm.
The stringer runs along the pitch from the bottom of the first riser to the top of the last one, so its length is the hypotenuse of the total rise and the total run:
Stringer length = √(total rise² + run²)
Add a little for the level cut at the bottom and the plumb cut at the top. The calculator adds 300 mm and rounds up to the next common timber length, from 2.4 m to 6.0 m in 600 mm steps. If the stringer would be longer than 6 m, split the flight with a landing, which also makes a long stair safer.
Cutting the notches removes a triangle of timber at every step. The solid wood left between the inside corner of each notch and the bottom edge of the board is called the throat, and it carries the load. The deeper the notch, the less is left:
Throat = timber width − (rise × going ÷ √(rise² + going²))
A common rule of thumb is to keep at least 100 mm of throat. With a 185 mm rise and 250 mm going the notch is about 149 mm deep, so 47 × 275 mm timber leaves about 126 mm, while 225 mm timber would leave only 76 mm. Use C24 graded timber, treated for outdoor use, and keep the stringers close enough together for the treads to span between them: around 400 mm for decking boards. For the deck itself, our decking joist calculator checks joist sizes and spans.
A stair inside a home with a total rise of 2,600 mm and a width of 900 mm, using 47 × 275 mm stringers up to 400 mm apart:
The calculator chooses the number of risers that keeps each rise within the limit and closest to a comfortable height. It sets the going to make 2R + G about 620 mm, then keeps it within the going limits and, inside a home, steep enough to stay under 42°. The stringer length is the pitch length plus 300 mm, rounded up to stock timber. The throat is the timber width less the depth of each notch measured square to the pitch, and the number of stringers is the width divided by the spacing, rounded up, plus one. The table shows the same stair with one step fewer and up to two more, so you can choose a gentler or steeper flight.
Divide the total rise into equal risers of about 190 mm, choose a going so 2 × rise + going is about 620 mm, then the stringer length is √(total rise² + run²), where the run is the number of treads times the going.
47 × 225 mm C24 is common for short flights, but wider timber such as 47 × 275 mm leaves more throat after cutting and suits longer stairs.
220 mm for a private stair under Approved Document K, with a going of at least 220 mm and a pitch of no more than 42°.
One at each side and enough between so the treads span no more than they can carry, about 400 mm apart for decking boards. A 900 mm stair needs 4.
About 4.2 m along the pitch with 14 steps of 250 mm going, so buy 4.8 m lengths.
The top floor or deck acts as the last step, so a stair with 14 risers has 13 treads.
The solid timber left between the inside corners of the notches and the bottom edge. Keeping at least about 100 mm is a common rule of thumb.
Not normally, but using the same rise and going rules makes them safer and more comfortable.
Rise, going, pitch and headroom limits from Approved Document K (England). Timber lengths are common UK stock sizes. Reviewed November 2026.