Stairs· 3 min read
How to Calculate Stairs: Number of Steps, Riser Height and Tread Depth
Stairs for a 2,800 mm floor-to-floor height step by step: how many risers, riser height and going from 2R + G, pitch, stringer length and saw angles.
With stairs, millimetres matter. Everything starts from one measurement — the height from the finished floor below to the finished floor above. We will work through a house with a 2,800 mm floor-to-floor height and a straight flight on two cut stringers.
1. Riser height: divide the height by the number of risers
Divide the height by the number of risers. Do not round the riser height — every step must be exactly the same, or people will trip. With 16 risers: 2,800 ÷ 16 = 175 mm.
2. Going from the 2R + G rule
The going G is the horizontal distance from one tread edge to the next, without the nosing. It follows from the stride rule: two risers plus one going should match an average human stride. German DIN 18065 asks for 590–650 mm, Czech practice designs to 630 mm, and in England Approved Document K allows 2R + G between 550 and 700 mm. With 175 mm risers: G = 630 − 2 × 175 = 280 mm.
| Risers | Riser | Going | Pitch | Total run | Stringer |
|---|---|---|---|---|---|
| 14 | 200.0 mm | 230.0 mm | 41.0° | 2,990 mm | 3,936 mm |
| 15 | 186.7 mm | 256.7 mm | 36.0° | 3,593 mm | 4,420 mm |
| 16 | 175.0 mm | 280.0 mm | 32.0° | 4,200 mm | 4,932 mm |
| 17 | 164.7 mm | 300.6 mm | 28.7° | 4,809 mm | 5,465 mm |
All four options meet 2R + G = 630 mm, but they feel different. 14 risers give a steep stair, and the 230 mm going is below the 240 mm limit the calculator uses by default. 17 risers are gentle, but the stair is 609 mm longer than with 16. For a house, 16 risers of 175 × 280 mm is a good compromise.
When the run is fixed
If the space is given, enter the available run — from the face of the first riser to the edge of the upper floor. The calculator tries every riser count and picks the one whose 2R + G is closest to 630 mm while staying within your limits. With 4,200 mm it lands exactly on 16 risers of 175 × 280 mm. With 3,900 mm it is still 16 risers, but with a 260 mm going: the 610 mm stride stays within 600–650 mm and the pitch rises to 33.9°.
3. Treads, pitch and floor space
- There is one tread fewer than risers: 15. The last step is the upper floor.
- Total run: 15 × 280 = 4,200 mm. With the 30 mm nosing of the first tread, the stair takes 4,230 mm of floor.
- Tread board depth is 280 + 30 = 310 mm, its length is the stair width, here 900 mm.
- Pitch = arctan(175 ÷ 280) = 32.0°.
4. Stringer: length and cut angles
A cut stringer from 300 × 50 mm board (roughly a 2×12) needs a board at least 4,932 mm long. That is the shortest board that holds the whole sawtooth, from the seat on the floor to the last notch under the upper floor. 152 mm of board remains below the notches, measured square to its edge.
- Plumb cut (notch faces and the top end at the upper floor): 32.0° off square — as you set it on a circular or mitre saw.
- Level cut (seat on the floor and the tread seats): 58.0°.
- Framing square: 175 mm on the tongue and 280 mm on the blade; hold it to the board edge and mark notch by notch.
The tread thickness (40 mm) is taken off the bottom of the stringer, so the first notch is 40 mm lower. Once the treads are on, every finished riser is the same 175 mm.
StairsWork out stairs for your heightThe calculator does geometry and quantities, not structural design. Stringer size, fixings, guards and handrails must be designed to your local building rules. Limits differ by country — in the US the IRC allows at most a 7¾ in riser and asks for at least a 10 in tread — so check the rules that apply where you build.