Concrete volumes
Solid concrete steps volume
- where
- volume of the steps (m³)
- width of the steps (m)
- going of each step (mm)
- rise of each step (mm)
- number of steps
- volume of the landing (m³)
- depth of the top landing (mm)
- total concrete volume (m³)
Explain this equation
Works out the concrete in a flight of solid steps built up from the ground, with an optional top landing.
Treat the flight as stacked blocks: the bottom step is one rise high and runs the full length, the next sits on top, and so on. Seen from the side, the step profile adds up to G × R × (1 + 2 + … + N), and that sum is N(N + 1)/2. Times the width gives volume. The landing is a block P deep at the full height N × R. G, R and P are in mm and B in m, so dividing by a million gives m³.
The triangular-number sum counts the step blocks.
Sense check: four 150 mm rises with 300 mm goings, 1.2 m wide, is about 0.54 m³.
Watch out: steps against a wall or on a sloping bank need less concrete; this assumes solid fill from level ground.
Works out the concrete in a flight of solid steps cast on the ground, with an optional landing at the top.
Enter your values to see the result.
Good to know
The flight is treated as solid concrete down to the bottom step level: step 1 is one rise high, step 2 is two rises high, and so on, which is where N(N+1)/2 comes from. If you fill the core with hardcore, deduct its volume. Approved Document K sets limits on rise and going for private and public stairs.
Common mistake
Multiplying the number of steps by one step block, which ignores the solid concrete under the upper steps and badly under-orders.
Limits
Solid steps on level ground, all with the same rise and going. Waist-slab (suspended) flights, curved steps and sloping ground need a separate take-off.
Sources
- Geometry: prism volume = plan area × depth; cylinder volume = π d²/4 × h
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS 8500, BS EN 206, BS EN 752, Building Regulations Part H, manufacturers’ data and your engineer’s design. Structural concrete and foundations need a competent designer.