How to Calculate Concrete for Stairs
A solid concrete staircase is poured as a monolithic structure. Unlike timber stairs where each step is independent, a concrete staircase fills all the material beneath each step as well. This means the bottom step requires concrete for its full height, and each step above it adds another layer of material on top of what is already there.
The volume formula for a solid concrete staircase is:
Volume (m³) = width × tread × rise × n(n+1) / 2
Where n is the number of steps. This is derived from the sum of the series 1 + 2 + 3 + ... + n = n(n+1)/2. Each step contributes a rectangular prism equal to the tread depth multiplied by the accumulated height up to that step, multiplied by the stair width.
Worked Example
Using the default values: 5 steps, 175 mm rise, 300 mm tread, 1,200 mm width.
| Dimension | Value | In metres |
|---|
| Number of steps (n) | 5 | - |
| Rise | 175 mm | 0.175 m |
| Tread | 300 mm | 0.300 m |
| Width | 1,200 mm | 1.200 m |
| n(n+1)/2 | 5 × 6 / 2 = 15 | - |
| Net volume | 1.2 × 0.3 × 0.175 × 15 | 0.945 m³ |
| + 10% waste | 0.945 × 1.10 | 1.040 m³ |
| 20 kg bags (0.009 m³ each) | 1.040 / 0.009 | 116 bags |
NZ Stair Proportions
The New Zealand Building Code (Clause D1: Access routes) and NZS 4121 set minimum and maximum dimensions for stairs. A common comfort rule used in residential design is:
2R + G = 600 mm to 700 mm (where R = rise, G = going/tread)
| Rise (mm) | Going (mm) | 2R + G | Comfort rating |
|---|
| 150 | 300 | 600 | Good (shallow) |
| 175 | 300 | 650 | Ideal residential |
| 190 | 260 | 640 | Acceptable |
| 200 | 250 | 650 | Steeper |
For outdoor residential concrete stairs, a rise of 150 mm to 175 mm and going of 280 mm to 330 mm is most common. Avoid a rise greater than 190 mm or a going less than 250 mm for frequently used external stairs.
Bags vs Ready-Mix
For small staircases (under about 0.5 m³), bagged concrete mix is convenient. For volumes above 0.5 m³, ordering ready-mix concrete delivered by truck is usually more economical per cubic metre, though minimum delivery charges apply (typically 0.3 m³ to 1.0 m³ minimums depending on the supplier). Ready-mix also allows you to specify the concrete strength (for example, 25 MPa is commonly specified for residential concrete stairs).
Formwork Tips
- Build formwork from 18 mm plywood or 100 mm timber boards staked firmly in place.
- Oil or wet the formwork before pouring to prevent adhesion.
- Pour from the bottom step upwards and compact each layer with a rod or vibrator.
- For stairs wider than 1.5 m, add a central stringer for extra formwork support.
- Cure the concrete by keeping it damp for at least three days, especially in hot or windy weather.
- Do not apply loads for at least 24 hours; leave formwork in place for at least 48 hours.
Related Calculators
Sources and method: Volume formula derived from the geometric series sum for a solid staircase (each step is a rectangular prism of width × tread × cumulative rise). NZ Building Code Clause D1 Access Routes (Ministry of Business, Innovation and Employment). NZS 4121:2001 Design for access and mobility. Bag yield based on standard NZ product data sheets (approximately 0.009 m³ per 20 kg bag of premixed concrete).
This calculator gives indicative material quantities only. Actual concrete volumes depend on stair geometry, formwork accuracy, and pour method. Always confirm quantities with your concrete supplier. Prices shown are estimates only and vary by region and supplier. This tool does not account for landing slabs, reinforcement, or sub-base preparation.
