How staircase concrete is estimated
An RCC stair calculator estimates the volume of concrete in a straight flight of reinforced concrete stairs. It adds three parts: the sloped waist slab that carries the stairs, the triangular steps cast on top of it, and an optional flat landing. You enter the stair width, number of steps, riser height, tread depth and waist slab thickness.
This is a simplified estimating method for ordering material. It's widely used for quantity takeoffs, but it isn't a structural calculation, and it doesn't size the slab or its reinforcement.
The formulas
- Total going = Steps × Tread depth
- Total rise = Steps × Riser height
- Waist slab length = √(Total going² + Total rise²)
- Waist slab volume = Waist length × Stair width × Waist thickness
- Step volume = ½ × Riser × Tread × Stair width × Steps
- Landing volume = Landing length × Landing width × Waist thickness
- Total volume = Waist + Steps + Landing
Each step is treated as a solid right triangle sitting on the waist slab, which is why its volume is half of riser × tread × width. The landing uses the same thickness as the waist slab. The calculator shows the sloped waist length to three decimal places, and the total volume in m³ and ft³.
Input limits are 1 to 60 steps, risers of 100 to 220 mm, treads of 200 to 350 mm, and a waist of 100 to 300 mm.
Worked example
A flight 1 m wide with 10 steps, 150 mm risers, 250 mm treads, a 150 mm waist slab, and a 1 m × 1 m landing:
- Total going: 10 × 0.25 = 2.5 m. Total rise: 10 × 0.15 = 1.5 m.
- Waist length: √(2.5² + 1.5²) = √8.5 = 2.915 m.
- Waist volume: 2.915 × 1 × 0.15 = 0.437 m³.
- Step volume: 0.5 × 0.15 × 0.25 × 1 × 10 = 0.1875 m³.
- Without a landing, the total is 0.625 m³ (22.065 ft³).
- Landing: 1 × 1 × 0.15 = 0.15 m³, bringing the total to 0.775 m³ (27.363 ft³).
Ready-mixed concrete is sold in set increments and some always stays in the pump line or the barrow, so round up and add a margin when you order.
Riser and tread dimensions in building codes
The calculator accepts a wider range than most codes allow, so check your dimensions against the rules where you're building. In the US, the International Residential Code (section R311.7.5) sets these limits for homes:
| Dimension | IRC limit | Approximate metric |
|---|---|---|
| Riser height | 7¾ in maximum | 196 mm |
| Tread depth | 10 in minimum | 254 mm |
| Variation within a flight | ⅜ in maximum | 9.5 mm |
Other countries set different limits, and commercial buildings usually have stricter ones, so use the code that applies to your project.
Steps to take off a staircase
- Divide the floor-to-floor height by your intended riser height and round to a whole number of risers. Recalculate the riser height so they're all equal.
- Enter that number of risers as the number of steps.
- Enter the tread depth and the stair's clear width.
- Enter the waist thickness from the structural drawing.
- Add a landing if the flight has one. Calculate a second flight separately and add the two.
Limitations
- Straight flights only. Dog-leg stairs need each flight and landing entered separately. Spiral and curved stairs aren't covered.
- Nosings, finishes and any supporting beams aren't included.
- Formwork and reinforcement aren't estimated.
Staircase geometry, waist thickness and reinforcement must follow your local building code and be designed or checked by a qualified structural engineer. Use this result only for ordering and budgeting.
Related calculators
- Concrete calculator: volume and cement, sand and aggregate for other pours.
- RCC slab calculator: for the floor slabs the stairs connect.
- Beam calculator: concrete for the beams that often support a landing.
- Steel weight calculator: weight of reinforcing bars once you know their sizes and lengths.
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