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Concrete Stair Prism Volume

Estimate concrete for a repeated stair cross-section with a sloping carriage and optional nosing.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

In initial display units, Number of steps 10, Riser rise (r) 30, Effective tread run (t) 40, Throat depth (dₜ) 10, Stair width 100, Nosing depth (dn) 0, Wastage 0 gives End area of a step's triangle 0.06, Area of carriage portion 0.05, End area of each step 0.11, Concrete volume needed 1.1, Concrete volume to purchase 1.1, Total run 4, Total rise 3, Total carriage length 5.

Step end area = rise×run/2 + throat depth×√(rise²+run²); concrete volume = steps×end area×stair width; purchase volume = volume×(1+waste).

Worked example

Enter these known values and leave the other values blank.

Number of steps
10 steps
Riser rise (r)
30 cm
Effective tread run (t)
40 cm
Throat depth (dₜ)
10 cm
Stair width
100 cm
Wastage
0 %
Concrete volume needed
1.1 m³
Concrete volume to purchase
1.1 m³
Stair pitch
36.87 deg
Total rise
3 m
Total run
4 m
Total carriage length
5 m
End area of a step's triangle
0.06 m²
Area of carriage portion
0.05 m²
End area of each step
0.11 m²
Total end area of steps
1.1 m²

Assumptions and limitations

  • This is geometric volume for repeated equal steps, without landings or footings. Throat depth follows the captured perpendicular carriage convention. Nosing adds a triangular end area only when selected. Structural reinforcement and applicable stair requirements need separate design.
  • Select compatible units and clear the quantity to solve before supplying the remaining measurements. Rounded purchase counts cannot uniquely recover a continuous dimension. Currency choices label amounts and do not convert exchange rates.

Common questions

How can I solve for a missing measurement?

Clear that field, then enter independent known values. Lock a known measurement to preserve it while changing another value. Procurement counts are rounded upward and cannot be reversed uniquely.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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