Select the stair shape:
Stair inclination angle: °
Concrete volume for the stair: m³
Please fill in all fields with valid values. The specified dimensions are not suitable for the selected stair shape.
About Concrete Stair Calculation
This calculator determines the concrete volume for a cast-in-place concrete stair from its geometry. The calculation is suitable for a straight flight, a two-flight staircase with a landing, a two-flight staircase with a 90° turn, and a three-flight staircase with 90° turns.
The calculation logic is based on dividing the staircase into simple geometric parts. First, the slope angle is calculated from the step dimensions, then the longitudinal section area of each flight and landing is determined, after which this area is multiplied by the relevant width, and the final result is converted from mm3 to m3.
Reference points and recommendations
Geometric basis of the calculation
Slope angle. First, the calculator determines the flight slope angle from the tread length a in mm and the riser height h in mm. The relationship α = arctan(h / a) is used. This angle is displayed in degrees and is then used for trimming calculations and for checking the geometry of turning sections.
Length of the sloping part. For each step in the flight, the length of the sloping line is calculated using the Pythagorean theorem. The expression l = √(a2 + h2) is used. It defines the length of the sloping part of one step in the longitudinal section.
Conversion to volume. After the longitudinal section area in mm2 is found, the calculator multiplies it by the width of the relevant section in mm. The result is then divided by 1 000 000 000 to obtain the concrete volume in m3.
How a single-flight staircase is calculated
Main section. For a straight staircase, the longitudinal section area is made up of the triangular part formed by the rise of the steps and a strip of constant thickness along the sloping line of the flight. The input data for this stage are a, h, t, the number of steps n, and the staircase width B. All linear dimensions are entered in mm.
Thickness trims. Since the bottom slab of the flight has a thickness t and is sloped, the calculator subtracts two correcting triangles at the ends of the section. These corrections depend on the angle α and are calculated through the tangent so that the volume is not overstated at the start and at the end of the flight.
S = a × h × n / 2 + √(a2 + h2) × n × t - t × (t / tan α) / 2 - t × (t / tan (90° - α)) / 2
V = S × B / 1 000 000 000
How staircases with landings and turns are calculated
Division into sections. For two-flight and three-flight layouts, the calculator does not use one general formula for the entire outline. It calculates the sections of each flight and each intermediate rectangular part separately, and then sums their volumes.
Two-flight staircase with a landing. For the first flight, its longitudinal section is used, then the landing is calculated separately as a rectangle A × t, where A is the landing length in mm and t is the thickness in mm. After that, the second flight is calculated separately. The final volume is the sum of the three parts.
V = (S1 × B1 + S2 × (B - B1) + S3 × B2) / 1 000 000 000
Turning staircases with a 90° turn. For turning layouts, the calculator introduces an additional geometric value related to angular trimming. First, β = (180° - α) / 2 is determined, then the correction x = t / tan β is calculated. This value shows how much plan space is required for the correct connection of the sloping flight to the turning section.
Validity check. If, after taking the trim into account, the turning or intermediate section becomes negative in length or width, the volume calculation is not performed. In such cases, the calculator displays a message that the specified dimensions do not fit the selected staircase shape.
How the final value is selected
Final volume. If the layout consists of several flights and landings, the calculator does not average the values and does not take the largest section. The final volume is strictly the sum of the volumes of all calculated parts of the structure.
Result rounding. The slope angle is displayed rounded to 0.1°, and the concrete volume is displayed rounded to 0.001 m3. This is convenient for a preliminary estimate of concrete quantity, although an additional practical allowance is often used when ordering ready-mix concrete.
Practical size guidelines
Step proportions. In residential buildings, a riser height of about 150-180 mm and a tread depth of about 250-300 mm are often used. Such ratios usually produce a slope angle that is convenient for everyday use, although a specific project may require different values.
Thickness and width. In private construction, a flight slab thickness of about 100-150 mm and a flight width of about 900-1200 mm are often used for cast-in-place staircases. The calculator also works with other values, but the result directly depends on the entered geometry, without adjustments for reinforcement, concrete cover, or construction details.
Connection with European standards
Geometry and loads. In practical use, the results are commonly checked against the requirements of EN 1990 Eurocode - Basis of structural design and EN 1991-1-1 Eurocode 1 - Actions on structures. Part 1-1. Densities, self-weight, imposed loads for buildings. These documents define the general principles of action combinations and design approaches within which the calculated volume and geometry are then used.
Reinforced concrete design. For cast-in-place reinforced concrete staircases, the reference document is EN 1992-1-1 Eurocode 2 - Design of concrete structures. Part 1-1. General rules and rules for buildings. This standard is applied at the stage of checking thickness, reinforcement, anchorage, and serviceability, while the calculator itself determines the geometric concrete volume only.
FAQs
Why does the calculator show the staircase slope angle first?
The slope angle is not only a reference value. It is used in the thickness trim calculations and in checking whether the turning section fits without geometric conflict.
Why is the concrete volume for a staircase calculated by parts instead of by overall dimensions?
A staircase has a stepped and sloping shape, so calculating it from the outer rectangular envelope would overstate the result. Dividing it into flights and landings gives a concrete volume for the staircase that is closer to the actual geometry of the structure.
What does the message that the dimensions do not fit mean?
It means that after the slab thickness and slope angle are taken into account, part of the turning or intermediate section becomes negative or zero. In other words, the specified staircase layout does not work geometrically in the selected configuration.
Does the calculator include a concrete allowance?
No, the calculation gives the pure geometric volume from the entered dimensions. When ordering concrete, an additional practical allowance is often considered, depending on the placing method, formwork, and construction accuracy.
Can this calculation be used for a preliminary material estimate?
Yes, this online staircase concrete volume calculation is suitable for a preliminary estimate of concrete demand and for comparing geometry options. For a working design, the final result is usually checked together with reinforcement design and the requirements of the applicable European standards.