Understanding Concrete Stair Geometry
The volume of a straight run of concrete stairs is calculated by determining the **cross-sectional area** of the staircase profile and multiplying it by the **width**. The cross-section is composed of a series of right-angle triangles, one for each step.
Volume Calculation Principle
The formula used here is based on the summation of the triangular area for each step, which is the most accurate for a uniform staircase. **1. Area of One Step Triangle ($\mathbf{A_{step}}$):** $$\text{Area} = \frac{1}{2} \times \text{Riser (ft)} \times \text{Tread (ft)}$$ **2. Total Cross-Sectional Area ($\mathbf{A_{total}}$):** $$\text{Area} = \text{Total Risers} \times A_{step}$$ (This accounts for the entire sloped section volume) **3. Total Volume ($\mathbf{V}$):** $$\text{Volume (ft}^3) = A_{total} \times \text{Width (ft)}$$ $$\text{Volume (yd}^3) = \frac{\text{Volume (ft}^3)}{27}$$ Note: This calculator assumes a uniform "full" triangular section for all steps, which is standard for monolithic (one-piece) concrete stair pours.
Design and Pouring Best Practices
Code Requirements
- **Consistency:** All risers in a flight must be within $3/8$ inch of each other for safety.
- **Standard Ratio:** A comfortable step often adheres to the "two risers plus one tread" rule, equaling approximately $25$ inches (e.g., $2 \times 7" + 11" = 25"$).
- **Rebar:** The concrete stair must be reinforced with **rebar** (steel reinforcement) to prevent cracking and failure, especially where the stairs meet the ground or a landing.
Formwork and Pouring
- **Base:** Stairs must sit on a stable base, usually a compacted gravel bed, to prevent settling and cracking.
- **Form Strength:** Stair forms are complex and must be extremely strong to resist the weight and pressure of the wet concrete.
- **Finishing:** The treads require a smooth, durable finish, often using a steel trowel, while the risers can be finished with a hand float.
Note on Landings:
This calculation only includes the steps. If your stairs include a **landing** at the top or in the middle, you must use a separate **Concrete Slab Volume Calculator** to find the volume for that section and add it to the final order quantity.