Key Takeaways
- Steps are not one block; they are stacked blocks, so volume grows faster than step count
- Doubling the number of steps at the same size more than doubles the volume
- The formula assumes solid, closed-riser steps with no landing
- Rise and run should follow local code, which often sets minimums and maximums
A set of concrete steps looks like it should scale in a straight line with the number of steps, but it does not. Each step sits on top of solid concrete filling in everything below it, so a taller staircase needs disproportionately more material than a shorter one at the same rise and run.
Why volume outpaces step count
Picture each step as its own rectangular block: width times run times rise. The bottom step is one block. The second step sits on top of the first and needs its own block, but that block also has to be as tall as two risers, because it is stacked above the first step’s full height. By the time you reach the top step, its block is n risers tall, where n is the step’s position counting from the bottom.
Summed across all the steps, the total volume comes out to width times run times rise times n(n+1)/2 stacked-block factor, not simply the step count. Concretely, going from one step to two steps at the same size doesn’t double the volume, it roughly triples it, because the stacked factor goes from 1 to 3.
Worked example
Three steps at a 7 inch rise, 11 inch run, and 3 foot width need about 9.6 cubic feet of concrete before waste: 3 x (11/12) x (7/12) x (3x4/2) = 3 x 0.917 x 0.583 x 6. With a 10 percent waste allowance that comes to roughly 0.39 cubic yards.
What this formula assumes
This is the volume for a solid, closed-riser staircase with no landing partway up and no hollow form underneath, the shape of a typical small poured-concrete stoop or porch step. An open-riser design, a staircase with a landing, or steps built over a hollow form or void will need less concrete than this estimate, since they do not fill the full stacked solid this formula assumes.
Rise and run are code questions
A common comfortable rise is around 7 inches with an 11 inch run, but local building codes typically set specific minimum and maximum values, and often require consistent rise and run across an entire staircase for safety. Check your local code before finalizing step dimensions, particularly for anything more than a couple of steps.
Use the concrete steps calculator to work out volume, bags and cost for your own step count, rise, run and width. For the broader stair layout, including risers, treads and stringers, see the stair calculator.