How the math works
The formula. Each step is a solid block poured from the ground up, so the first step is one rise tall, the second is two rises tall, the third is three, and so on. Every block is as wide as the set and as deep as one tread.
Add those blocks up and you get a simple rule: width × tread × rise × (steps × (steps + 1) ÷ 2). With a landing on top, add width × landing depth × (steps × rise).
Take three steps with a 7 inch rise, an 11 inch tread and a 48 inch width. The blocks are 7, 14 and 21 inches tall, which adds up to 6 rises of 7 inches, so 48 × 11 × 7 × 6 = 22,176 cubic inches. That is 12.8 cubic feet, or 0.48 cubic yards. With 10% extra you order about 0.52 yards, and you need 24 bags of 80 lb mix.
What this assumes
The steps are solid concrete from the ground up. If you build a hollow form and fill the middle with gravel or compacted fill, you need less concrete, and you should work out the fill separately with the gravel calculator. Footings and a slab under the steps are extra, so run those through the concrete calculator.
Concrete for common step sets
All of these use a 7 inch rise, an 11 inch tread and a 48 inch width, with no landing and no waste added.
| Steps | Cubic feet | Cubic yards | 80 lb bags |
|---|---|---|---|
| 1 | 2.1 | 0.08 | 4 |
| 2 | 6.4 | 0.24 | 11 |
| 3 | 12.8 | 0.48 | 22 |
| 4 | 21.4 | 0.79 | 36 |
| 5 | 32.1 | 1.19 | 54 |
Notice how fast it climbs. Going from three steps to five does not add two thirds more concrete, it more than doubles it. The upper steps are tall blocks. That is why people often fill the core of larger stairs instead of pouring solid.
Rise and tread: the code limits
For residential stairs the International Residential Code (R311.7.5) limits the riser to 7-3/4 inches and asks for a tread of at least 10 inches. Within one flight, the tallest riser can be no more than 3/8 inch taller than the shortest, and treads have the same limit.
That last rule is the one people trip over. Pour the first and last step a half inch apart and you have a stair an inspector can fail. Your local rules can be stricter, so check them before you build forms.
See the bags per cubic yard chart if you want other bag sizes, or the concrete cost calculator to put a price on it.
Frequently asked questions
How much concrete do I need for 3 steps?
With a 7 inch rise, an 11 inch tread and a 48 inch width, solid steps need about 0.48 cubic yards, or 0.52 with 10% extra. Change the numbers above for your own steps.
How many bags of concrete for concrete steps?
Divide the cubic feet by 0.6 for 80 lb bags. The three-step example is 12.8 cubic feet, so about 22 bags before extra, and 24 with 10% extra.
What is the maximum riser height for concrete steps?
The residential code limit is 7-3/4 inches for the riser, with a tread of at least 10 inches. Your local code can differ.
Do steps need to be solid concrete?
No. Many are poured over a compacted gravel or fill core, or as a hollow form. That cuts the concrete a lot, and you should ask your building department what they allow.
Sources
- City of Boise: Residential stair treads and risers (IRC R311.7.5)
- Quikrete: Concrete Mix 1101 data sheet (bag yields)
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