Concrete Stairs Calculator
A concrete stairs calculator uses width × riser × tread × n(n+1)/2 for a solid stepped pour. Four 7 × 11 in steps, 4 ft wide, take 0.79 yd³ or 36 80 lb bags.
How much concrete do concrete stairs need?
A concrete stairs calculator finds the volume of a solid poured flight from four numbers: step count, riser height, tread depth, and width. Cubic inches = width (in) × riser × tread × n(n+1) ÷ 2, where n is the number of steps. Divide by 46,656 for cubic yards. Four steps with 7 in risers and 11 in treads, 4 ft wide, need 0.79 yd³, which is 21.39 ft³ or 36 bags of 80 lb concrete.
The result assumes the steps are solid all the way down to grade, which is how most short entry stoops are poured.
Why the n(n+1)/2 part matters
Picture the side of the stairs as a stack of blocks:
- Step 1 is 1 riser tall and 1 tread deep.
- Step 2 sits behind it and is 2 risers tall.
- Step 3 is 3 risers tall, and so on.
Adding 1 + 2 + 3 + 4 for four steps gives 10 riser-by-tread blocks. That is what n(n+1)/2 counts. Each block is then multiplied by the stair width.
The full formula
- Width in inches = width in feet × 12.
- Cubic inches = width × riser × tread × n(n+1) ÷ 2.
- Cubic yards = cubic inches ÷ 46,656 (36 × 36 × 36).
- Cubic feet = cubic inches ÷ 1,728.
- 80 lb bags = cubic yards × 27 ÷ 0.6, rounded up.
Worked examples
Front stoop: 4 steps, 7 in riser, 11 in tread, 4 ft wide
- Block count: 4 × 5 ÷ 2 = 10
- Cubic inches: 48 × 7 × 11 × 10 = 36,960
- Cubic yards: 36,960 ÷ 46,656 = 0.79 yd³
- Cubic feet: 21.39 ft³
- Bags: 21.39 ÷ 0.6 = 35.6, rounded up to 36 bags
Back door steps: 3 steps, 7.5 in riser, 11 in tread, 3 ft wide
- Block count: 3 × 4 ÷ 2 = 6
- Cubic inches: 36 × 7.5 × 11 × 6 = 17,820
- Cubic yards: 0.38 yd³, or 10.31 ft³
- Bags: 18 bags of 80 lb
Concrete by step count (7 in risers, 11 in treads)
| Steps | 3 ft wide | 4 ft wide | 5 ft wide |
|---|---|---|---|
| 2 | 0.18 yd³ | 0.24 yd³ (11 bags) | 0.30 yd³ |
| 3 | 0.36 yd³ | 0.48 yd³ (22 bags) | 0.59 yd³ (27 bags) |
| 4 | 0.59 yd³ | 0.79 yd³ (36 bags) | 0.99 yd³ (45 bags) |
| 5 | 0.89 yd³ (41 bags) | 1.19 yd³ (54 bags) | 1.49 yd³ |
| 6 | 1.25 yd³ | 1.66 yd³ (75 bags) | 2.08 yd³ |
Volume climbs quickly with each added step. Going from 4 to 6 steps more than doubles the concrete, because each new step is taller than the last.
How to measure
- Total rise: measure from the ground where the bottom step will sit up to the door threshold or landing. Divide by a comfortable riser (about 7 in) and round to whole steps.
- Tread depth: usually 10 to 12 in for each step.
- Width: the full outside width of the formed stairs, including any side walls.
- The stair calculator works out step count and riser height from total rise.
Common mistakes
- Forgetting the landing. A top platform outside a door is extra slab volume. Add it with the concrete calculator.
- No footing under the bottom step. In frost areas, steps attached to a house usually need footings below the frost line. Check local code and size them with the concrete footing calculator.
- Uneven risers. A short top or bottom step is a trip hazard. Keep every riser the same height.
- Filling with only concrete. On tall flights, builders often fill the core with compacted gravel or rubble, which cuts concrete, but the calculator assumes solid concrete.
Set rebar before the pour. Steps connected to a house are structural, so confirm footings, reinforcement, and dimensions with a licensed contractor or engineer and your local building department.
Frequently asked questions
How is concrete stair volume calculated?
Viewed from the side, solid poured steps form a staircase of stacked blocks. The bottom step is one riser tall, the next two risers tall, and so on, each one tread deep. Adding them gives riser × tread × n(n+1)/2, which is then multiplied by the stair width. For 4 steps, n(n+1)/2 = 10.
How many bags of concrete for 3 steps?
Three steps with 7 in risers and 11 in treads, 4 ft wide, need 12.83 ft³ (0.48 yd³). At 0.6 ft³ per 80 lb bag that is 21.4, which the calculator rounds up to 22 bags. Buy a couple more for spillage.
Should I order ready-mix or bags?
Up to about 40 to 45 bags (roughly 1 yd³) is manageable with a mixer and a small crew. Larger flights, such as 5 steps at 4 ft wide (1.19 yd³, 54 bags), are usually easier with ready-mix. Running out partway leaves a cold joint, so plan the pour as one continuous placement.
Do concrete stairs need rebar?
Poured steps are normally reinforced and tied to the slab, footing, or foundation they sit against, to control cracking and stop the flight pulling away from the house. Use the rebar calculator for quantities and follow local code or an engineer's detail.
What riser and tread should I use?
Many US codes based on the IRC limit residential risers to 7¾ in and require treads of at least 10 in, with all risers in a flight nearly equal. Around 7 in risers and 11 in treads feel comfortable. Check your local code, as exterior and commercial rules can differ.
Does this include the landing or footing?
No. It covers the stepped mass only. Add a top landing slab and any footing under the bottom step separately with the concrete or footing calculator.
Estimates only. Verify quantities with your supplier before purchasing.