A flight of 4 concrete steps, 4 feet wide with 11-inch treads and 7-inch rises, poured solid, needs about 21.4 cubic feet of concrete (0.79 cubic yards). A separate 4×3-foot landing slab 4 inches thick, supported on fill rather than poured solid to the ground, adds 4.0 cubic feet, for about 25.4 cubic feet (0.94 cubic yards) in total. Your actual volume depends on your step count and dimensions – the math below covers one stated case: a solid flight of equal-depth tread sections plus a separate, non-overlapping landing slab.
The math
Treat each tread section as a tread-depth prism at its own height: the first section is one rise tall, the second two rises, and so on, so a flight of n equal-depth tread sections is made of prisms at heights r, 2r, … nr. Flight volume = width (ft) × tread (in) ÷ 12 × rise (in) ÷ 12 × n(n+1)/2, where n is the number of equal-depth tread sections included – if the top tread is replaced by the landing, don’t count it in n. The landing adds only when it is a separate, non-overlapping slab with its supporting volume excluded (for example, a slab on fill); a fully solid raised landing is a different, larger volume. Landing slab = length (ft) × width (ft) × thickness (in) ÷ 12. Add the two, then divide by 27 for cubic yards.
Worked example: 4 steps plus a landing
Flight: 4 × 11/12 × 7/12 × (4×5/2) = 4 × 0.917 × 0.583 × 10 = 21.4 cubic feet. Landing (assumed to be a separate slab on fill, not overlapping the flight): 4 × 3 × 4/12 = 4.0 cubic feet. Total: 25.4 cubic feet = 0.94 cubic yards. These dimensions are the example’s stated inputs – your plan’s step count, tread depth, rise, and landing size govern your result.
Flight volume by step count (4 ft wide, 11-inch tread, 7-inch rise, solid flight of n tread sections)
- 3 sections: 12.8 cubic feet – 0.48 cubic yards
- 4 sections: 21.4 cubic feet – 0.79 cubic yards
- 5 sections: 32.1 cubic feet – 1.19 cubic yards
- 6 sections: 44.9 cubic feet – 1.66 cubic yards
- 8 sections: 77.0 cubic feet – 2.85 cubic yards
If you mix from bags
Bag yields differ by brand, so read the yield printed on your bag. As an example, if an 80 lb bag yields 0.6 cubic feet, the 4-section flight alone needs 21.4 / 0.6 = 35.7, so 36 bags, and the flight-plus-landing total needs 25.4 / 0.6 = 42.3, so 43 bags. Flights this size are often ordered ready-mix instead, since mixing that many bags by hand is slow work.
This is a solid-pour estimate: it treats the flight as solid concrete. Forms, any fill or voids under the steps, and thickened edges change the total, so confirm the build-up before ordering.
Related
Try the concrete calculator for other shapes, see stair stringer calculator for rise and run layout, or read how many bags of concrete you need. For hiring the pour out, see concrete steps cost.
Estimates only. This is general guidance, not professional advice. Confirm details with your supplier, installer or local building department.