Concrete Steps Calculator

How it works

Solid poured steps are modelled as a stack of rectangular blocks, one per step, each one tread deep and the full width of the flight. The bottom step is one riser tall, the next two risers tall, and so on up to the top step, which is as tall as the whole flight.

Adding the blocks gives width × tread × riser × (1 + 2 + … + n), and the sum of the first n whole numbers is n(n + 1) ÷ 2. A landing behind the top step is one more block: width × landing depth × total rise.

Riser height and tread depth are entered in inches and converted to feet. The total is converted to cubic yards (27 cu ft per yard), the waste allowance is added for the amount to order, and the bag count divides the volume with waste by the yield of one bag and rounds up.

Formula

steps (cu ft)   = width × (tread ÷ 12) × (riser ÷ 12) × n(n + 1) ÷ 2
landing (cu ft) = width × landing depth × n × (riser ÷ 12)
total (cu yd)   = (steps + landing) ÷ 27
to order        = total cu yd × (1 + waste ÷ 100)
bags            = ⌈ (steps + landing) × (1 + waste ÷ 100) ÷ yield per bag ⌉
n = number of risers; yield per bag: 40 lb ≈ 0.30, 60 lb ≈ 0.45, 80 lb ≈ 0.60 cu ft (QUIKRETE No. 1101, rev. Oct 2022)

Example

Three 7 in risers with 11 in treads, 4 ft wide: the steps are 4 × (11 ÷ 12) × (7 ÷ 12) × 6 = 12.83 cu ft. A 3 ft landing at the top adds 4 × 3 × (21 ÷ 12) = 21 cu ft, for 33.83 cu ft, or 1.25 cu yd.

With 10% waste the amount to order is 1.38 cu yd. In 80 lb bags that is 33.83 × 1.1 ÷ 0.60 = 62.03, so 63 bags.

Assumptions and limitations

• The steps are solid concrete down to a flat base, with every riser the same height and every tread the same depth. Nosings, sloped risers, side walls, a hollow or fill-cored interior and the footing below the steps are not modelled.
• The landing depth is measured beyond the top tread: the top tread is level with the landing, so a 3 ft landing behind an 11 in top tread is 3 ft 11 in of level surface. The landing block is the full width of the steps and the full height of the flight.
• Bag yields are the approximate figures on the QUIKRETE Concrete Mix No. 1101 data sheet (revised October 2022): 0.30 cu ft per 40 lb bag, 0.45 per 60 lb and 0.60 per 80 lb. Other brands and mixes yield differently and the bag label governs.
• The waste allowance is a typical figure and is editable.
• The calculator does not check riser height, tread depth, landing size or handrails against any code. Stairs serving a dwelling are regulated by the International Residential Code, section R311.7 (stairways), as adopted locally; the result is a material estimate, not a code determination.

Frequently asked questions