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Concrete Stairs Pour Volume

Determine exactly how many cubic yards of ready-mix concrete or 80lb bags are required to pour solid structural stairs, factoring in triangular steps and throat thickness.

Staircase Geometry

Qty
FT
IN
IN
IN

The "throat" is the minimum thickness of solid concrete measured diagonally beneath the lowest inner corner of the step notch. Commercial stairs usually require a minimum 5" to 6" structural throat.

10% Waste Factor

Buffer for spillage/form blowout

Concrete Pour Dimensions

Total with 10% Waste

Order This Amount:

0.59

Yards³

Equivalent Sack Mix

27

80lb Bags

Throat Target Length

5.43

Feet

Ready-Mix Caution: Puddling and filling structural stair runs represents some of the highest blowout pressures in concrete forming. Always order at least 10% more mud than mathematically required to account for inevitable form bowing or subgrade sinkage.

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What is The Two-Part Physics of Structural Stairs?

Ordering concrete for stairs trips up many builders because stairs are not simple geometric blocks. A concrete staircase consists of two entirely separate physical volumes poured simultaneously: a series of stacked triangular steps sitting on top of a solid diagonal ramp (the 'throat').

Mathematical Foundation

Triangular Step Volume
Step Volume=Tread×Riser2×Width×Steps\text{Step Volume} = \frac{\text{Tread} \times \text{Riser}}{2} \times \text{Width} \times \text{Steps}
Tread×RiserTread × Riser= A stair step physically forms a Right Triangle. Multiplying horizontal tread by vertical riser gives a rectangle area; divide by 2 to get the triangle area.
Throat Slab Volume
Throat=Run2+Rise2×Thickness×Width\text{Throat} = \sqrt{\text{Run}^2 + \text{Rise}^2} \times \text{Thickness} \times \text{Width}
Run2+Rise2\sqrt{Run^2 + Rise^2}= The Pythagorean Theorem finds the true diagonal length of the staircase from top to bottom.
ThicknessThickness= The structural 'throat' — the solid mass of concrete poured unbroke underneath the lowest 'V' cut notches of the stairs.

Laws & Principles

  • The 'Throat' is the True Structure: The triangular steps themselves provide almost no structural integrity. The load-bearing strength of the stair assembly comes entirely from the unbroken diagonal slab of concrete poured underneath the steps, officially called the 'throat'.
  • Building Code Minimums: Commercial and residential building codes dictate minimum throat thicknesses depending on the clear span of the staircase. A 5-inch or 6-inch solid throat thickness is the baseline standard to prevent catastrophic cracking across the mid-span.
  • The 46,656 Cubic Inch Problem: Because stairs are built utilizing measurements in Inches, you will naturally calculate massive volumes in cubic inches. To place a Ready-Mix truck order in Cubic Yards, you must divide your final cubic inch number by exactly 46,656 (36 x 36 x 36).

Step-by-Step Example Walkthrough

" A mason is forming a set of 8 basement stairs. They are 4 feet (48') wide. Each step has an 11' tread and a 7' riser. The plan calls for a 6' structural throat. "

  1. 1. Step Area: (11 x 7) / 2 = 38.5 Square Inches per step.
  2. 2. Step Volume: 38.5 sqIn x 48 inches wide = 1,848 Cubic Inches per step.
  3. 3. Total Steps Volume: 1,848 x 8 steps = 14,784 Cubic Inches of steps.
  4. 4. Find Throat Length: Total Run = 88'. Total Rise = 56'. sqrt(88^2 + 56^2) = 104.3 inches diagonally.
  5. 5. Find Throat Volume: 104.3' long × 6' thick × 48' wide = 30,038 Cubic Inches for the slab.
  6. 6. Total Master Volume: 14,784 (steps) + 30,038 (throat) = 44,822 Cubic Inches.
  7. 7. Convert to Yards: 44,822 / 46,656 = 0.96 Cubic Yards required.
Final Result: At 0.96 cubic yards calculated exactly, the mason applies a 10% form-bowing waste factor and orders roughly 1.1 Cubic Yards from the concrete plant to safely pour the monolithic stair assembly.

Quick Answer: How do you calculate concrete for stairs?

Concrete stairs are calculated in two parts: the steps (Right Triangles) and the throat (the diagonal slab underneath). Calculate the volume of one triangular step: (Tread × Riser ÷ 2) × Width. Multiply by the number of steps. Calculate the throat using Pythagorean theorem for diagonal length: Diagonal × Throat Thickness × Width. Add both volumes in cubic inches and divide by 46,656 to get Cubic Yards. Always add 10% waste for form-bowing.

Concrete Stair Volume Formula

Step Vol = (tread × riser ÷ 2) × width × number_of_steps

Throat Vol = √(total_run² + total_rise²) × throat_thickness × width

Total Yards = (Step Vol + Throat Vol) ÷ 46,656

Concrete stairs are effectively poured as two distinct geometric shapes merged into one solid object. All calculation inputs should typically be placed in inches, leading to a massive cubic inch output that must be reduced down using the 46,656 divisor (the number of inches in a cubic yard).

Common Stair Yardage Reference

Tread Size Steps & Width Throat Thickness Ready-Mix Yield (yd³) 80lb Bags Req (+10% waste)
11" T × 7" R3 Steps (36" W)4"0.18 yd³9 Bags
11" T × 7" R5 Steps (48" W)5"0.45 yd³23 Bags
11" T × 7" R8 Steps (48" W)6"0.96 yd³Mxd Truck ~ 1.25 yds
12" T × 6" R10 Steps (60" W)8"1.84 yd³Mxd Truck ~ 2 yds
10" T × 7.5" R14 Steps (48" W)6"1.57 yd³Mxd Truck ~ 1.75 yds

Volumes are theoretical exact cubic yardages (no waste added). For orders over 0.75 cubic yards, it is almost always more cost effective to order a short-load from a ready-mix company rather than manually mixing bagged concrete.

Construction Scenarios

Porch Step Add-On

A homeowner is adding 3 short steps to their back patio. The steps are 48 inches wide, with 10 inch treads and 7 inch risers. A 4-inch minimum throat thickness applies. Volume: 3 steps = 5,040 cubic inches. The throat is 41" diagonal × 4" thick × 48" wide = 7,872 cubic inches. Total = 12,912 cubic inches = 0.27 cubic yards. This small job requires about 13 (80 lb) bags of concrete mix.

Commercial Fire Escape

A concrete contractor is pouring a 15-step exterior run at a warehouse. Width is 72 inches (6 feet). Treads are 11" and risers 7". Commercial code dictates a 7-inch structural throat. Step Volume = 42,768 cubic inches. Throat Volume = (195" diagonal × 7" × 72") = 98,280 cubic inches. Total mass = 141,048 cubic inches = 3.02 Cubic Yards. A ready-mix truck is required, ordering 3.5 yards to cover waste.

Concrete Stair Pro Tips

Do This

  • ✓Account for formwork bowing. Wet concrete exerts immense hydrostatic pressure. The wood forms creating your stringers and risers will naturally bow outwards anywhere from 1/4" to 1/2" between braces. Over a 5-foot wide set of stairs, this bowing can consume an extra 5% to 8% concrete you didn't plan for.
  • ✓Pour with a low slump. Stair concrete must be stiff. If you pour a "soup" mix with a 5-inch slump, the concrete pumped into the top steps will literally flow out from under the bottom riser forms. Order a 3-inch or 4-inch slump maximum to ensure the concrete holds its shape against the inclined forms.
  • ✓Vibrate the throat, tap the risers. Use a mechanical vibrator deep into the throat slab to ensure the structural core consolidates around the rebar grid. Conversely, use a rubber mallet against the exterior of the wooden riser forms to release trapped air bubbles (honeycombing) off the visible step faces.

Avoid This

  • ✗Don't ignore the bottom landing embedment. If your bottom stair ties into an existing slab or requires a frost footing, you must add that rectangular volume to your calculation separately. The Stair Formula assumes the bottom step terminates exactly at grade level.
  • ✗Don't strip forms too early. While flatwork concrete can walk-on cured in 24 hours, structural stairs have their center of gravity suspended in the air. Stripping the diagonal throat support forms before the concrete reaches 70% of its design strength (usually 7 days) can cause permanent micro-fractures in the span.

Frequently Asked Questions

How many bags of concrete do I need for stairs?

It takes approximately forty-five (45) standard 80lb bags of concrete to cover one cubic yard (27 cubic feet). Once you calculate your total volume using the calculator, convert your Cubic Yards to bags by multiplying by 45. For example, 0.50 cubic yards of stairs will require roughly 23 bags of concrete.

What is the "throat" of a concrete stair?

The throat is the solid, unbroken diagonal ramp of concrete poured directly beneath the "V" shapes of the stair steps. It is the core structural element of the staircase that carries the actual weight of the people walking on it. Throat thickness is measured perpendicular to the diagonal slope of the stairs, not straight vertically down.

Why do I get such a massive number before dividing by 46,656?

Because stairs are drafted and built using precision cuts in Inches, the initial calculation computes the volume entirely in Cubic Inches. There are 46,656 cubic inches inside of one Cubic Yard (36 inches × 36 inches × 36 inches = 46,656). Dividing your massive cubic inch number by this constant reduces it to the standard Cubic Yard measurement used by ready-mix dispatchers.

Should I pour the stairs from the top or bottom first?

Always begin pouring concrete stairs from the very bottom step and work your way upward. Filling the lowest step locks in the base weight, preventing the hydrostatic pressure of the wet concrete poured from the top from "blowing out" under your lower form boards. Fill a step, vibrate it, screed it, then shift up to the next step.

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