A poured concrete stair is two shapes stacked on each other: a sloping structural slab, and a sawtooth of steps sitting on top of it. The concrete stairs calculator above computes both, adds them, multiplies by the width, and returns the volume in cubic yards or cubic metres — plus the bag count if you are mixing on site, and the formwork contact area you have to build before any concrete arrives. It is a preliminary quantity and teaching tool. It is not a structural design, it is not stamped, and it does not replace a licensed engineer.
Arb Digital publishes this as part of a free construction estimating library. It deliberately does a different job from our live stair calculator, which solves stringer geometry — riser height, tread depth, stringer length and headroom for a timber or steel flight. This page assumes that geometry is already settled and answers the question that follows it: how much concrete, how many bags, and how much form. If you have not fixed your rise and run yet, start there and come back here.
What This Concrete Stairs Calculator Does
It splits the flight into two volumes. The stepped portion — everything above the line drawn along the underside of the nosings — is a repeating triangle, and for a flight of N risers with rise R and run G it comes to N × R × G ÷ 2 per unit of width. That halving surprises people, but it is exact: the sawtooth above the slope line is precisely half the rectangle that encloses it.
The throat is the structural slab underneath, and its thickness is measured perpendicular to the slope, not vertically. Its cross-section is throat thickness multiplied by the slope length, and the slope length is the hypotenuse of the total rise and total run. Add the two cross-sections, multiply by stair width, and you have the flight. The calculator then applies your waste factor and reports both the raw figure and the rounded, orderable figure, because ready-mix is sold in fixed increments and bags are sold whole.
Formwork contact area is reported separately because it drives labour and plywood cost more than the concrete does. It is the sum of two side panels at the cross-sectional area each, the riser boards across the width, and the soffit form running the full slope length.
How to Use It
- Count risers, not steps. A flight landing on an upper floor has one more riser than tread. Getting this off by one is the single most common input error on the page.
- Enter rise and run as built. Use the dimensions on your approved drawing, not a nominal figure. Riser height and tread depth limits come from your adopted building code, and this tool does not enforce them.
- Enter the throat thickness your engineer specified. There is no default table here on purpose — throat depends on span, reinforcement and loading, and nobody should read one off a free web page.
- Set the waste factor. Ten percent is a common starting point for a formed stair. Spillage at risers and over-filled treads make stairs wastier than a flat slab.
- Read the raw and ordered figures together. The raw number tells you what the geometry needs; the ordered number tells you what to buy.
The Formula / How It's Calculated
Working in feet throughout, with N risers, rise R, run G, width W and throat T:
Stepped cross-section = N × R × G ÷ 2. Total rise = N × R and total run = N × G. Slope length = √(total rise² + total run²). Throat cross-section = T × slope length. Volume = (stepped + throat) × W.
Take the default flight: 13 risers at 7 in rise and 11 in run, 4 ft wide, on a 6 in throat. In feet that is R = 0.5833, G = 0.9167, T = 0.5. The stepped cross-section is 13 × 0.5833 × 0.9167 ÷ 2 = 3.476 sq ft. Total rise is 7.583 ft, total run is 11.917 ft, so the slope length is √(57.51 + 142.01) = 14.125 ft and the throat cross-section is 0.5 × 14.125 = 7.063 sq ft. Together that is 10.538 sq ft of cross-section; times 4 ft of width gives 42.15 cu ft, which is 1.561 cubic yards. Add 10 percent waste and you are ordering about 1.72 cubic yards. Note that the throat is two thirds of the pour, and the visible steps are only one third.
Bag count divides the wasted volume by the yield printed on the bag. At 0.6 cu ft per 80 lb bag, 46.4 cu ft needs 78 bags. That number is why almost nobody bags a full flight — it is a ready-mix job, and mixing 78 bags by hand guarantees cold joints between batches.
Why the Throat, Not the Steps, Dominates the Order
Estimators who sketch a stair by eye tend to focus on the steps, because that is the part you can see. The arithmetic disagrees. In the worked example the sawtooth is 3.48 sq ft of cross-section and the throat is 7.06 sq ft, so two thirds of the concrete is buried under the flight where nobody will ever look at it. Increase the throat from 6 in to 8 in and the total jumps from 1.56 to 1.84 cubic yards, a 17 percent rise, without a single dimension of the visible stair changing.
This has a practical consequence at ordering time. If the engineer revises the throat late — which happens when a span grows or the reinforcement schedule changes — your concrete order changes materially and your formwork does not. Re-run the calculation after any structural revision, not just after an architectural one. And measure throat perpendicular to the slope: measuring it vertically overstates the slab by roughly the secant of the stair angle, which on a typical 33 degree flight is about 19 percent.
Formwork Is the Real Cost, and It Is Not Proportional to Volume
Concrete for a domestic flight might be two cubic yards. The forms are two side panels, a soffit deck, riser boards, and enough bracing to resist a fluid pushing outward at roughly 150 pounds per cubic foot. The tool reports contact area so you can size plywood and count riser boards, but be clear about what drives the labour: it is the number of risers, not the cubic yards. A 13-riser flight needs 13 riser boards cut, levelled and secured, whether the stair is three feet wide or eight.
Riser boards are usually bevelled along the bottom edge so a trowel can reach into the back of the tread. That bevel slightly reduces the concrete volume and slightly increases the finished tread depth, and both effects are small enough to sit inside the waste factor. What is not small is form movement: an unbraced riser board bows under wet concrete and produces a belly on the face of every step, which is very difficult to fix after the pour.
Rise, Run and the Checks This Tool Does Not Make
The calculator reports total rise and total run so you can compare them with your opening, but it does not police them. Maximum riser height, minimum tread depth, maximum variation between risers in a flight, nosing projection, headroom and handrail geometry are all set by the building code your jurisdiction has adopted — in most of the United States that is a state-amended edition of the International Residential Code or International Building Code, available through the ICC digital codes library. Editions and amendments differ by state, province and country, and it is the local authority having jurisdiction that decides compliance.
The one geometric relationship worth knowing is not a code rule at all: the tradesman's comfort formula, twice the rise plus the run landing between about 24 and 25 inches. The default flight above gives 2 × 7 + 11 = 25 in, which sits at the top of that band. A stair outside it usually still passes code and still feels wrong underfoot, because the human stride does not care what the code says. The tool prints this figure alongside the volumes as a sanity check, not as a compliance test.
Reinforcement, Mix and the Things a Volume Number Hides
A cubic yard figure tells you nothing about what makes a stair last. Reinforcement, cover, mix design and curing all sit outside this page, and all of them matter more to durability than getting the volume to two decimal places. Design and detailing rules for reinforced concrete come from the structural code your engineer works to — in North America the American Concrete Institute publishes the reference standards, and the American Cement Association publishes background material on cement and mix behaviour. Neither substitutes for a stamped design.
Two practical points do belong here. First, an exterior stair in a freeze-thaw climate needs an air-entrained mix and adequate cover over the steel, and both of those are specified, not chosen on site. Second, a stair poured in one continuous operation behaves very differently from one poured in stages with cold joints across the throat. If your volume is large enough that a single delivery cannot cover it, that is a scheduling decision with a structural consequence, and it should be raised with the engineer rather than solved in the yard.
Fitting the Stair Into the Rest of the Job
Stairs rarely stand alone. The landing at the top and the pad at the bottom are ordinary slabs — send those through the concrete calculator and add the result to what you get here. If the flight sits against a retaining structure, the retaining wall calculator covers that side of the work, and reinforcement quantities for the flight and its landings go through the rebar calculator. Where a cheek wall or balustrade is masonry, the concrete block calculator handles the unit count.
For the guarding above the finished stair, the baluster spacing calculator divides a run into legal, even gaps. And if the same level change also has to be reachable without steps, the wheelchair ramp calculator works out the ramp length and landings the rise demands.
Arb Digital builds free, fast, search-friendly tools that bring contractors and suppliers steady organic traffic. Browse the library or tell us what your customers keep asking you to work out.
Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Entering treads instead of risers — a flight to an upper floor has one more riser than tread, and one riser out is roughly an eight percent error on a typical flight.
- Measuring the throat vertically — throat is perpendicular to the slope. Measuring it vertically overstates the slab by around a fifth on a normal stair angle.
- Forgetting the landing and the bottom pad — they are separate slabs and are frequently larger than the flight itself.
- Ordering the raw volume — spillage at risers and over-filled treads make a formed stair wastier than a flat pour, and running short mid-flight creates a cold joint.
- Treating the output as a design — throat depth, reinforcement and mix are the engineer's call, and this page reports quantities only.
Related Free Tools From Arb Digital
Set your geometry with the stair calculator, pour the landings with the concrete calculator, schedule steel with the rebar calculator, guard the flight with the baluster spacing calculator and price the whole thing per unit area with the cost per square foot calculator. Everything else is on the free online tools hub.
Frequently Asked Questions
For 13 risers at 7 in rise and 11 in run, 4 ft wide on a 6 in throat, the geometry gives 42.15 cubic feet, or 1.56 cubic yards. With a 10 percent waste factor you would order about 1.72 cubic yards. Change any one of those five inputs and the answer moves, which is why the tool takes them all.
It is the structural slab that runs underneath the steps, measured perpendicular to the underside slope rather than vertically. It is usually the larger part of the pour, and its thickness is set by the structural engineer based on span, loading and reinforcement.
The stair calculator solves geometry — riser height, tread depth, stringer length and headroom for a flight of any material. This page assumes the geometry is fixed and returns the concrete volume, bag count and formwork area for pouring it. They are used one after the other, not instead of each other.
Divide the volume including waste by the yield printed on the bag. At 0.6 cubic feet per 80 lb bag, the default flight needs about 78 bags, which is exactly why most flights are ready-mix. Hand mixing that many batches risks cold joints between them.
The sawtooth above the slope line is mathematically half of the rectangle enclosing it, so it is smaller than it looks. The throat slab underneath runs the full sloping length at full thickness, and on a typical flight it accounts for roughly two thirds of the total volume.
No. Riser height, tread depth, nosing, headroom and handrail rules come from the code edition your jurisdiction has adopted, and amendments differ by state, province and country. The tool reports total rise, total run and the 2R+G comfort figure so you can compare them yourself, and the authority having jurisdiction decides compliance.
Yes. Switch the unit selector, enter rise, run and throat in millimetres and the width in metres, and results come back in cubic metres with bag yield read in litres. The underlying geometry is identical.
This tool produces preliminary material quantities for teaching and estimating only. It is not a structural design and carries no engineering stamp. Throat thickness, reinforcement, cover, mix design and compliance with your adopted building code must be set and signed off by a licensed structural engineer or architect before anything is poured.
