Stair Calculator

How to use the Stair Calculator

Measure the total rise: finished floor to finished floor, including both floor coverings. Getting this wrong by the thickness of the flooring is the classic way to end up with one riser half an inch off every other one, which is uncomfortable to walk and a code failure.

On the Design a Staircase tab, enter a target riser height, seven inches is a sound starting point, and the calculator divides the total rise by the nearest whole number of risers, then reports the riser height that actually results. You almost never get a round number, and that is normal. The tread count is always one less than the riser count, because the top floor is the last surface you step on.

The other two tabs answer narrower questions. Fixed Number of Risers is for when the riser count is already settled, by a landing, a stairwell opening, or a flight elsewhere in the house you have to match, and you need the riser height and total run that follow from it. Diagonal of a Rise and Run is pure geometry: the straight-line length across any rise and run. Useful for a ramp, a handrail or a rough check, but it does not know the step count, so it is not a stringer cut list.

Stair formula

• risers = round(total rise ÷ target riser height)
• riser height = total rise ÷ risers
• treads = risers − 1
• total run = treads × tread depth
• one step = √(riser² + tread²)
• stringer length = treads × one step
• board to buy = risers × one step
• angle = arctan(riser height ÷ tread depth)

Both the stringer and the angle are measured along the tread nosings, not across total rise and total run. A flight has one more riser than it has treads, because the top riser lands on the upper floor. So total rise and total run count different numbers of step, and √(total rise² + total run²) is the hypotenuse of a triangle whose two legs disagree, it matches no line on the staircase. For the example below it overstates the stringer by four inches and the angle by nearly two degrees.

The board to buy carries one step more than the stringer, because laying out with a framing square steps off once per riser. Add your own allowance on top for the bottom and top cuts.

The three classical comfort rules, all of which should land in range at once:

Rule	Target	What it controls
2 × riser + tread	24 to 25 in	Stride length, the strictest of the three
riser + tread	17 to 18 in	Overall step size
riser × tread	71 to 74	Proportion

Code limits under IRC R311.7: maximum riser 7¾ in, minimum tread 10 in, and no more than ⅜ in variation between the tallest and shortest riser in a flight.

Worked example

A 9 ft floor-to-floor rise (108 in) with a 7 in target and 10½ in treads:

• Risers: 108 ÷ 7 = 15.43, rounded to 15 risers
• Riser height: 108 ÷ 15 = 7.20 in (under the 7¾ limit)
• Treads: 15 − 1 = 14 treads
• Total run: 14 × 10.5 = 147 in (12 ft 3 in)
• One step: √(7.20² + 10.5²) = 12.73 in
• Stringer: 14 × 12.73 = 178.24 in (14 ft 10¼ in)
• Board to buy: 15 × 12.73 = 190.97 in (15 ft 11 in)
• Angle: arctan(7.20 ÷ 10.5) = 34.4°
• Check: 2(7.20) + 10.5 = 24.9, inside the 24 to 25 range

What the result means

The riser height is almost never a round number, and it does not need to be. What matters is that every riser in the flight is the same, within an eighth of an inch. Uneven risers are the single most common cause of stair falls, which is why code is stricter about consistency than about the actual dimension.

The stringer length is the line along the tread nosings, the sloped line the staircase actually travels. The board to buy is one step longer, because a framing square steps off once per riser during layout, and you should add your own allowance beyond that for the bottom and top cuts and for the width of the sawtooth.

The bottom riser gets shortened by one tread thickness when the stringer sits on the floor and treads land on top of it. Otherwise the bottom step ends up one tread thickness taller than all the others, the exact fault code is written to prevent.

Common mistakes

• Measuring to the subfloor. Total rise is finished floor to finished floor. Carpet, tile and underlay at either end all count.
• Forgetting the bottom stringer drop. Cut the bottom riser short by one tread thickness, or the first step is taller than the rest.
• Counting treads and risers as the same number. There is always one fewer tread than riser.
• Chasing a round riser height. 7.20 in is fine. Fifteen identical 7.20 in risers is what code wants; fourteen at 7.25 and one at 6.5 is not.
• Ignoring headroom. Code wants 6 ft 8 in measured vertically from the tread nosing line. A long flight under a low ceiling can pass every rise and run check and still fail.
• Forgetting the landing. A landing at top and bottom needs to be at least as deep as the stair is wide.

Frequently asked questions

How many stairs do I need for 9 feet?

Fifteen risers at 7.20 inches each, and fourteen treads. With 10.5 inch treads the flight runs 147 inches, 12 feet 3 inches, horizontally, at about 36 degrees.

What is the maximum riser height?

Seven and three quarter inches under the IRC for residential stairs, with a minimum tread depth of 10 inches. Commercial codes are stricter. Risers within one flight may not vary by more than three eighths of an inch.

How do I calculate stringer length?

Measure it along the tread nosings: work out one step as the square root of riser squared plus tread squared, then multiply by the number of treads. For 14 treads at a 7.20 inch riser and a 10.5 inch tread, one step is 12.73 inches and the stringer is 178.24 inches, or 14 feet 10 and a quarter inches. Buy a board one step longer again, 15 feet 11 inches here, because laying out with a framing square steps off once per riser, then add your own allowance for the end cuts. Do not use the square root of total rise squared plus total run squared: a flight has one more riser than it has treads, so those two totals count different numbers of step and the answer comes out about four inches long.

Why is there one fewer tread than riser?

Because the upper floor is the last surface you step onto. A flight with 15 risers has 14 treads plus the landing or floor at the top.

What is the 2R plus T rule?

Twice the riser height plus the tread depth should come to between 24 and 25 inches. It approximates a comfortable stride on a slope, and it is the most useful of the three classical rules, a staircase that satisfies it usually feels right.

What angle should stairs be?

Between about 30 and 37 degrees for ordinary residential stairs. Steeper than 37 feels like a ladder and usually means the riser is too tall or the tread too shallow for code. Measure the angle along the nosings, one riser over one tread, arctangent of riser divided by tread. Dividing total rise by total run instead gives an answer a degree or two too steep, because a flight has one more riser than it has treads.