Stair Calculator

Calculate riser height, tread count, total run, stair angle, and code compliance for any staircase.

Total Rise (inches, floor to floor)

Desired Riser Height (in)

Tread Depth (in)

Stair Width (ft)

IRC R311.7 Code Requirements

Max riser height: 7-3/4" (7.75")
Min tread depth: 10"
Min headroom: 6’8" (80")
Min stair width: 36"

Stair Layout

14 risers / 13 treads

Actual riser: 7.71" | Angle: 37.6°

Number of risers	14
Actual riser height	7.71"
Number of treads	13
Total run	130.00" (10.83 ft)
Stair angle	37.6°
Stringer length	14.08 ft
Stair width	3 ft

Stair Profile

info

Sarah Torres:“The 7-10 rule: 7-3/4 max riser, 10 min tread. But the comfortable sweet spot is 7 to 7.5 inch rise with 10 to 11 inch run. Going right to the code max makes a steep stair that your client will complain about.”

Methodology

Number of risers = round(total rise / desired riser height). Actual riser = total rise / number of risers. Treads = risers - 1 (top landing is not a tread). Total run = treads x tread depth. Stair angle = arctan(riser / tread). Stringer length = hypotenuse of total rise and total run. Code references: IRC R311.7 (2021) for residential stairs. Always verify with local building codes — some jurisdictions adopt amendments.

Frequently Asked Questions

How many stairs for a 9-foot ceiling?

A 9-foot ceiling is 108 inches floor to floor (assuming standard floor construction adds about 10-12 inches, making the actual total rise closer to 118-120 inches). At a 7.5-inch riser, that is 16 risers (120 / 7.5). At the code maximum of 7.75 inches, you could use 15 risers (120 / 7.75 = 15.48, round to 15, actual riser = 8.0 inches — which exceeds code). Stick with 16 risers for a comfortable, code-compliant stair.

What is the 7-10 rule for stairs?

The 7-10 rule refers to IRC code maximums: 7-3/4 inch maximum riser height and 10 inch minimum tread depth. These are absolute limits, not targets. A comfortable stair has a 7 to 7.5 inch rise and 10 to 11 inch tread. The classic comfort formula is: 2 x riser + tread = 24 to 25 inches. So a 7-inch riser pairs well with a 10 to 11 inch tread (2(7) + 10 = 24).

How to calculate stair angle?

Stair angle = arctan(riser height / tread depth). For a 7.5-inch riser and 10-inch tread: arctan(7.5/10) = 36.9 degrees. Comfortable residential stairs fall between 30 and 37 degrees. Steeper than 40 degrees feels like a ladder. Shallower than 25 degrees feels like a ramp. Most building codes result in stairs between 30 and 38 degrees when you follow the riser and tread limits.

What is the minimum headroom for stairs?

IRC R311.7.2 requires a minimum 6 feet 8 inches (80 inches) of headroom measured vertically from the stair nosing to any overhead obstruction. This is measured along the entire walking line of the stair, including at the top and bottom landings. Basement stairs often have headroom challenges — if the opening is too small, the header may need to be cut back and reframed.

How the stair calculator works

The stair calculator turns a floor-to-floor measurement into a complete, code-checked stair layout. You enter four numbers: the total rise in inches (the vertical distance from one finished floor to the next), your desired riser height in inches, the tread depth in inches, and the stair width in feet.

The number of risers is the total rise divided by your desired riser height, rounded to the nearest whole number, because you cannot build a partial step. The tool then divides the total rise back by that whole number of risers to find the actual riser height every step is built to. The number of treads is always one less than the number of risers, since the top landing is not counted as a tread. Total run is the tread count multiplied by the tread depth. The stair angle is the arctangent of the actual riser height divided by the tread depth, converted to degrees. Stringer length is the hypotenuse of the total rise and total run: the square root of the two values squared and added together.

Every result is checked against IRC R311.7: a maximum riser height of 7.75 inches, a minimum tread depth of 10 inches, minimum headroom of 80 inches (6 feet 8 inches), and a minimum stair width of 36 inches. If your actual riser climbs above 7.75 inches or your tread depth drops below 10 inches, the tool shows a warning so you can add a riser or reduce the total rise before you cut a single stringer.

Worked example: with a 108-inch total rise, a 7.5-inch desired riser, and a 10-inch tread depth, 108 divided by 7.5 is 14.4, which rounds to 14 risers. Dividing 108 by 14 gives an actual riser height of 7.71 inches, comfortably under the 7.75-inch code maximum. That leaves 13 treads and a total run of 130 inches, about 10.8 feet. The stair angle works out to the arctangent of 7.71 divided by 10, roughly 37.6 degrees, and the stringer length is the square root of 108 squared plus 130 squared, about 169 inches or 14.1 feet.

Frequently Asked Questions

How many risers do I need for my staircase?

The calculator divides your total rise by your desired riser height and rounds to the nearest whole number, because you cannot build a fraction of a step. For a 108-inch total rise with a 7.5-inch target riser, 108 / 7.5 = 14.4, which rounds to 14 risers.

Why is the actual riser height different from what I entered?

Your desired riser height is only a target. Once the number of risers is rounded to a whole number, the tool divides the total rise back by that count to get the real height every step is built to. For 14 risers over 108 inches, each riser is 108 / 14 = 7.71 inches.

Does this stair meet IRC code?

The tool checks your results against IRC R311.7: a maximum riser height of 7.75 inches, a minimum tread depth of 10 inches, minimum headroom of 80 inches (6 feet 8 inches), and a minimum stair width of 36 inches. It flags a warning if your actual riser exceeds 7.75 inches or your tread depth falls under 10 inches. Confirm local amendments with your building department.

How is stringer length calculated?

Stringer length is the hypotenuse of the total rise and total run: the square root of total rise squared plus total run squared. For a 108-inch rise and a 130-inch run, that is the square root of (11,664 + 16,900), about 169 inches or roughly 14.1 feet.