Steps that divide evenly, ramps that state their slope plainly
For stairs: enter the total rise and the riser height you are aiming at, and this calculator finds the whole number of steps that divides the rise exactly, because a staircase is a division problem whose remainder is a trip hazard. It then works out the tread from your available run (or the run from your tread), the angle, the stringer length and the three classic comfort checks, including the Blondel rule. For ramps: rise and run become a slope in percent, ratio and degrees. Code comparisons appear only against the named reference set you select, and the page claims compliance with nothing: your local code is the authority, as the notes keep saying.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Stair and ramp rules are set by your local building code and accessibility law, which this page does not replace; verify any design with your building department before building.
What this calculator does
Stairs fail on paper before they fail in wood: a total rise divided by a guessed riser leaves a remainder, and the remainder becomes one short or tall step, which is precisely the step that trips people, because feet learn the rhythm of a flight and believe it. So the stairs tool starts from the integer: the number of risers is the smallest whole count that keeps each riser at or under your target, and every riser then comes out identical to the hundredth of an inch. The ramp tool is simpler arithmetic with heavier consequences: slope stated three ways, because percent, ratio and degrees each mislead a different reader, and accessibility is a property of all three being understood at once.
How to use it
- Measure the rise floor to finished floor. Not to the subfloor, not to the landing’s framing: the finished surfaces the feet will meet, including flooring thicknesses at both levels, since an inch of tile and underlayment is an inch of riser error at the first or last step.
- Count risers, then treads. A flight has one more riser than treads, because the upper floor is the last tread. The results keep the two counts separate and labelled, as mix-ups here are the classic layout error.
- Give the run you truly have. Well openings and door swings bound the run; a tread derived from an honest run beats a beautiful tread that needs a wall moved.
- Headroom is a site check, not a result. The opening’s edge must clear the nosing line by your code’s headroom (commonly about 6 ft 8 in in US residential work); the limitations explain the measurement, which depends on the opening you cut, not on the flight alone.
The method
- Riser count N = the smallest whole number with rise / N at or under the target maximum riser. Actual riser = rise / N. Treads = N − 1.
- Tread = available run / treads, or total run = target tread × treads when the tread is given instead.
- Comfort checks: Blondel’s rule 2 × riser + tread, comfortable around 24 to 25 in; riser + tread around 17 to 18 in; riser × tread around 74 to 76 sq in. The three together catch what any one misses.
- Angle = arctangent of riser / tread. Stringer length (straight flight) = square root of (total run² + total rise²), the hypotenuse the board must cover before layout allowances.
- Ramp: slope percent = rise / run × 100; ratio = 1 : (run / rise); angle = arctangent of rise / run.
Worked examples
The 105-inch rise. A floor-to-floor rise of 105 in with a 7 in target riser: 105 / 7 = exactly 15 risers of 7.00 in, and 14 treads. Over a 143 in run the tread comes out at 143 / 14 = 10.21 in. Blondel reads 2 × 7.00 + 10.21 = 24.21 in, inside the comfortable band; the angle is 34.42 degrees; and the stringer needs the hypotenuse of 143 and 105, which is 177.41 in of board before layout.
The ramp. A 24 in rise over a 288 in run is a slope of 8.33 percent, a ratio of 1:12.00 and an angle of 4.76 degrees: exactly the reference maximum for new accessible ramps in the selected US-style reference, which is a coincidence worth having pointed out rather than discovered by an inspector.
Reading your results
Read the riser figure first: identical risers are the whole safety story, and any design that cannot divide evenly wants a different step count, not a fudged last step. Read the comfort trio as a jury: all three in band is a stair that feels right to strangers; one out of band is a stair to re-plan while it is still arithmetic. Read the ramp’s three slope statements against whichever document governs your project, since percent and ratio are confused for each other with expensive regularity.
Limitations
- No universal code compliance is claimed, anywhere. Stair and ramp rules differ by country, state, occupancy and year of adoption. The selectable references are named, dated styles of rules for comparison; your building department’s adopted code is the only compliance that exists.
- Straight flights only. Winders, curved stairs and landings split a flight into layouts this page does not draw; the riser arithmetic still governs each straight run between landings.
- Headroom, width, handrails and guards are separate requirements. The calculator sizes rise and run. Width minimums, rail heights, baluster spacing, nosing and lighting rules all live in the code, not in these results.
- Ramp landings and cross-slope are not in the slope figure. Real accessible routes also limit cross slope, landing sizes, surface and edge protection; a compliant slope on an otherwise wrong ramp is still wrong.
Frequently asked questions
What is a comfortable riser and tread?
For most adults, risers between about 7 and 7.75 in with treads of 10 to 11 in feel natural, which is why residential references cluster there; the comfort rules in the results (Blondel’s 2R + T near 24 to 25 in chief among them) are the centuries-old formalisation of that feel. Shallower risers with deeper treads suit older users and exterior steps; steeper flights save run at the price of effort and safety margin, a trade the numbers let you make knowingly.
Why must all risers be equal?
Because stair climbing is rhythmic: after two or three steps the body predicts the next, and a step that breaks the prediction by even a quarter inch is a stumble delivered by design. Codes enforce uniformity within tight tolerances for exactly this reason. The calculator’s integer method is the guarantee: divide the true total rise by a whole count and uniformity is automatic, while any method that starts from a favourite riser and adjusts the last step builds the hazard in.
How long a ramp does a 30-inch rise need?
At the 1:12 reference slope, 30 × 12 = 360 in of run, 30 feet, plus landings, which surprises everyone the first time and is why accessible entrances are designed into sites rather than appended to them. Steeper short ramps exist in some rules for tiny rises and existing sites, under conditions the governing document spells out; the selected reference comparison on the page will show how a shorter run scores, and the local code decides what is permitted.
What is the stringer length used for?
It is the minimum board length the flight’s hypotenuse demands, the starting point for laying out the stringer before adding the allowances for the top and bottom cuts, the tread returns and the way the stringer meets the floors. Carpenters order above it and lay out from the actual riser and tread the results give; treating it as the purchase length exactly is how a stringer comes up short at the last cut.
Related calculators
Method: integer riser division of the total rise, tread derived from run or run from tread, the three classical comfort checks, and ramp slope in percent, ratio and degrees; code comparisons only against the named reference selected. Last reviewed: 15 October 2026.