Three ways to describe the same slope
| Expression | Formula | Typical use |
|---|---|---|
| Ratio (rise:run) | rise : run, simplified | Quick comparison, ramps, roofs |
| Pitch percentage | (rise ÷ run) × 100 | Site drawings, some ramp specs |
| Pitch angle (degrees) | arctan(rise ÷ run) | Handrail fitting selection, code limits stated in degrees |
For a staircase, "rise" and "run" almost always mean the total rise and total run of the whole flight, not a single riser and single tread going — though the ratio comes out the same either way, since the individual step and the whole flight are geometrically similar triangles.
Worked conversions
| Riser height | Tread going | Ratio (rise:run) | Pitch % | Pitch angle |
|---|---|---|---|---|
| 178mm / 7.0in | 280mm / 11.0in | ≈1:1.57 | ≈63.6% | ≈32.4° |
| 190mm / 7.5in | 250mm / 9.8in | ≈1:1.32 | ≈76.0% | ≈37.2° |
| 200mm / 7.9in | 220mm / 8.7in | ≈1:1.10 | ≈90.9% | ≈42.3° |
Notice that as the ratio approaches 1:1, the pitch percentage climbs toward 100% and the angle climbs toward 45 degrees — a genuinely steep stair. Most comfortable residential stairs sit well below that, in the roughly 30-40 degree band.
Converting between the three
- From ratio to angle: divide the rise part by the run part, then take the arctangent of the result.
- From angle to percentage: take the tangent of the angle, then multiply by 100.
- From percentage to ratio: divide the percentage by 100 to get rise ÷ run, then express as rise:run in simplest form.
- For a whole flight, use total rise and total run; for a single step, use riser height and tread going — the ratio should match either way.
Ramps and stairs use rise/run differently
Ramp gradients are very often expressed as a percentage or a ratio like 1:12, and accessible ramp limits are usually far shallower than any stair. Do not confuse a stair's rise/run figures with ramp gradient requirements — they follow separate, much stricter rules for ramps.
Why pitch angle matters for hardware, not just code
Handrail rake fittings, stringer brackets and some baluster shoes are manufactured for specific pitch angle bands, so knowing your exact pitch angle (not just 'roughly standard') avoids ordering a fitting that will not sit flush. This is covered in more depth in our handrail calculator guide, but the rise-over-run conversion is the first step in getting that angle.
Know your numbers in 30 seconds
Enter your step count, tread depth and riser height — the stair runner calculator gives you the exact length to order, in metres and feet, with waste included.
Open the stair runner calculatorChecking pitch against code limits
Where a code expresses a limit in degrees (as UK guidance commonly does, with a maximum private-stair pitch often cited around 42 degrees), converting your measured rise and run to an angle is the most direct way to check compliance, rather than trying to compare riser and going figures separately. Where a code instead expresses limits as riser height and going numbers (as much US guidance does), check those numbers directly and treat the angle as a useful cross-check rather than the primary test.
Common rise/run conversion mistakes
- Mixing units (millimetres in the rise, inches in the run) before converting, which throws off every downstream figure.
- Confusing stair pitch angle with roof pitch or ramp gradient conventions, which use different reference angles or expressions.
- Using a single step's rise and going when a whole-flight figure was actually needed, or vice versa (though the ratio is the same, absolute lengths are not).
- Rounding the angle too early in a multi-step calculation, which compounds error by the time you reach a final fitting selection.
- Assuming a percentage figure is automatically a ratio, without converting through rise ÷ run first.
Whatever you decide, get the numbers first: the stair runner calculator doubles as a stair runner length calculator, adding nosing wrap, landings, winders, pattern repeat and waste so you order the right length the first time.
Frequently asked questions
How do I calculate rise over run for stairs?
Divide total rise by total run to get the ratio, multiply that result by 100 for pitch percentage, or take the arctangent of the result for pitch angle in degrees.
What is a typical rise-over-run ratio for stairs?
Many comfortable residential stairs fall around 1:1.3 to 1:1.6 (rise:run), corresponding to a pitch angle roughly in the 32-40 degree range, though exact figures depend on your chosen riser and going.
How do I convert stair pitch angle to a percentage?
Take the tangent of the angle and multiply by 100. For example, an angle of about 37 degrees converts to a pitch of roughly 75%.
Is stair rise/run the same as ramp gradient?
No. Ramps use their own, generally much shallower gradient limits (often expressed as a ratio like 1:12), separate from stair rise/run figures — do not compare the two directly.
Does rise/run ratio use total rise and run, or a single step?
Either works for the ratio itself, since a single step and the whole flight form similar triangles, but be consistent — mixing a single step's rise with the whole flight's run will give a wrong answer.
Why does pitch angle matter for handrail fittings?
Rake fittings, brackets and some baluster shoes are made for specific pitch angle bands, so an accurate rise/run-to-angle conversion helps you order the correct fitting rather than one that will not sit flush.
What angle is considered a steep staircase?
There is no single universal cutoff, but stairs approaching 45 degrees (a 1:1 rise:run ratio) are generally considered steep, while many comfortable residential stairs sit in the 30-40 degree range.
How do I check my stair pitch against a code limit stated in degrees?
Convert your measured total rise and total run to an angle using arctan(rise ÷ run), then compare directly against the stated maximum, such as the roughly 42-degree UK private-stair limit.
Know your numbers in 30 seconds
Enter your step count, tread depth and riser height — the stair runner calculator gives you the exact length to order, in metres and feet, with waste included.
Convert my rise and runEvery guide is written from hands-on measuring and fitting experience, checked against the calculator’s own maths, and re-reviewed whenever prices or methods change. Read our editorial standards.