Estimate risers, equal rise and horizontal run for a straight stair with the upper landing acting as the final walking surface. At the example 108-inch total rise and 7-inch maximum target, the form chooses 16 risers of 6.75 inches and 15 treads. It reports a rise/run diagonal for planning, not a cut-ready stringer length or a code-approved design.
Plan the stair project beyond rise and run
Keep this geometry estimate separate from your material list and budget. Do not use the bounding diagonal as the length of lumber to buy. Settle the stair design, supports and connections before pricing the stringers, treads, landings, rails, hardware and finishes that your project actually needs.
Use our home-improvement planning guide to build an itemized quote. Keep demolition, disposal, delivery, labor and permit costs separate from materials, and compare quotes for the same scope. This calculator does not price those items or confirm that the proposed stairs are safe or allowed locally.
How the stair geometry works
Risers = total finished rise / maximum target riser, rounded up.
Equal riser height = total rise / riser count.
Separate treads = riser count – 1.
Horizontal run = separate treads x horizontal going.
Bounding diagonal = square root of (total rise² + horizontal run²). The right-triangle diagonal follows the Pythagorean theorem.1
Rounding up keeps the calculated equal riser at or below your entered maximum target. The target is your planning input, not a verified legal limit. The old nearest-integer approach could exceed it: 108 / 7 = 15.428571, rounding to 15 gave 7.2-inch risers, while rounding up to 16 gives 6.75 inches.
Rise and run chart
Our calculated table assumes a 7-inch maximum target and 10-inch horizontal going, with the upper landing replacing the last tread. These are math examples, not approved stair layouts. The diagonal is only the full-rise/run bounding distance.
| Total rise | Risers / treads | Equal rise | Run | Bounding diagonal |
|---|---|---|---|---|
| 24 inches | 4 / 3 | 6.0000 in | 30 in | 38.4187 in |
| 30 inches | 5 / 4 | 6.0000 in | 40 in | 50.0000 in |
| 36 inches | 6 / 5 | 6.0000 in | 50 in | 61.6117 in |
| 48 inches | 7 / 6 | 6.8571 in | 60 in | 76.8375 in |
| 60 inches | 9 / 8 | 6.6667 in | 80 in | 100.0000 in |
| 72 inches | 11 / 10 | 6.5455 in | 100 in | 123.2234 in |
| 108 inches | 16 / 15 | 6.7500 in | 150 in | 184.8351 in |
Three checked examples
1. The 108-inch default
108 / 7 = 15.428571, so round up to 16 risers. Equal finished rise: 108 / 16 = 6.75 inches. The upper landing is the final surface, so there are 15 separate treads. At 10-inch going, run = 15 x 10 = 150 inches or 12.5 feet. The bounding diagonal is sqrt(108² + 150²) = 184.835061 inches, about 15.40 feet. Do not use that diagonal as a cut-ready board length.
2. A 36-inch rise
36 / 7 = 5.142857, rounded up to 6 risers. Equal rise is 36 / 6 = 6 inches. Five separate treads at an example 11-inch going give 55 inches of run. The bounding diagonal is sqrt(36² + 55²) = 65.734314 inches. Top and bottom cuts, stock width and tread thickness are still unresolved by this calculation.
3. An exact target division
For 42 inches of total rise and a 7-inch maximum target: 42 / 7 = 6 risers, each 7 inches. Five separate treads at 10-inch going give 50 inches of run. Bounding diagonal: sqrt(42² + 50²) = 65.299311 inches. No extra riser is added when the division is exact.
Risers are not the same as separate treads
A riser is a vertical height change. A tread is a walking surface between rises. This form assumes the finished upper floor or deck is the final surface, so a flight with six risers has five separate treads below it. It does not model a top tread flush with or attached differently to the landing, winders, spiral stairs or an intermediate landing.
For a one-riser result, there are zero separate treads and zero calculated run under this convention. The reported diagonal then equals the rise. That is not a conventional cut-stringer layout or an instruction to build a vertical board. Review the landing and step arrangement separately.
Use going, not an unverified tread-board width
Enter the horizontal distance advanced by each step in the chosen layout. A tread board can project beyond a riser as a nosing; its full physical width is not automatically the going. The form does not add or subtract nosing, gaps or riser-board thickness. Confirm the finished tread geometry before marking a framing square.
Why the diagonal is not a stringer cutting length
The rise/run diagonal connects the corners of a bounding right triangle. A real stringer has a different outline: notches, remaining throat, top attachment, bottom bearing and tread-thickness adjustments matter. Its required stock length and width depend on that full layout. This calculator does not provide a saw-cut pattern, stock-size recommendation or safe unsupported span.
The American Wood Council’s DCA6 deck guide includes separate stringer span, attachment, footing, tread and guard requirements, and says local amendments apply.2 Its cited edition is based on the 2015 IRC, so do not treat it as the current adopted code everywhere. A geometry result cannot replace those structural checks or the exact decking manufacturer’s stair-support requirements.
Finished surfaces and uniform rise
Measure total rise from the final lower walking surface to the final upper one. Account for tread thickness and final landing finishes when drawing top and bottom cuts. Dividing the total evenly gives a mathematical equal rise, but the calculator cannot verify that the finished first and last rises match the others after construction.
Check the local authority’s current limits for rise, going, variation within a flight, headroom, stair width, landings, handrails and guards. DCA6 separately discusses stairs and intermediate landings.2 We do not label a result compliant just because its equal rise is below the entered target.
Metric mode
Use centimeters for all three inputs in metric mode: total rise, maximum target riser and horizontal going. Equivalent measurements give the same counts. The default 108, 7 and 10 inches converts to 274.32, 17.78 and 25.4 centimeters; it still gives 16 risers and 15 separate treads. Results show metric first, with US dimensions alongside.
FAQ
Why does this round the riser count up?
The field is a maximum target, not a preferred average. Rounding up prevents the equal rise from exceeding it. If that produces an unsuitable rise or flight layout, revise the plan with current local rules; do not assume the target itself is permitted.
Does the result tell me how many stringers to use?
No. Stair width, tread material, spacing, loading, species, grade and support details determine that. The form has no inputs for those facts. It also does not calculate a structural stringer span or required lumber size.
Can I use the diagonal to buy an exact-length board?
No. Treat it as a planning dimension only. Complete the real stringer outline and top/bottom connection details to determine usable stock dimensions before buying or cutting.
Can this handle two flights and a landing?
Not as one straight flight. Plan each flight and the landing separately, checking their geometry, supports and code requirements. Adding all rises and runs into this form would not describe the actual two-flight layout.
Related calculators
Use the deck board calculator for surface-board counts and the board-foot calculator for rectangular lumber volume. Neither chooses a safe stair structure.
Sources
- Math Is Fun: Pythagorean Theorem (right-triangle diagonal formula)
- American Wood Council: DCA6 Prescriptive Residential Wood Deck Construction Guide (2015 IRC-based edition, stair structure and local-amendment scope)
What you’ll need
A plain checklist. Needs vary by project, so follow the instructions on your materials.
- Framing square with stair gauges – to mark rise and run on the stringer.
- Pressure-treated lumber for outdoor stairs – check the grade for ground contact.
- Circular saw and hand saw – to cut the notches.
- Level – to check the stringers.
- Fasteners and connectors made for outdoor structures – check the label.
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Estimates only. Confirm quantities and product details with your supplier before you order.