Civil & Structural Engineering

Stair Calculator

Calculate the number of risers, actual riser height, total run, and stringer length for a straight staircase.

Formula N = max(1, round(R / rh))Reviewed Sep 8, 2026

Building a straight staircase? This calculator tells you exactly how many risers to cut, the actual (uniform) riser height once your total rise is evenly divided, the total run, and the stringer length. Enter the total floor-to-floor rise and your target riser height and tread depth - the calculator recomputes the exact riser height needed to keep every step identical, and flags dimensions that fall outside the commonly cited IRC limits.

Calculation Bench

Stair Dimensions

01Total Rise

R · Total floor-to-floor vertical height

02Target Riser Height

rh · 7-7.5 in comfortable; IRC max 7¾ in

03Target Tread Depth

td · 10-11 in common; IRC min 10 in

Solution

Enter total rise and target riser/tread dimensions to calculate your stair layout.

N = max(1, round(R / rh))

Formula Sheet

N = \max(1, \text{round}(R / rh))

rh_{actual} = R / N

\text{Run} = (N - 1) \times td

L = \sqrt{R^2 + \text{Run}^2}

NNumber of Risers
RTotal Rise
rhTarget Riser Height
tdTarget Tread Depth

Variables & Units

Symbol	Variable	Description	Common Units
N	Number of Risers	Total risers in the flight, rounded from total rise divided by target riser height.
R	Total Rise	Total vertical floor-to-floor (or floor-to-landing) height.	in, ft, m
rh	Target Riser Height	Desired height per riser before rounding to a whole number of risers.	in, mm
td	Target Tread Depth	Desired depth per tread, front to back.	in, mm

How to Use This Calculator

01Measure the total rise - the exact vertical floor-to-floor (or floor-to-landing) height the staircase needs to climb.
02Enter a target riser height. 7 to 7.5 in is a common comfortable target; the IRC maximum is 7¾ in.
03Enter a target tread depth. 10 to 11 in is common; the IRC minimum is 10 in.
04The calculator instantly shows the number of risers, the actual riser height (recomputed so every riser is identical), total run, and stringer length - with a note if either dimension falls outside the commonly cited IRC limits. Check headroom, landing, handrail, guard, and local amendments separately before building.

How the Formula Works

Total rise rarely divides evenly by a target riser height, so the calculator first finds the number of risers by rounding total rise ÷ target riser height to the nearest whole number, then recomputes the actual riser height as total rise ÷ that number of risers. This is the standard approach for a code-compliant stair: every riser in a flight must be the same height (within a small tolerance), so the height is adjusted slightly to fit the rise evenly, not the count.

The number of treads is one less than the number of risers - the top riser lands on the upper floor, which serves as its own tread, so a flight of 16 risers has 15 physical tread surfaces, not 16. Total run is the number of treads times the tread depth, since that's the actual horizontal distance covered walking from the bottom of the stair to the top.

Stringer length is the straight-line distance from the bottom of the first riser to the top of the last one - the hypotenuse of a right triangle with total rise as one leg and total run as the other, the same Pythagorean relationship this site's Rafter Length Calculator uses for a roof rafter.

The calculator checks the actual riser height and target tread depth against the commonly cited IRC limits (7.75 in max riser, 10 in min tread) and flags either one if it falls outside - an informational check, not a substitute for the actual code and inspector governing a specific project, since amendments vary by jurisdiction.

Worked Example 01

10 ft floor-to-floor rise

Known

Total Rise (R): 120 in
Target Riser Height (rh): 7.5 in
Target Tread Depth (td): 10 in

Formula

N = max(1, round(R / rh))

Substitution

N = round(120 / 7.5) = 16, Actual Riser = 120 / 16 = 7.5 in, Run = 15 × 10 = 150 in, Stringer = √(120² + 150²)

Result

16 risers · 7.5 in actual riser · 15 treads · 150 in run · 16.01 ft stringer

A 120-inch total rise divides evenly by a 7.5-inch target, giving exactly 16 risers at 7.5 in each - within the 7.75 in IRC maximum. With 15 treads at 10 in each, total run is 150 in, and the stringer works out to just over 16 feet.

Worked Example 02

Metric flight, uneven division

Known

Total Rise (R): 2.8 m
Target Riser Height (rh): 180 mm
Target Tread Depth (td): 280 mm

Formula

N = max(1, round(R / rh))

Substitution

N = round(2.8 / 0.18) = 16, Actual Riser = 2.8 / 16 = 175 mm, Run = 15 × 280 = 4,200 mm, Stringer = √(2.8² + 4.2²)

Result

16 risers · 175 mm actual riser · 15 treads · 4.2 m run · ≈5.05 m stringer

2.8 m ÷ 180 mm is 15.56, which rounds to 16 risers - the actual riser height then comes out to 175 mm, slightly under the 180 mm target, so every one of the 16 risers ends up identical rather than 15 equal ones plus a mismatched 16th.

Applications

01Laying out a straight staircase's riser count, riser height, and stringer length before cutting
02Checking a proposed riser height and tread depth against commonly cited IRC limits before building
03Comparing stringer length and step count across different target riser heights for the same total rise
04Checking whether a proposed stair layout has enough horizontal run before framing starts

Assumptions

01A single straight flight of stairs with no winders, landings, or turns.
02Total run is measured to the nosing of the top tread (the edge of the upper floor/landing) - the standard geometric convention. Some deck-specific stair layouts measure to the outer face of the top framing instead, which adds roughly one more tread depth to the total run.
03All risers are uniform, and all treads are uniform - required by code (typically within 3/8 in tolerance across a flight), and the standard assumption for a straight run of stairs.

Where This Model Stops

01Does not model landings, winders, spiral stairs, or a flight that changes direction - a staircase requiring a landing (commonly required above about 12 ft of total rise) needs each flight calculated separately.
02Does not calculate stringer lumber size or board count. Actual stock (commonly 2×12) must leave at least 3½ in of net width after notching, per the IRC - verify against your specific riser/tread combination, not just this calculator's output.
03Does not check headroom, handrail height, guard requirements, or stairway width - all separate code requirements beyond rise, run, and riser/tread dimensions.
04The IRC limits checked here are commonly cited defaults, not a substitute for the actual code adopted and any local amendments in your jurisdiction.

References

[1]
Stairway Basics
Fine Homebuilding
Reference for current IRC maximum riser height (7¾ in) and related residential stairway code context.
[2]
Complete Guide to Building Code-Compliant Stairs (IRC & IBC)
Construction Bros
Reference for IRC minimum tread depth (10 in), riser/tread uniformity tolerance, and stringer net-width requirements after notching.

Frequently Asked Questions

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

Because total rise almost never divides evenly by a target riser height. The calculator rounds to the nearest whole number of risers, then spreads the total rise evenly across that many risers - which shifts the actual height slightly from the target so every riser in the flight comes out identical, which code requires.

Why does the calculator use one fewer tread than the number of risers?

Because the top riser lands on the upper floor, which serves as its own tread - a flight of 16 risers has 15 physical tread surfaces, not 16. Total run is based on tread count, since that's the actual horizontal distance a person walks climbing the stairs.

What if my actual riser height comes out above 7.75 inches?

That's flagged as exceeding the commonly cited IRC maximum. Add one more riser to the flight (which lowers the actual riser height) or increase the total rise if that's not fixed. A too-tall riser is a real trip hazard, not just a code technicality.

What's a comfortable rise-and-run combination, beyond the code minimums?

Two widely used rules of thumb: riser height × 2 plus tread depth should land around 24-25 inches, or riser height plus tread depth should land around 17-18 inches. Both aim for a stride that feels natural - a steep riser with a shallow tread (or the reverse) tends to feel awkward even if it technically meets code.

Does this calculate landings and handrails?

No. It calculates the straight-flight geometry only: risers, treads, run, and stringer length. Landing size, handrail height, guard details, headroom, and stair width are separate code checks.

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