🪜 Stair Calculator

What This Calculator Does

This calculator lays out a staircase from one measurement: the total rise, floor to floor. Enter it with your intended tread depth and it returns the number of risers, the exact height of each, the tread count, and the total horizontal run the stairs will occupy. It is the arithmetic core of stair building — the part that must be exact before a single stringer is cut.

Stairs are unforgiving of estimation: every riser must be equal, code sets hard limits, and the total run must fit the space. All three constraints resolve from the same division, which this tool performs the way carpenters do it.

The Stair Math, Step by Step

Start with total rise — the vertical distance between finished floors, measured, not assumed. Divide by the maximum riser (7.75″ under the common US residential code) and round up to get the riser count: 108″ ÷ 7.75 = 13.9 → 14 risers. Then divide the rise by that count for the actual riser height: 108 ÷ 14 = 7.71″ — every step identical, comfortably under the limit. Rounding up is the crucial move; rounding down would leave risers over code.

Treads number one fewer than risers, because the upper floor itself serves as the final landing: 14 risers, 13 treads. Total run is treads times tread depth — 13 × 10″ = 130″ of floor space, before any landing. That run figure is where designs live or die: if 130″ does not fit the room, the options are a deeper reality check (steeper is capped by code), a landing with a turn (L or U shape splits the run), or relocating the staircase. Discovering this on paper costs nothing; discovering it mid-build costs the framing.

Codes and the Comfort Rule

US residential code (the IRC, adopted with local variations) sets the envelope: risers at most 7.75″, treads at least 10″, riser variation within a flight no more than 3/8″, minimum 6′8″ headroom, and handrail requirements. Commercial stairs run gentler (7″ max risers, 11″ treads). Local jurisdictions amend details, so the permit office's numbers govern — but a design passing the IRC envelope is the right starting point everywhere.

Within the legal envelope lives the comfort tradition: riser plus tread should total about 17-18 inches (the older doubled form: 2R + T ≈ 24-25). It encodes how human gait trades step height against step depth — tall risers want shallow treads and vice versa. The calculator's 7.71″ riser pairs beautifully with a 10-10.5″ tread (sum ≈ 18). A 6″ riser with a 10″ tread, though legal, walks awkwardly (sum 16 — stubby); comfort math catches what code alone permits. Checking both takes seconds and is the difference between stairs people notice and stairs nobody thinks about — the goal being the latter.

From Numbers to Stringers

Building translates the figures onto stringers — the sawtooth boards carrying the steps — laid out with a framing square set to the riser and tread dimensions and stepped along the board. Two details adjust the pure math: the bottom riser is cut shorter by one tread's thickness (once treads are installed, every step gains that thickness except the floor-level start — skipping this “dropping the stringer” step is the classic first-timer error, producing a tall first step), and the top connection method shifts the last rise similarly. Three stringers minimum for standard widths; closer spacing for thick loads or thin treads.

Order of operations protects the result: measure the true finished-floor-to-finished-floor rise (flooring thicknesses included on both levels), run the math here, verify the run fits with required headroom along the slope, check local amendments, then cut one stringer and test-fit it before duplicating. Deck stairs follow identical logic with the landing pad's finished height as the lower floor. The calculator owns the arithmetic; the tape measure and the test fit own the truth — and stairs built in that order come out with the machine-like evenness good stairs have.

Quick Tips

• Risers = ⌈rise ÷ 7.75⌉, then divide the rise evenly — never stack max-height steps.
• Treads = risers − 1; total run = treads × tread depth.
• Comfort rule: riser + tread ≈ 17-18″ (7″ × 11″ is the classic).
• Drop the stringer by one tread thickness at the bottom — the classic first-build miss.

Frequently Asked Questions

How do I calculate the number of stairs?

Divide the total rise by the maximum comfortable riser (US residential code caps risers at 7.75 inches) and round up. A 108-inch floor-to-floor rise needs ⌈108 ÷ 7.75⌉ = 14 risers, making each exactly 108 ÷ 14 ≈ 7.71 inches.

What is a comfortable stair riser and tread size?

US residential code allows risers up to 7.75″ and treads at least 10″. The classic comfort rule: riser + tread ≈ 17-18 inches (or 2 × riser + tread ≈ 24-25). A 7″ riser with an 11″ tread is the traditional sweet spot.

How do I find the total run of a staircase?

Treads count one fewer than risers (the top floor is the last 'tread'). Fourteen risers means 13 treads; at 10 inches each, the staircase runs 130 inches horizontally — the floor space it consumes.

Why must all risers be equal?

Feet learn the rhythm on the first step, and a riser differing by more than about 3/8 inch is a trip hazard code explicitly forbids. That is why you divide the rise evenly rather than stacking 7.75-inch steps and leaving a short one.

Exact Layout, Free to Use

This calculator runs entirely in your browser, dividing the rise the way carpenters do the moment you type. It needs no account or download and works on any device. Like every tool here, it is free to use as often as you like.

Related Tools

For more building math, the board foot calculator prices the lumber, the fraction calculator handles the inch fractions, and the concrete calculator sizes a landing pad.