The US International Residential Code stairway section. Specifies: max riser 7.75″, min tread 10″, max riser variation across the staircase 0.375″, headroom 6'8″ minimum, nose projection 0.75-1.25″. Most municipalities adopt IRC; check yours.

What's the "rise + run = 17-18" rule?

A heuristic from carpentry practice: total stride length when climbing stairs is roughly constant. Steep stairs (small tread, big rise) sum higher; shallow stairs (big tread, small rise) sum lower. 17-18″ is the comfort sweet spot.

IRC 2021 R311.7 (Stairways); ANSI A117.1 (accessibility); Architectural Graphic Standards 12th ed (Ramsey/Sleeper). Stair-construction reference: Wagner JW (2014) "Constructing Stairs, Steps, Doors, Windows and Cabinets".

The US International Residential Code stairway section. Specifies: max riser 7.75″, min tread 10″, max riser variation across the staircase 0.375″, headroom 6'8″ minimum, nose projection 0.75-1.25″. Most municipalities adopt IRC; check yours.

What's the "rise + run = 17-18" rule?

A heuristic from carpentry practice: total stride length when climbing stairs is roughly constant. Steep stairs (small tread, big rise) sum higher; shallow stairs (big tread, small rise) sum lower. 17-18″ is the comfort sweet spot.

IRC 2021 R311.7 (Stairways); ANSI A117.1 (accessibility); Architectural Graphic Standards 12th ed (Ramsey/Sleeper). Stair-construction reference: Wagner JW (2014) "Constructing Stairs, Steps, Doors, Windows and Cabinets".

Stair Stringer Calculator (rise/run/length)

From total rise + tread depth, compute riser count, individual rise, stringer length (Pythagorean), and IRC compliance check.

Result

Stringer length

167.11″ (13.926 ft)

14 risers @ 7.500″, 13 treads @ 10″; angle 38.9°.

Total rise (floor-to-floor)105″ (8.75 ft)
Target riser height7.5″
Number of risers14
Individual riser height7.5000″
Number of treads13
Tread depth (run)10″
Total run (horizontal)130.00″ (10.83 ft)
Stringer length (Pythag)167.11″ (13.926 ft)
Stringer board min length172″ (round up to 2× lumber: 14'+ 2×12)
Stair angle38.93°
Nose projection1″
— IRC R311.7 compliance —
Check 1✓ Riser 7.500″ ≤ IRC max 7.75″.
Check 2✓ Tread 10″ ≥ IRC min 10″.
Check 3✓ Rise + run = 17.500″ within 17-18″ comfort range.
Check 4⚠ Stair angle 38.9° > 38° — steep, may feel unsafe. Typical residential 30-37°.
Check 5✓ Nose projection 1″ within IRC range.

Step-by-step

Riser count = round(105″ / 7.5″) = 14.
Individual rise = 105″ / 14 = 7.5000″.
Total run = (risers − 1) × tread = 13 × 10 = 130.00″.
Stringer length = √(rise² + run²) = √(11,025.0 + 16,900.0) = 167.11″.
Stair angle = atan(rise / run) = 38.93°.

How to use this calculator

Measure total rise from finished lower floor to finished upper floor in inches.
Target riser height 7-7.5″ for comfortable residential stairs.
Tread depth (run) 10-11.5″ residential, 11+ for commercial.
Nose projection 0.75-1.25″ per IRC.
Read the IRC compliance checks — anything flagged ✗ is a code violation.

About this calculator

Stair-stringer math is a direct application of the Pythagorean theorem: stringer = √(rise² + run²). The trick is sizing the individual riser correctly first — divide total floor-to-floor rise by a target riser height (~7-7.5″ typical residential), round to a whole number of risers, then divide back to get the EXACT riser height. That number must clear IRC R311.7.5.1 (max 7.75″ residential). Tread depth (run) must be ≥ 10″. The classic carpenter's rule "rise + run = 17-18 inches" produces stairs that feel natural to climb; outside that range stairs feel either steep (sum < 17) or shallow (sum > 18). The total horizontal run = (riser count − 1) × tread depth — the top "step" IS the upper-floor landing, not an extra tread. Standard stringer boards are 2×12 in lengths of 8', 10', 12', 14', 16' — pick the smallest that exceeds the Pythagorean length by at least 4″ for cuts and overhang.

Frequently asked

A "riser" is a vertical face between treads. Going from floor 1 to floor 2 you climb N risers but only step on N−1 treads — the last "step" is the landing on floor 2, not a tread. Common counting mistake.