Stair Calculator

The Three Numbers That Control a Staircase

Every stair calculation starts from three values:

• Total rise. The vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. Finished to finished, including tile, carpet, hardwood or whatever is going down later.
• Riser height. The vertical distance from one tread to the next. Total rise divided by the number of risers.
• Tread depth. The horizontal walking surface of each step, measured from nosing to nosing, not including the nosing overhang beyond the tread below.

Get total rise wrong and everything downstream is wrong. Measure it before the flooring goes in only if the flooring thicknesses on both levels are known and accounted for, and write down the assumption.

Dividing the Rise Into Equal Risers

A staircase cannot have a leftover fraction at the bottom. The total rise has to divide into a whole number of identical risers, and the International Residential Code allows a maximum variation of 3/8 inch between the tallest and shortest riser in a flight. The same 3/8 inch tolerance applies to tread depths.

That limit exists because people climb stairs by feel, not by looking. After two or three steps the body locks into a rhythm and stops watching. A single riser that is half an inch off breaks the rhythm and is one of the most common causes of falls on residential stairs.

A Worked Example

A basement stair has a total rise of 108 inches, floor to floor.

• Target riser height: 7 inches. 108 divided by 7 = 15.43.
• Round to 15 risers. 108 divided by 15 = 7.2 inches per riser, which is 7 3/16 inches at the closest practical framing fraction.
• Treads: 15 minus 1 = 14 treads.
• At a 10 inch tread depth, total run = 14 x 10 = 140 inches, or 11 feet 8 inches of floor space.
• Check the comfort rule: (2 x 7.2) plus 10 = 24.4 inches. Inside the 24 to 25 inch target.
• Check code: 7.2 inches is under the 7 3/4 inch maximum riser, and 10 inches meets the minimum tread. Legal.

Had the count been rounded down to 14 risers, each riser would be 108 divided by 14 = 7.71 inches. That still squeaks under the 7 3/4 inch maximum, and it saves 10 inches of floor run, but the stair is noticeably steeper and (2 x 7.71) plus 10 = 25.4 inches, outside the comfort range. On a main stair, take the 15 riser version.

Note also that 7.2 inches is not a friendly tape measure number. Rather than trying to hold 7 3/16 inches fifteen times in a row, lay the stringer out with a framing square and stair gauges set to the exact rise and run, and step it down the board so the small error never accumulates.

Code Limits: The 7-11 Rule

Residential stairs in the United States generally follow the International Residential Code:

• Maximum riser height: 7 3/4 inches.
• Minimum tread depth: 10 inches, measured nosing to nosing.
• Maximum variation: 3/8 inch between the largest and smallest riser, and separately between the largest and smallest tread, within a flight.
• Nosing: where the tread depth is less than 11 inches, a nosing of 3/4 inch to 1 1/4 inch is required. Solid risers are required on most residential stairs.

Commercial stairs under the International Building Code are stricter, typically a 7 inch maximum riser and 11 inch minimum tread, which is where the phrase "7-11 rule" comes from. Some states and cities amend either code, and a few jurisdictions still enforce older limits such as 8 1/4 inch risers. Always confirm the numbers with the local building department before cutting stringers.

The 2R Plus T Comfort Rule

Code sets the legal boundary. Comfort is a separate question, and the old carpenter's formula still holds up:

Stairs that fall outside the range feel wrong even when they are legal. A 7 3/4 inch riser with a 10 inch tread gives 25.5, which reads as steep. A 5 inch riser with a 10 inch tread gives 20, which forces an awkward mincing gait, the reason shallow monumental stairs feel odd to climb quickly.

Common Total Rise Reference

Riser counts below are the nearest whole number to a 7 inch target. The run column assumes 10 inch treads. Every riser height shown is within code.

Clearances and Guards

• Headroom: 6 feet 8 inches minimum, measured vertically from a line connecting the tread nosings to any ceiling, soffit, beam or header above. This is what usually kills a stair relocation in a remodel, since the opening above has to be long enough.
• Stair width: 36 inches minimum, measured above the handrail height. Below the handrail the clear width may narrow to 31 1/2 inches with one handrail, or 27 inches with handrails on both sides.
• Handrail height: 34 to 38 inches, measured vertically from the tread nosings. At least one handrail is required on flights with four or more risers, it must be continuous the full length of the flight, and it needs a graspable profile with a 1 1/4 to 2 inch diameter for a round rail.
• Guards: 36 inches minimum height on open sides where the drop exceeds 30 inches, with balusters spaced so a 4 inch sphere cannot pass through. On the open side of the stair itself, a 4 3/8 inch sphere is the limit for the triangular opening formed by the riser, tread and bottom rail.
• Landings: required at the top and bottom of each flight, at least as wide as the stair and at least 36 inches deep in the direction of travel. A door may swing over a landing at the top of an interior stair only under limited conditions.

Stringer Layout and Cutting

Stringers are usually cut from 2x12 stock, which at 11 1/4 inches wide leaves enough material behind the notches. Lay out the cuts with a framing square: set stair gauges at the riser height on the tongue and the tread depth on the blade, then walk the square down the board, marking each step.

The remaining solid wood behind the notch is called the throat, and code and common practice both call for at least 3 1/2 inches. With a 7.2 inch rise and a 10 inch run on a 2x12, the throat works out to roughly 5 3/8 inches, which is comfortable. Deeper treads or taller risers cut that down fast, and a 7 3/4 by 11 layout on a 2x12 leaves closer to 4 1/4 inches.

Stringer stock length is the diagonal of the stair. For the 108 inch by 140 inch example, that is the square root of (108 squared plus 140 squared), which is 176.8 inches, or 14 feet 9 inches. Order 16 foot stock so there is material for the top and bottom cuts.

Use three stringers for a 36 inch wide stair with nominal 1 inch treads, or two if 2x material is used for treads and the span allows. Cut one stringer, test fit it in place before cutting the others, and use it as the pattern.

The Dropped Stringer Adjustment

This is the step that catches people. If the stringer is laid out with every riser at 7.2 inches and then set on the floor as cut, the bottom step will be too tall by the thickness of the tread material and the top step will be too short by the same amount, because every tread except the bottom one sits on top of a cut but the bottom one sits on the floor.

At the top, the stringer usually hangs from a header. If the top tread is the finished upper floor itself, the top riser must land so the last rise matches all the others once the upper floor covering is in place. Dry fit and measure both ends before committing.

Outdoor Stairs

Exterior stairs follow the same rise and run rules, but practice differs in a few ways:

• Risers are usually held to 6 to 7 inches with treads of 11 to 12 inches, since outdoor stairs are walked in boots, in the dark and in bad weather.
• Treads are pitched about 1/8 to 1/4 inch per foot away from the house so water drains rather than pooling and freezing.
• Open risers are commonly allowed outdoors, but a 4 inch sphere still must not pass through the opening on stairs serving a required exit.
• Stringers and posts in contact with the ground or concrete need ground contact rated pressure treated lumber and stainless or hot dipped galvanized fasteners, since standard zinc corrodes fast against modern treatment chemicals.
• Landings and stair footings in cold climates need to bear below the local frost line, or the stair will heave and throw the riser heights out of tolerance in the first winter.

Stair codes carry local amendments more often than almost any other part of the residential code, so confirm riser, tread, handrail and guard requirements with the local building department before framing.