Stair Calculator

How the Stair Calculator Works

This stair calculator turns one measurement, the total rise from finished floor to finished floor, into a full stair layout. It divides the rise into equal risers no taller than the maximum you set, counts the treads, multiplies out the total run and works out the stair angle, the stringer length and the stairwell opening needed for headroom. It then checks the result against the stair rules of the International Residential Code (IRC) for homes or the International Building Code (IBC) for commercial buildings.

The number of risers must be a whole number, so the calculator rounds up. Rounding up guarantees that the exact riser height never exceeds your maximum. Every riser in the flight comes out identical, which matters because the IRC allows the tallest riser in a flight to exceed the shortest by no more than 3/8 inch.

There is one fewer tread than riser because the top floor acts as the last step. The total run is measured horizontally from the face of the bottom riser to the face of the top riser and does not include the nosing overhang or the landings. US results also show the nearest 1/16 inch, the mark you would set on a tape measure.

Stair Code Requirements: IRC, IBC and OSHA

Three sets of rules cover most stairs in the United States. The IRC applies to one and two family homes and townhouses, the IBC applies to commercial and public buildings, and OSHA 1910.25 applies to stairs in general industry workplaces. The table lists the limits from the 2021 IRC and IBC and the current OSHA standard.

The IRC measures headroom vertically from a sloped line through the tread nosings, and the 36 inch width is the clear width above handrail height. A handrail may reduce the width at and below handrail height to 31 1/2 inches with a rail on one side, or 27 inches with rails on both sides. The IBC lets stairs serving fewer than 50 occupants narrow to 36 inches, which the calculator flags as "Under 50 occupants only" instead of a failure.

How to Calculate Stair Rise and Run Manually

1. Measure the total rise. Measure plumb from the finished floor at the bottom to the finished floor at the top, at the spot where the stair will land. Floors are rarely level, so do not measure at a different point in the room.
2. Divide by the maximum riser. Use 7.75 inches for the IRC limit, 7 inches for the IBC, or a lower number for a gentler stair, and round the answer up to a whole number of risers.
3. Find the exact riser height. Divide the total rise by the whole number of risers.
4. Count the treads. Subtract one from the riser count.
5. Multiply out the run. Multiply the tread count by the tread depth, then add landing space at each end.

Take a 10 foot ceiling over a floor system 10.5 inches thick. The floor to floor rise is 120 + 10.5 = 130.5 inches. At the IRC maximum, 130.5 ÷ 7.75 = 16.84, so 17 risers of 7.68 inches (about 7 11/16 inches) and 16 treads. With 10 inch treads the run is 160 inches, or 13 feet 4 inches. A 7.5 inch maximum gives 18 risers of exactly 7.25 inches and 17 treads, which needs 170 inches, or 14 feet 2 inches, of floor space with the same treads.

Each extra riser adds one tread to the run. That trade between a shorter, steeper stair and a longer, gentler one appears in the "Other riser counts" table of the results.

Comfortable Stair Dimensions and the 2R + T Rule

Code limits set the steepest legal stair, not the most comfortable one. A long standing rule of thumb links the riser and tread to the length of a normal walking stride. NIST Technical Note 1623 describes Blondel's formula, in which twice the riser plus the tread equals 24 inches, and notes that the common US "7/11" stair satisfies 2R + G = 635 mm, or 25 inches. The National Bureau of Standards publication Guidelines for Stair Safety cites Grandjean's version, 2r + t = 63 cm (24.8 inches), with 17 cm risers and 29 cm treads.

The calculator reports 2R + T in the Step comfort tile and says whether it falls inside the 24 to 25 inch band (610 to 635 mm) spanned by Blondel's formula and the 7/11 stair. A value outside the band is still legal if the riser and tread meet code. It simply means the stride differs from these traditional proportions.

Headroom and Stairwell Opening Size

When a stair climbs through a floor, the opening in that floor must be long enough to keep 6 feet 8 inches of headroom above the nosing line. The nosing line drops one riser for every tread you move down the stair, while the ceiling under the upper floor stays level. Headroom is reached where the drop equals 80 inches plus the floor thickness.

The opening is measured horizontally from the top riser back toward the bottom of the stair. In the default example it is about 11 feet long, while the stair itself runs 12 feet 3 inches, so the floor above may extend over the bottom 15 inches of the run. If the calculated opening is longer than the run, the floor above cannot cover any part of the stair. For an outdoor deck stair with nothing overhead, leave the floor thickness blank and the opening tile disappears.

Cutting Stair Stringers

A stringer is the notched board that carries the treads. Its length is the diagonal of a right triangle whose legs are the total run and the total rise, which is why the calculator uses the Pythagorean theorem. Buy stock longer than the result so there is room for the top connection and the bottom cut.

1. Set a framing square on the board with the riser height on the tongue and the tread depth on the blade, for example 7 3/16 inches and 10 1/2 inches.
2. Trace the notch, then slide the square along the edge so the next riser mark starts where the last tread mark ends. Repeat once for each riser.
3. Cut the bottom of the stringer shorter by one tread thickness. With 1 inch treads and 7.2 inch risers, the bottom notch is 6.2 inches tall, so the first finished step matches the rest after the treads go on.
4. Cut one stringer, test it in place, and use it as the pattern for the others.

Tread boards are deeper than the tread depth by the nosing projection. A 10.5 inch tread with a 1 inch nosing needs an 11.5 inch board, which the calculator shows in the Tread board tile.

Deck, Commercial and Metric Examples

Deck stair, 40 inch rise

With six risers the IRC handrail rule applies, because a rail is required on at least one side of any flight with four or more risers. The 11 inch tread also means a nosing is not required.

Commercial stair, 12 foot rise

A rise of exactly 144 inches is the most the IBC allows in a single flight. Anything taller needs an intermediate landing, and the calculator marks the rise per flight row "Add a landing".

Metric stair, 2700 mm rise

The metric limits come from the dimensions printed in the codes: 196 mm risers and 254 mm treads for the IRC, and 102 to 178 mm risers with 279 mm treads for the IBC. The Tight space example shows a failing layout: 9 inch treads under 7.71 inch risers give a 40.6 degree stair that is 1 inch short of the IRC tread minimum.

Frequently Asked Questions

Sources & References

• International Code Council. 2021 International Residential Code, Chapter 3: Building Planning, Section R311.7 Stairways (width, headroom, rise per flight, risers, treads, nosings, landings, handrails). codes.iccsafe.org
• City of Fort Smith, Arkansas. 2021 IRC Code and Commentary excerpt, Section R311.7 (published code text with commentary). fortsmithar.gov
• City of Bath, Maine, Codes Department. Commercial and Multi Family Stairways: General Requirements, 2021 International Building Code (IBC 1011 and 1014 riser, tread, uniformity, width, headroom, nosing, landing, vertical rise and handrail rules). cityofbathmaine.gov
• UpCodes. 2021 IBC Section 1011.5.2 Riser Height and Tread Depth (4 inch minimum and 7 inch maximum riser, 11 inch minimum tread). up.codes
• U.S. Occupational Safety and Health Administration. 29 CFR 1910.25 Stairways (angle, riser, tread, width, headroom and landing limits for general industry). osha.gov
• Bukowski, R. W. Emergency Egress from Buildings, NIST Technical Note 1623, 2009 (Blondel's formula and the 7/11 stair). nist.gov
• Archea, J., Collins, B. L. and Stahl, F. I. Guidelines for Stair Safety, NBS Building Science Series 120, 1979 (Grandjean's 2r + t = 63 cm rule). doi.org

Results are planning estimates for a single straight flight and do not replace review by your local building official. Every number on this page was recomputed with the same formulas the calculator uses. Methodology reviewed: 2026.