Stair calculator: risers, treads and stringer layout

What this calculator does

It works out a straight stair with equal steps: how many risers there are, how high each one is, how many treads you need and how far the stair reaches along the floor. When the total rise is higher than one flight may be, it splits the stair into flights with landings between them.

For a cut stringer it gives the layout: the distance between marks along the top edge of the board, a table of every mark measured from the first one to the nearest millimetre or 1/16 in, the height of the first riser after the tread thickness is taken off, and the depth of board left below the notches. A drawing of the stringer can be printed.

It does not check your stair against a building code. Codes also regulate width, headroom, handrails, guards, landings and the nosing of the treads. Confirm every dimension with your local building authority before you build.

How to use it

1. Choose metric or US units. Dimensions are entered in millimetres or inches.
2. Measure the total rise: the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor, including floor coverings.
3. Enter the highest riser that your building code allows, or a lower value if you prefer shallower steps.
4. Enter the tread depth, also called the going or the run of one step: the horizontal distance from the front edge of one tread to the front edge of the next.
5. For the stringer, enter the tread thickness, choose the board and enter the least throat you want to leave.
6. For landings, enter the highest rise one flight may have and the depth of a landing.
7. Select Calculate. The stringer layout below the result follows your values; use Print the layout to print the drawing and the table.

In US units you can type feet, inches and fractions as they read on the tape, such as 8' 11 1/2" or 7 3/4.

How the result is calculated

1. Number of risers = total rise ÷ highest riser allowed, rounded up to a whole number, so that no riser is higher than the limit.
2. Height of each riser = total rise ÷ number of risers.
3. Risers per flight = highest rise of one flight ÷ riser height, rounded down. Flights = number of risers ÷ risers per flight, rounded up; the risers are shared as evenly as possible, so the largest flight has the number of risers ÷ flights, rounded up.
4. Number of treads = number of risers − number of flights, because the upper floor or a landing is the last step of each flight.
5. Total run = number of treads × tread depth + number of landings × landing depth.
6. Length along the slope of the largest flight = square root of ((risers × riser)² + ((risers − 1) × tread depth)²).
7. Angle = arctangent of (riser height ÷ tread depth).
8. Distance between marks = square root of (riser² + tread depth²). Mark n lies (n − 1) × that distance from mark 1.
9. First riser on the stringer = riser − tread thickness, so that the finished first step is as high as the others.
10. Throat = board width − riser × tread depth ÷ distance between marks: the board left below the deepest point of a notch, measured square to the edge.
11. Stringer edge length = risers of the largest flight × distance between marks, before the cuts at both ends.

Lengths in US units are also shown to the nearest 1/16 in, and the layout table uses sixteenths too.

The last result, twice the riser plus the tread depth, is a rule for comfortable proportions that several building codes use. The codes of England and Australia require it to be between 550 mm and 700 mm.

Worked example

The height from floor to floor is 2600 mm, the highest riser allowed is 190 mm and the tread depth is 260 mm. Risers: 2600 ÷ 190 = 13.7, rounded up to 14. Each riser is 2600 ÷ 14 = 185.7 mm.

There are 14 − 1 = 13 treads, so the total run is 13 × 260 = 3380 mm, or 3.38 m. The length along the slope is the square root of (2600² + 3380²) = 4264 mm, or 4.26 m. The angle is the arctangent of 185.7 ÷ 260, which is 35.5 degrees. Twice the riser plus the tread depth is 2 × 185.7 + 260 = 631 mm.

The flight is below the 3835 mm example limit, so there is 1 flight and no landing. Stringer: the marks are the square root of (185.7² + 260²) = 320 mm apart. With 25 mm treads the first riser on the stringer is 185.7 − 25 = 161 mm. A board 286 mm wide keeps a throat of 286 − 185.7 × 260 ÷ 319.5 = 135 mm, more than the 127 mm entered. The edge of the stringer is 14 × 319.5 = 4473 mm, shown rounded up as 4.48 m.

In US units: a total rise of 108 in with risers of at most 7.75 in gives 108 ÷ 7.75 = 13.9, rounded up to 14 risers of 108 ÷ 14 = 7.71 in, which is 7 11/16 in to the nearest sixteenth. With 13 treads of 10 in, the total run is 130 in, or 10.83 ft. The length along the slope is 169 in, or 14.08 ft, and the angle is 37.6 degrees. Twice the riser plus the tread depth is 2 × 7.71 + 10 = 25.4 in.

The stringer marks are the square root of (7.71² + 10²) = 12.63 in apart, about 12 5/8 in. With 1 in treads the first riser on the stringer is 6.71 in. A 2×12 of 11 1/4 in keeps a throat of 11.25 − 7.71 × 10 ÷ 12.63 = 5.14 in, just above the 5 in entered, and the edge of the stringer is 14 × 12.63 = 176.8 in, or 14.74 ft. There is 1 flight, because 108 in is less than 151 in.

With a landing: a total rise of 4500 mm with risers of at most 190 mm needs 24 risers of 187.5 mm. One flight may rise 3835 mm, which is 20 risers, so the stair has 2 flights of 12 risers and 1 landing. The total run is 22 treads × 260 mm + 914 mm = 6634 mm.

Stringers and throat depth

Cutting the notches takes a triangle out of the board. What is left below the notches, the throat, carries the stair. Published deck guidance sets a minimum: the commentary of the American Wood Council deck guide DCA 6 says cut stringers were analysed with an effective depth of 5.1 in, and the stringer details of ICC code change proposal RB268-13 and of the Wisconsin deck code appendix show a minimum throat of 5 in. The example uses 5 in (127 mm); your code or engineer may require something else.

With risers of 7 1/2 in and treads of 10 in, the notch is 6 in deep, square to the edge. A 2×12 of 11 1/4 in keeps 5 1/4 in and passes the 5 in check; a 2×10 of 9 1/4 in keeps only 3 1/4 in. The actual widths of 11 1/4 in and 9 1/4 in are those of the American Softwood Lumber Standard PS 20 for dry lumber.

The calculator does not size the stringer for a span or a load. DCA 6 also limits how far cut stringers may span and how far apart they may be; check the rules that apply to your stair.

Limits in building codes

The table shows the limits for the steps of a stair inside a home in four codes, as published. Codes are revised and adopted locally, so the edition that applies to you may differ.

In the 2024 edition of the International Residential Code, the same limits appear in section R318.7.5.

Landings: the International Residential Code limits the rise of one flight between floors or landings to 151 in (3835 mm) in R311.7.3 of the 2021 edition and R318.7.3 of the 2024 edition, and requires landings of at least 36 in (914 mm) in the direction of travel. The Australian National Construction Code 2022 allows at most 18 risers per flight and landings of at least 750 mm; to follow it, enter 18 times your riser height as the highest rise of one flight. Approved Document K for England sets no riser limit per flight for stairs in dwellings, but asks for a change of direction after 36 risers in consecutive flights.

The metric example uses a riser limit of 190 mm and a tread depth of 260 mm, because these values lie inside all three metric ranges in the table. The US example uses the limits of the International Residential Code. They are examples, not a statement of what your code requires.

Common mistakes

• Measuring the total rise between unfinished floors. Flooring that is added later changes the height of the first and the last riser.
• Counting as many treads as risers. A straight flight between two floors has one tread fewer.
• Making the risers unequal to use up a remainder. Uneven steps are a tripping hazard, and codes limit the difference.
• Confusing the tread depth with the width of the board. The board is usually deeper than the going, because it overhangs the riser below.
• Forgetting to take the tread thickness off the first riser of the stringer. The first step then ends up higher than the others by the thickness of a tread.
• Stepping off the marks one at a time with a framing square. Small errors add up over a long stringer; measure every mark from the first one.