Stair Stringer Calculator (Rise, Run and Angle)
Lay out a stair stringer. Enter the total rise to get the number of risers and treads, riser and tread sizes, stringer length and angle, with warnings against residential code limits.
Finished floor to finished floor.
Blank uses 10.5 in treads.
Enter the total rise from the lower floor to the upper floor.
About the stair stringer calculator
The Stair Stringer Calculator tells you how long a stringer must be and which rise and run to mark on it. A stringer is the sloped board that carries the treads. Enter the total rise of the stair, and optionally the total run you have available. The calculator returns the number of risers and treads, the unit rise and unit run for your framing square, the straight-line stringer length and the angle at which the board is cut. Results are given in inches, to two decimal places, with the metric equivalent in whole millimetres.
The same calculation also checks the stair against the main residential limits in the International Residential Code, so you find out before cutting whether a tread is too shallow or the stair too steep.
What you need to know before cutting
Steps
- Measure the total rise from the finished lower floor to the finished upper floor.
- Enter it, and add the total run if the stair has a fixed length in the plan. Without a run, the calculator uses a 10.5 in tread.
- Keep the target riser at 7.5 in, or change it if you want taller or shorter steps.
- Pick standard mounting if the upper floor acts as the last tread, or flush if the stair ends with a tread at floor level.
- Read the unit rise, unit run, stringer length and angle, then transfer the numbers to the board.
The numbers on the square
A framing square is set to two numbers, the unit rise and the unit run. The unit rise is the riser height, which is the total rise divided by the number of risers. The unit run is the tread depth. You place the square on the board with the unit rise on one leg and the unit run on the other, then mark along the edges and step along the board once for each tread.
Formulas
The number of risers is the total rise divided by the target riser, rounded to the nearest whole number. The stringer then follows from the right triangle formed by the total rise and total run :
Here is the unit rise and the unit run. A standard stair has one tread fewer than risers, so .
Worked examples
Standard stringer. A total rise of 108 in gives 14 risers of 7.71 in (196 mm), with 13 treads. At the default 10.5 in (267 mm) tread the total run is 136.5 in, the straight-line length is 174.06 in (4,421 mm) and the cut angle is 36.3 degrees. You step off the square 13 times.
Even rise. A rise of 105 in divided by 7.5 is exactly 14, so there are 14 risers of 7.50 in and 13 treads. The run is 136.5 in, the stringer is 172.21 in and the angle is 35.5 degrees.
Limited run. A rise of 96 in gives 13 risers of 7.38 in and 12 treads. If you only have 110 in of run, each tread is 9.17 in (233 mm). The stringer comes to exactly 146.00 in and the angle is 38.9 degrees. The calculator warns that the tread is under 10 in and the angle is over 37.5 degrees, so the stair needs more run or a different layout.
Why the board must be longer
The stringer length from the calculator is the straight-line distance along the nosings, from the foot of the stair to the top. A real board has to be longer, because the stringer needs wood left under the notches. Many builders leave at least 3-1/2 in of uncut wood beneath the notches, and the board also needs extra length for the plumb and level cuts at each end. Choose a board that covers the calculated length plus the notch depth and end cuts, then check the cut-out against the actual stock before you start.
Adjusting the bottom and top
The bottom riser is usually cut shorter by the thickness of the tread, so that after the treads are fitted every riser measures the same. The code limits variation between the tallest and shortest riser in a flight to 3/8 in, so errors of a sixteenth that repeat across 14 steps matter. If you convert 7.71 in to the nearest sixteenth, you get 7-11/16 in, which is slightly low, so lay out the steps and check that the last one lands on the upper floor.
Code limits and your area
The calculator flags a riser over 7.75 in (197 mm), a tread under 10 in (254 mm) and an angle over 37.5 degrees, which are the IRC R311.7 limits. It does not check local code. Rules vary, including in Canada and under the UK Building Regulations, so confirm yours with your local authority.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
For a full planning view with headroom, use the Stair Calculator. The Length Converter converts the stringer length and layout numbers between inches, feet and millimetres, and the Angle Converter changes the cut angle between units. If the stair lands on a pad, the Concrete Calculator estimates the volume.
Frequently asked questions
What is a stair stringer?
A stringer is the sloped structural board, usually a 2x12, that supports the treads and risers. A stair normally has one at each side, and often a third in the middle when the treads are wide.
How is stringer length calculated?
It is the hypotenuse of the right triangle formed by the total rise and the total run: the square root of rise squared plus run squared. A 108 in rise with a 136.5 in run gives 174.06 in. This is the length along the nosing line, so the board you buy must be longer.
What rise and run do I set on the framing square?
Use the unit rise, which is the riser height, and the unit run, which is the tread depth. For a 108 in rise with the default tread, set 7.71 in on one leg and 10.5 in on the other. Many carpenters round these to the nearest sixteenth and check the total.
How many times do I step off the square?
Once per tread. A standard stair has one tread fewer than risers, so 14 risers means 13 treads. A flush stair has as many treads as risers.
Why does my run not give a 10 in tread?
When you enter a total run, the calculator divides it by the number of treads, so the tread depth follows from the run. A 96 in rise with only 110 in of run gives 9.17 in treads, which is under the 10 in code minimum, and the calculator warns about it.
Does the stringer length include the notches?
No. It is the straight-line distance from the foot to the top of the stair along the nosings. Allow extra for the wood left under the notches and for the plumb and level cuts at each end.
Is my data sent anywhere?
No. The stringer sums run in your browser, so your rise and run values are never uploaded or stored on a server. They stay on this device and are not shared with anyone.