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Stair Riser and Tread Guide: Rise, Run, Angle and Stringer Length
Work out risers, treads, run, angle and stringer length from total rise, with typical US residential limits (check your local code) and a chart of layouts.
Quick answer
Divide the total rise by the riser height you want and round to a whole number of risers: 105 in ÷ 7.25 in rounds to 14 risers of 7.5 in each. A flight has one fewer tread than risers, so 13 treads of 10 in give a 130 in run (10 ft 10 in), a 36.87° angle and a layout line of about 167 in, which needs a 14 ft board with only 0.9 in to spare. Typical US residential limits are a riser no taller than 7-3/4 in and a tread at least 10 in deep (IRC R311.7). Check your local code.
Formula
risers = round(total rise ÷ target riser) | riser = total rise ÷ risers | treads = risers − 1 | run = treads × tread depth | 2 × riser + tread ≈ 24 to 25 in
Accuracy
Reference table
Search by name or sort by any column. Each row links to the matching calculator.
10 of 10 rows · sorted by total rise
| Calculator | ||||||||
|---|---|---|---|---|---|---|---|---|
| 30 in | 4 | 7.5 in | 3 | 30 in | 36.87° | 25 in | 8 ft | Stair stringer calculator |
| 42 in | 6 | 7 in | 5 | 50 in | 34.99° | 24 in | 8 ft | Stair stringer calculator |
| 56 in | 8 | 7 in | 7 | 70 in | 34.99° | 24 in | 8 ft | Stair stringer calculator |
| 64 in | 9 | 7.111 in | 8 | 80 in | 35.42° | 24.22 in | 10 ft | Stair stringer calculator |
| 72 in | 10 | 7.2 in | 9 | 90 in | 35.75° | 24.4 in | 10 ft | Stair stringer calculator |
| 84 in | 12 | 7 in | 11 | 110 in | 34.99° | 24 in | 12 ft | Stair stringer calculator |
| 96 in | 13 | 7.385 in | 12 | 120 in | 36.44° | 24.77 in | 14 ft | Stair stringer calculator |
| 105 in | 14 | 7.5 in | 13 | 130 in | 36.87° | 25 in | 14 ft | Stair stringer calculator |
| 108 in | 15 | 7.2 in | 14 | 140 in | 35.75° | 24.4 in | 16 ft | Stair stringer calculator |
| 120 in | 17 | 7.059 in | 16 | 160 in | 35.22° | 24.12 in | 20 ft | Stair stringer calculator |
How it works
From total rise to a whole number of risers
Measure the total rise from finished floor to finished floor, then decide on a riser height you would like. Divide, and round to the nearest whole number of risers, because you cannot build half a step. For 105 in and a 7.25 in target, 105 ÷ 7.25 = 14.48 rounds to 14 risers, and the exact riser is 105 ÷ 14 = 7.5 in. Every riser in a flight should be the same, so always divide the measured rise equally rather than cutting each one to the target; typical rules allow only a small difference between risers in one flight, often about 3/8 in. The top of the flight lands on the upper floor, so there is one fewer tread than risers: 14 risers and 13 treads. If the treads are 1 1/2 in thick, cut the first riser 1 1/2 in shorter, 6 in here, so the bottom step is the same height as the rest once its tread is fitted.
Typical limits and comfort rules of thumb
For US residential stairs the commonly cited limits are a riser no taller than 7-3/4 in, a tread at least 10 in deep and headroom of at least 6 ft 8 in, taken from IRC R311.7. Headroom is typically measured straight up from the line along the front edges of the treads. These are typical values: your local code decides, and it can differ. Separate from code, two rules of thumb describe stairs that feel comfortable: twice the riser plus the tread usually falls between 24 and 25 in, and riser plus tread between 17 and 18 in. The default layout gives 2 × 7.5 + 10 = 25 in and 7.5 + 10 = 17.5 in, at the upper end of both. A steeper stair has a taller riser and shorter tread; a shallower one needs more run, so check there is room before you pick a tread depth.
Stringer length, angle and the wood left under the notches
The stringer follows the diagonal of the whole flight, so its layout line is the square root of (total rise² + total run²): √(105² + 130²) = 167.11 in, or 13.93 ft. The calculator then picks the next standard board length that covers it, from 8, 10, 12, 14, 16 or 20 ft, here 14 ft, and warns that 0.9 in of spare length is tight because the end cuts need extra. The angle is arctan(riser ÷ tread) = arctan(7.5 ÷ 10) = 36.87°. The throat is the wood left under the deepest part of each notch. On a 2×12 (11.25 in deep) the default layout leaves a 5.25 in throat; the calculator warns below 3.5 in. The throat is a layout number only: check span, support and fixings with your local code or an engineer.
Work it out
Change the inputs to work out your own numbers. Each step of the working is shown with the answer.
Your measurements
Enter the total rise and the step sizes you would like. Everything updates as you type.
The flight
From the finished lower floor to the finished upper floor, measured at the stairs.
What you would like. The calculator rounds to a whole number of risers, then gives the exact height.
The horizontal depth of each step along the stringer, not counting the overhang.
The stringer board
The real width, not the nominal one. A 2x12 is about 11.25 in.
Used to shorten the first riser cut. Two 2x boards or one 5/4 deck board are typical; measure yours.
Results
Number of risers
risers
= 13 treads, the upper floor is the top step
Each riser is 7.5 in. The stringer angle is 36.87 degrees and 5.25 in of wood is left under the notches.
- Riser height
- 7.5 in
- = 191 mm
- Target was 7.25 in
- Total run
- 130 in
- = 3302 mm
- 13 × 10 in
- Board to buy
- 14 ft
- Layout line 13.93 ft (167.11 in)
- First riser cut
- 6 in
- = 152 mm
- Riser less 1.5 in tread
Check before you cut
- The 14 ft board is only 0.9 in longer than the layout line. The end cuts need some extra, so check the layout on the board or buy the next length up.
Layout marks
Height of each step and its distance from the first riser, in tape-measure fractions. Step 1 is the bottom step; the last step is the upper floor.
Layout marks
Height of each step and its distance from the first riser, in tape-measure fractions. Step 1 is the bottom step; the last step is the upper floor.
| Step | Height of the step | Distance from the first riser |
|---|---|---|
| 1 | 7 1/2" | 0" |
| 2 | 15" | 10" |
| 3 | 22 1/2" | 20" |
| 4 | 30" | 30" |
| 5 | 37 1/2" | 40" |
| 6 | 45" | 50" |
| 7 | 52 1/2" | 60" |
| 8 | 60" | 70" |
| 9 | 67 1/2" | 80" |
| 10 | 75" | 90" |
| 11 | 82 1/2" | 100" |
| 12 | 90" | 110" |
| 13 | 97 1/2" | 120" |
| 14 | 105" | 130" |
How this was calculated
Risers, run, stringer length, angle and throat, with your numbers.
How this was calculated
Risers, run, stringer length, angle and throat, with your numbers.
Step 1: Number of risers
total rise ÷ target riser, rounded to a whole number
= 105 ÷ 7.25 = 14.48
= 14 risersA flight has a whole number of risers, so the target riser height is only a starting point. The top step is the upper floor, so it counts as a riser but has no tread.
Step 2: Exact riser height
total rise ÷ risers
= 105 ÷ 14
= 7.5 in (7 1/2")Every riser is this height. Code usually limits how much risers may differ from each other, so cut them all the same.
Step 3: Treads and total run
treads = risers − 1, total run = treads × tread depth
= 14 − 1 = 13, 13 × 10
= 13 treads, 130 in of runThe upper floor is the last step, so there is one less tread than risers. The run is how far the stairs reach along the floor.
Step 4: Stringer length
√(total rise² + total run²)
= √(105² + 130²)
= 167.11 in (13.93 ft)This is the layout line along the stringer. Buy the next standard length, 14 ft. The end cuts need a little extra, so check the layout on the board before you cut.
Step 5: Stringer angle
atan(riser ÷ tread)
= atan(7.5 ÷ 10)
= 36.87 degreesThe angle of the stairs from the floor. A framing square set to the riser and tread gives you this angle without measuring it.
Step 6: Wood left under the notches (throat)
board width − (riser × tread) ÷ √(riser² + tread²)
= 11.25 − (7.5 × 10) ÷ √(7.5² + 10²)
= 5.25 inThe shortest distance from the inside corner of a notch to the far edge of the board. This is the wood that carries the load, so a thin throat is a weak stringer.
Step 7: First riser cut
riser − tread thickness
= 7.5 − 1.5
= 6 in (6")The bottom of the stringer is cut shorter by the thickness of a tread, so the first step is the same height as the others once its tread is on.
Step 8: Comfort check
2 × riser + tread, and riser + tread
= 2 × 7.5 + 10, 7.5 + 10
= 25 in and 17.5 inRules of thumb: stairs that feel comfortable usually have 2 × riser + tread between 24 and 25 in, and riser + tread between 17 and 18 in. They are guides, not code.
Troubleshooting
What usually goes wrong, how to check for it, and how to prevent it.
The bottom or top step is a different height from the others
- Cause
- The first riser was not shortened by the tread thickness, or total rise was measured to a subfloor instead of the finished floor
- How to check
- Measure every riser from tread surface to tread surface once the treads are fitted
- Prevention
- Measure rise between finished surfaces and subtract the tread thickness from the first riser cut (6 in with 1 1/2 in treads and a 7.5 in riser)
Risers vary from step to step
- Cause
- Each riser was cut to a target height instead of dividing the measured total rise equally
- How to check
- Measure all the risers; typical rules allow only a small difference within a flight, often about 3/8 in
- Prevention
- Divide the measured total rise by the number of risers and mark the stringer from a single story pole or one layout
The stringer comes up short or looks thin at the notches
- Cause
- The board was only as long as the layout line, leaving no allowance for end cuts, or the board is too narrow for the step size
- How to check
- Board length minus layout line is under about 6 in, or the throat is under 3.5 in
- Prevention
- Buy the next length up, choose a wider board or shallower steps, and lay the pattern out on the board before cutting
Common questions
How many steps do I need for a 105 inch rise?
With a 7.25 in target riser, 105 ÷ 7.25 rounds to 14 risers of 7.5 in each. A flight has one fewer tread than risers, so you build 13 treads. At 10 in per tread the total run is 130 in.
What is the maximum riser height and minimum tread depth?
Typical US residential limits are a riser no taller than 7-3/4 in and a tread at least 10 in deep, as commonly cited from IRC R311.7. Local codes are adopted and amended, so check your local code before you build.
What is the 2R + T rule?
It is a comfort rule of thumb, not code: twice the riser plus the tread usually falls between 24 and 25 in on comfortable stairs. A 7.5 in riser with a 10 in tread gives 25 in.
How do I work out the stringer length?
Take the square root of (total rise squared + total run squared). For 105 in of rise and 130 in of run that is 167.11 in, or 13.93 ft, so buy a 14 ft board at least, and a longer one if you want room for the end cuts.