How is the number of risers determined?

Divide the total rise by your target riser height and round to the nearest whole number, since every riser must be equal. The actual riser height is then the total rise divided by that whole number of risers.

Why is there one fewer tread than risers?

The top riser lands on the upper floor, which is not a tread, so a flight always has one more riser than treads. A stair with 14 risers has 13 treads, and the total run is 13 times the tread depth.

How is the stringer length calculated?

The stringer is the diagonal of the triangle formed by total rise and total run: length equals the square root of (total rise squared plus total run squared). This is the cut length of the stringer board before notching.

What are the IBC rise and run limits?

The International Building Code caps riser height at 7-3/4 inches and requires a minimum tread depth of 10 inches for most occupancies. Many builders also apply the comfort rule that twice the rise plus the run falls between about 24 and 25 inches.

Does this work in metric?

Yes. Switch units and the same geometry applies with millimetres. Common residential limits abroad differ, so the IBC checks shown are a guide; confirm against your local building regulations.

Stair Stringer Calculator

A safe, comfortable stair depends on equal risers and a consistent tread depth within code limits. This calculator takes your total floor-to-floor height, finds the riser count and exact dimensions, then gives the diagonal stringer length and the stair angle, flagging anything outside common IBC limits.

How it works

The total rise is divided into equal risers, and the treads follow:

riser count = round(total rise / target riser)
riser height = total rise / riser count
tread count  = riser count − 1
total run    = tread count × tread depth
stringer len = √(total rise² + total run²)
angle        = arctan(total rise / total run)

Code checks compare the riser height against 7-3/4 in max, the tread depth against 10 in min, and twice the rise plus the run against the 24 to 25 in comfort band.

Example and notes

A total rise of 108 in with a target 7.5 in riser gives round(108/7.5) = 14 risers, so each riser is 7.71 in and there are 13 treads. At 10.5 in tread depth the total run is 136.5 in and the stringer is sqrt(108² + 136.5²) = about 174 in at roughly 38.4 degrees. Always lay out from the actual measured total rise, and remember the bottom riser is cut shorter by one tread thickness when the treads sit on the stringers.