Stair Calculator

How do you calculate stair rise and run?

Divide the total rise by an ideal 7 in step, round to a whole number of risers, then divide the rise back by that count for the height every riser gets cut to. The run comes from multiplying the tread depth by the tread count, one less than the riser count.

Take a deck at 36 in of total rise: 36 over 7 gives 5.14, a fractional count that has to become a whole number because every riser in the flight is cut to one line. Rounding to 5 risers puts the real step height at 7.20 in. Five risers carry four treads, so at 10.5 in apiece the flight takes up 42 in of floor.

What is the maximum stair riser height?

The International Residential Code caps a riser in a home at 7 3/4 in and puts the minimum tread depth at 10 in, both under R311.7.5. Nearby subsections of R311.7 call for 36 in of clear stair width and 80 in of headroom, the vertical clearance measured plumb from the nosings, that is the front edges of the treads, to the ceiling over the flight.

Risers in one flight may not differ by more than 3/8 in. The classic failure is a carpenter who marks fourteen risers at 7.25 in off a story pole, forgets to shorten the bottom notch by one tread thickness, then finds the first step standing 1 1/2 in proud of the other thirteen, four times the tolerated variation.

A porch at 24 in of rise rounds to 3 risers of 8.00 in, a quarter inch over the cap, so the verdict turns red and the panel offers 4 risers of 6.00 in as the smallest count that passes.

Those figures are the common US residential values and cities and counties amend them often, so the building department with jurisdiction has the final say. Read what the calculator returns as a design starting point, never as an approval. Check the code year in force before touching an existing flight built under an older edition.

How do you calculate stair stringers?

The stringer, the sawtooth board cut to carry the treads, runs along the hypotenuse of the triangle drawn by the total rise and the total run, so Pythagoras gives its length. A basement flight of 105 in of rise over a 140 in run puts the diagonal at exactly 175 in.

A stair stringer calculator reports that raw diagonal before any joinery, so the board itself has to run longer to absorb the plumb cut at the top and the level cut at the bottom.

How steep can a staircase be?

The diagram redraws itself at the angle of the flight, the arctangent of the total rise over the total run. A deck at 36 in over a 42 in run reads 40.6°, steeper than the 34.4° pitch of any single step on it, because the run counts one tread fewer than the rise counts risers. The 108 in basement stair closes that gap at 36.3° against the same 34.4° step pitch.

The steepest step the IRC tolerates is a 7 3/4 in riser over a 10 in tread, about 37.8° measured step by step. The riser height and the tread depth are what an inspector puts a tape on.

Riser count and stringer length by total rise

Every row below uses a 10.5 in tread depth and the same rounding as the calculator. The rise most people arrive with is 108 in.

How do you size deck stairs for a 36 in rise?

Deck rise runs from the top of the decking down to the top of the landing pad, never down to bare soil, since the pad ends up an inch or two above grade and a flight sized to dirt sits short. A 36 in rise resolves to 5 risers of 7.20 in over a 42 in run.

Exterior treads change the comfort reading, since anyone using this as a deck stair calculator ends up with the standard outdoor build of two 2x6 boards with a drainage gap between them, close to 11.25 in of effective depth. That depth pushes 2R + T to 25.65 in and trips the amber note even though the riser and the tread both stay legal, a carpenter's comfort rule rather than a code limit.

Guards and handrails sit in separate sections of the code and come into play once the walking surface stands more than 30 in above grade. A 36 in deck clears that line by 6 in, so the flight needs a graspable handrail on at least one side.