Stair rise, run and stringers explained
What total rise, riser, tread run and stringer mean, how the step count and stringer length are found, and the comfort ratios that make stairs feel right.
The four measurements that define a stair
Every straight stair comes down to a few numbers. Total rise is the vertical distance from one finished floor to the next. The riser is the height of a single step, and the tread run is its depth. Add the treads together and you get the total horizontal run. The stringer is the sloped board the steps sit on, and its length ties the whole geometry together. Get these four right and the stair is safe and buildable.
How the step count and riser height are set
You do not choose the riser height directly; you choose a target and let the arithmetic settle the rest. The tool divides the total rise by your ideal riser and rounds to the nearest whole number of steps, because you cannot build a fraction of a step. It then divides the rise evenly by that count so every riser is identical. A 108 inch rise with a 7 inch target rounds to 15 steps, giving exact 7.2 inch risers.
The stringer as a right triangle
The stringer length falls straight out of the Pythagorean theorem. The total rise and total run are the two legs of a right triangle, and the stringer is the hypotenuse: the square root of rise squared plus run squared. A 60 inch rise and an 80 inch run form a familiar 3-4-5 style triangle and yield a 100 inch stringer. Longer or steeper stairs simply scale that same relationship.
Comfort rules and code ranges
Builders lean on rules of thumb so stairs feel natural underfoot. One common guide keeps twice the riser plus the tread run between about 24 and 25 inches, which is why a 7 inch riser pairs well with a 10 or 11 inch tread. Most residential codes cap risers near 7.75 inches and set a minimum tread depth around 10 inches. Staying inside those ranges keeps the climb even and reduces trips, but always verify the exact figures locally.