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Stairs are a stacked series of identical right-angle triangles maintaining a slope between 30° and 38°. Each rise and each tread are the same therefore each hypotenuse is the same. This means that the outside point of each tread is equal distant from the previous and the next one. Building Stairs Stairs are made up of risers(r) and treads(t). Risers are the height of each step and tread is the width of the step. NBCC allows risers between 4 7/8″ and 7 7/8″. Treads between 14″ and 9 1/4″. Ideal risers are between 7″ & 7 7/8″. Treads are between 11″ & 9 1/4″. NBCC - states that the ideal stair formula is 1 rise + 1 tread = 17″ & 18″ or 2r + 1t = 24″ to 25″. Example; rise = 7.5″, tread= 10″ ∴ 1r+1t= 17.5″ or 2r (2 x 7 1/2″ = 15″) + 1t (10″) = 25″. The rise may be adjusted but the run/ tread must also adjust accordingly. Stair calculations must always take into account the rise (height) and run(length) of the space where the stair is going. 
Calculating # of steps Staircase Over all Height (OH) is calculated from finished upper floor to finished lower floor. The number of treads in a run = the number of risers - 1 unless the top step is flush with OH We are looking for a step rise between 7″ and 7 7/8″. To calculate the number of risers, start by dividing the OH by 7 1/2″. If the answer is not even then round it off up or down and divide the OH by these numbers. Choose the answer that lies between 7″ & 7 7/8″. Example (OH-finished floor) OH = 10′-6 5/8″ = 126.625″ 126.625″ ÷ 7.5″ = 16.88 - round up to 17 126.625″ ÷ 17 = 7.45″ = 7 29/64″ = 7 7/16″ Riser height = 7.45&Prime = 7 7 /16″, tread = 10″, Hypotenuse/diagonal = 12.47″ = 12 15/32″ = 12 1/2″ Staircase will have 17 steps with a 7 7/16″ rise and 10″ run Stringer story pole The total stringer run(TSR) from the bottom tread to the top tread will be the length of the hypotenuse x the number of treads. TSR = 12 15/32″ x 17 = 211 31/32″ = 212″ calculate the increments of 12 15/32″ into 211 31/32″. 0, 12 15/32″, 24 15/16″, 37 13/32″, 49 7/8″... all the way to 211 31/32″ Write these numbers down. You will get a more accurate layout if equal distance between treads is the maintained. 
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