How to calculate staircase slope | standard slope for staircase | minimum and maximum slope for stairs | how to calculate slope of stairs.

Staircase or stairs is most important part of any type of building such as residential, commercial, factories, public, Hospital and etc. It helps people to comfortably access different floor of a building. When you are thinking about your new task designing and construction of staircase, slope of stair is important factor that ensure it is not too steep. It make comfortable flight between one floor to another.

Staircase may be straight, L shaped, U shaped, spirally curved cantilever split and winder shape. Stair may be in a straight run leading from one floor to another without turn or change in direction, it may change direction to flight connected at 90-degree angle landing and in a multistorey or high rise building its turn 180-degree angle.

Staircase have many component like riser, tread, flight, landing, slop etc. Tread is horizontal part of staircase on which we first apply foot on this for moving from ground floor to upper floor. The tread depth is measured from the back of one tread the back of next and their width is measured from one side to other. Riser is the vertical portion between each tread on the stair, it may be missing in open stair, riser height measured from bottom of each tread to next upper tread, or riser height may also called vertical distance between two tread.

Slope of staircase is defined as inverse tangent of ratio between height of Riser and width of tread or going. As per IS 456, the slope or pitch of staircase or stairs should be between 25 degrees to 40 Degrees. Ideal one is 31 degrees which is equivalent to slope of 6/10 or slope of that step will be 6″ rise over 10″ of horizontal run.

Calculation of staircase slope is very simple and easy process. You just need to know about your exact measurement of Riser height and width of going or tread. Generally height of Riser is range between 6″ to 7″ (150 to 180mm) and width of tread or going is about 10″ to 11″ (250 to 280mm) without nosing.

To calculate staircase slope you divide the height of riser by width of tread or going and then inverse tangent of resulting give you slope of stairs.

**How to calculate staircase slope**

Step1:- measure the height of riser and ensure that all the Riser should be in uniform size. Suppose height of Riser is 7″ (180mm).

Step2:- measure the width of tread or going without nosing if all the tread are in uniform size. Suppose width of tread is 11″ (280mm)

Step3:- take the ratio of Riser height and tread width such as 180/280 = 0.64.

Step4:- figure out the inverse tangent of 0.64 such as tanθ = 0.64, θ = tan^-1 (0.64) = 37 degrees.

**Staircase slope calculation formula**

Slope of staircase is calculated by trigonometric formula that is Tanθ which is equal to ratio of opposite to adjacent in a right triangle such as Tanθ = opposite/adjacent, and θ = tan^-1 (opposite/adjacent), and this value of theta (θ) will give us slope of staircase in degrees. The standard slope or pitch of staircase or stairs should be range between 25 degrees to 40 Degrees.

Slope for steep staircase is varies between 50 to 70 degree such as ship stair, spiral stairs, alternating tread stairs etc. It is used to save space and it shorten the horizontal Run.

Uniform size of Riser and going make easy measurement that ensure more accurate result. I advice you to build a not too steep stairs. 30° to 40° slope is considered as standard.