Stair Calculator (Rise and Run)
Enter your floor-to-floor height and preferred riser and tread dimensions to calculate how many steps you need, the exact riser height, total staircase run, and angle.
What is Stair (Rise and Run)?
A stair calculator determines the optimal number of risers and treads for a staircase based on the total vertical rise between two floors. It divides the total rise evenly among the risers so every step is the same height, which is critical for safety — uneven risers are the leading cause of stairway trips and falls. The total rise is the vertical distance from the finished floor at the bottom to the finished floor at the top. For a standard 9-foot ceiling with typical floor framing, the total rise is approximately 108 inches. The calculator divides this by the desired riser height (typically 7 to 7.75 inches) and rounds to the nearest whole number to determine how many risers are needed. It then recalculates the actual riser height by dividing the total rise evenly among that number of risers. The number of treads is always one less than the number of risers because the top floor serves as the final landing surface. Each tread has a depth (the horizontal surface you step on), typically 10 to 11 inches for residential stairs. The total run is the horizontal distance the staircase covers, calculated by multiplying the number of treads by the tread depth. Building codes govern stair dimensions strictly. The International Residential Code (IRC) requires a maximum riser height of 7.75 inches and a minimum tread depth of 10 inches. The riser-tread relationship should also satisfy the comfort rule: the sum of two risers and one tread should fall between 24 and 25 inches (2R + T = 24 to 25). For a 7.5-inch riser and 10-inch tread, the sum is 25 — ideal for a comfortable, natural gait. The stair angle affects both comfort and usability. Residential stairs typically fall between 30 and 37 degrees. Angles below 30 degrees feel like ramps and waste floor space. Angles above 37 degrees feel steep and are harder for elderly residents or when carrying items. The calculator computes this angle from the inverse tangent of the total rise divided by the total run. Getting these proportions right is essential for code compliance, safety, and daily comfort. Even a quarter-inch deviation in riser height is noticeable underfoot and can create a trip hazard over years of use.
How to Calculate
- Measure the total rise from finished floor to finished floor in inches
- Choose a desired riser height (7.5 inches is a good residential default)
- Choose a tread depth (10 inches meets code minimum)
- Review the number of risers and treads, actual riser height, total run, and angle
- Verify the actual riser height is under 7.75 inches (IRC maximum)
- Verify you have enough horizontal space to accommodate the total run
Formula
Number of Risers = round(Total Rise / Desired Riser Height) Number of Treads = Risers - 1 Actual Riser Height = Total Rise / Number of Risers Total Run = Number of Treads x Tread Depth Stair Angle = arctan(Total Rise / Total Run) in degrees The round function ensures you get a whole number of equal-height risers that divide the total rise exactly. The actual riser height may differ slightly from your desired height to achieve this even division.
Example Calculation
A staircase with 108 inches of total rise (9-foot ceiling), 7.5-inch desired riser, and 10-inch treads: Number of Risers = round(108 / 7.5) = round(14.4) = 14 risers Number of Treads = 14 - 1 = 13 treads Actual Riser Height = 108 / 14 = 7.714 inches (under 7.75 max — code compliant) Total Run = 13 x 10 = 130 inches (10 ft 10 in) Stair Angle = arctan(108 / 130) = 39.7 degrees Comfort check: 2(7.714) + 10 = 25.43 — slightly above the ideal 24-25 range. You could try a 7-inch desired riser for a shallower, more comfortable stair.
Frequently Asked Questions
What is the maximum riser height allowed by code?
The International Residential Code (IRC) sets a maximum riser height of 7 3/4 inches (7.75 inches) and a minimum tread depth of 10 inches. Some local jurisdictions may have stricter requirements, so always check your local building code before finalizing stair dimensions.
Why does the actual riser height differ from my desired height?
The calculator rounds to a whole number of risers so that every step is exactly the same height. If 108 inches divided by 7.5 gives 14.4, you cannot have 0.4 of a riser — so the calculator uses 14 risers and recalculates each to 7.714 inches. Uniform risers are a code requirement and critical safety feature.
How do I account for floor thickness in the total rise?
The total rise must be measured from finished floor surface to finished floor surface, including any subfloor, underlayment, and finish flooring (tile, hardwood, carpet) at both levels. If the finish floor is not yet installed, add its expected thickness to your measurement.
What is a comfortable stair angle?
Residential stairs are most comfortable between 30 and 37 degrees. This range corresponds to risers of about 6.5 to 7.75 inches with 10 to 11-inch treads. Steeper stairs save floor space but are harder to climb, especially for elderly residents or when carrying loads.
How much headroom do I need above the stairs?
Building code requires a minimum of 6 feet 8 inches (80 inches) of headroom measured vertically from the tread nosing to the ceiling or any overhead obstruction. This clearance must be maintained along the entire length of the stairway and at the landings.
Do I need a landing in my staircase?
The IRC requires a landing at the top and bottom of every stairway. The landing must be at least as wide as the stair and at least 36 inches deep in the direction of travel. Stairs with more than 12 feet of vertical rise typically require an intermediate landing as well.