Staircase Riser Calculator Formula
Understand the math behind the staircase riser calculator. Each variable explained with a worked example.
Formulas Used
Number of Risers
risers = round(total_rise / target_riser)Actual Riser Height
actual_riser_height = total_rise / round(total_rise / target_riser)Number of Treads
num_treads = round(total_rise / target_riser) - 1Total Horizontal Run
total_run = (round(total_rise / target_riser) - 1) * tread_depthRiser + Tread Sum
rule_check = total_rise / round(total_rise / target_riser) + tread_depthVariables
| Variable | Description | Default |
|---|---|---|
total_rise | Total Rise (Floor to Floor)(inches) | 108 |
target_riser | Target Riser Height(inches) | 7.5 |
tread_depth | Tread Depth(inches) | 10 |
num_risers | Derived value= round(total_rise / target_riser) | calculated |
How It Works
How to Calculate Stair Risers
Formula
Number of Risers = round(Total Rise / Target Riser Height)
Actual Riser Height = Total Rise / Number of Risers
Number of Treads = Risers - 1
The International Residential Code limits risers to a maximum of 7-3/4 inches and requires a minimum tread depth of 10 inches. A common comfort rule is that riser + tread should equal 17 to 18 inches.
Worked Example
A floor-to-floor height of 108 inches (9 feet) with a 7.5-inch target riser and 10-inch treads.
- 01Number of risers = round(108 / 7.5) = round(14.4) = 14 risers
- 02Actual riser height = 108 / 14 = 7.714 inches
- 03Number of treads = 14 - 1 = 13 treads
- 04Total run = 13 x 10 = 130 inches (10 ft 10 in)
- 05Comfort check: 7.714 + 10 = 17.71 in (within the 17-18 range)
Frequently Asked Questions
What is the maximum riser height allowed by code?
The IRC allows a maximum riser height of 7-3/4 inches (196 mm). The variation between the tallest and shortest riser in a flight must not exceed 3/8 inch.
Why is there one fewer tread than risers?
The top riser lands on the upper floor, which serves as the final stepping surface. So you only need treads for all the intermediate steps, which is one fewer than the number of risers.
What is the riser-tread comfort rule?
A widely used guideline is that the riser height plus tread depth should total between 17 and 18 inches. Another version uses 2R + T = 24 to 25 inches. Both help ensure a comfortable walking pace on the stair.
Learn More
Guide
How to Calculate Stair Dimensions: Rise, Run, and Stringer Layout
Learn how to calculate stair dimensions including riser height, tread depth, stringer length, and total run. Covers building code requirements and layout techniques.
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