Stair Calculator
Your Stair Dimensions:
Number of Risers
Riser Height
Number of Treads
Tread Depth
Total Run
Stair Angle
How Does This Work?
Building a safe and comfortable staircase requires precise calculations. This calculator automates the process based on standard building practices:
- Standardize to Inches: The calculator first converts your total rise from any unit (meters, cm, etc.) into inches to perform the calculations consistently.
- Ideal Riser Height: It divides the total rise by an ideal riser height (typically around 7 inches) to get an estimated number of steps, which is then rounded to the nearest whole number.
- **Actual Riser Height:** The total rise is then divided by the actual number of risers to get a precise, uniform height for each step. This ensures every step is identical, which is crucial for safety.
- Tread Depth: The tread depth is calculated based on a common building rule: 2 × Riser Height + Tread Depth = 25 inches. This rule ensures the staircase has a comfortable and safe angle.
- Total Run: The total horizontal distance the staircase will occupy is calculated by multiplying the tread depth by the number of treads. (There is always one less tread than there are risers).
The Surprising History of Staircase Design
For centuries, staircase design was more of an art form than a science. Many historical staircases are notoriously steep, uneven, and dangerous by today's standards. This was especially true in castles, where steep, narrow spiral staircases gave defenders an advantage against attackers.
The scientific study of staircase ergonomics began in earnest in the 17th century with a French architect named François Blondel. He was the first to mathematically analyze the relationship between the riser height and tread depth. He proposed the formula that is the basis for our modern "2R + T = 25" rule, determining that this ratio matched a person's natural walking stride. His work aimed to make stairs less tiring and safer to climb, moving staircase design from a defensive strategy to one centered on human comfort and safety.
Explore More Related Tools
While you're here, check out some of our other popular construction and math calculators:
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Frequently Asked Questions (FAQ)
Why is there one less tread than the number of risers?
This is because the final "riser" is actually the top floor itself. The last step you take brings you level with the upper floor, so there is no need for a final tread at that level.
What are common building code requirements for stairs?
While codes vary by location, common rules include a maximum riser height of 7.75 inches (~19.7 cm), a minimum tread depth of 10 inches (~25.4 cm), and that the variation between the tallest and shortest riser (or deepest and shallowest tread) should be no more than 3/8 of an inch (~1 cm).
What is the 'Total Run' of the staircase?
The total run is the total horizontal distance the staircase will cover from the front of the first step to the back of the last step. This is a critical measurement for ensuring the stairs will fit in the available space.