Stair Calculator
Calculate stair dimensions including rise, run, number of steps, and stringer length
Enter Your Measurements
Calculator will determine optimal rise (7.5") and run (11")
Quick Answer
Building code requires maximum 7.75" rise per step and minimum 10" run. The ideal rise is 7-7.5 inches with an 11" run for comfortable, safe stairs that meet IRC 2021 standards.
Designing safe, comfortable stairs requires precise calculations and code compliance. This calculator helps you determine the optimal number of steps, rise, run, and stringer length based on your total height (rise) while ensuring your stairs meet building code requirements.
Dr. Snezana Lawrence
Mathematical Historian
15+ years experience
PhD from Yale University. Published mathematical historian ensuring precision in all calculations.
Education
PhD in Mathematical History - Yale University
How to Calculate Stair Dimensions
- 1
Measure Total Rise
Measure the total vertical height from the lower floor to the upper floor in feet and inches.
- 2
Calculate Number of Steps
Divide total rise by ideal rise (7-7.5") to get number of steps.
- 3
Determine Rise Per Step
Divide total rise by number of steps = exact rise per step.
- 4
Choose Run Per Step
Select a run per step (10-11" is ideal).
- 5
Calculate Total Run
Total run = (Steps - 1) × Run per step
Example Calculation
Total rise = 108 inches (9 feet)
- • Steps needed: 108 ÷ 7.5 = 14.4, round to 15 steps
- • Rise per step: 108 ÷ 15 = 7.2 inches ✓
- • Run per step: 11 inches (your choice)
- • Total run: 14 × 11 = 154 inches (12' 10")
- • Stringer length: √(108² + 154²) = 188 inches (15' 8")
Building Code Requirements (IRC 2021)
| Requirement | Minimum | Maximum |
|---|---|---|
| Rise per step | 4 inches | 7.75 inches |
| Run per step | 10 inches | No max |
| Stair width | 36 inches | No max |
| Headroom | 80 inches | No max |
| Handrail height | 34 inches | 38 inches |
| Rise consistency | Within 3/8" | N/A |
| Nosing | 0.75 inches | 1.25 inches |
Key Rules
- • Maximum rise: 7.75 inches (7-3/4")
- • Minimum run: 10 inches
- • All rises must be within 3/8" of each other
- • All runs must be within 3/8" of each other
- • Minimum 36" width
- • Minimum 80" headroom
Stringer Sizing Guide
| Total Rise | Recommended Stringer |
|---|---|
| Up to 7 feet | 2×10 |
| 7-10 feet | 2×12 (most common) |
| 10-12 feet | 2×14 |
| Over 12 feet | Engineered or doubled 2×12 |
Stringer Calculation Tips
- • Length = √(Total Rise² + Total Run²)
- • Use Pythagorean theorem
- • Add 12-18" for top and bottom attachment
- • Minimum 3.5" remaining after notching
Frequently Asked Questions
How do I calculate the number of steps I need?
Divide your total rise (in inches) by 7.5. Round to the nearest whole number. Example: 108" ÷ 7.5 = 14.4, round to 14 or 15 steps.
What is the ideal rise and run for stairs?
Ideal rise is 7-7.5 inches per step with a 10-11 inch run. This creates comfortable, safe stairs that meet building codes.
How do I calculate stringer length?
Use Pythagorean theorem: √(Total Rise² + Total Run²). Example: √(108² + 154²) = 188 inches or 15 feet 8 inches.
What is the maximum rise per step allowed by code?
IRC 2021 code allows maximum 7.75 inches (7-3/4") rise per step and minimum 10 inches run per step.
How many stringers do I need for stairs?
Minimum 2 stringers for stairs up to 36" wide. For 36-48" wide stairs, use 3 stringers. Over 48", add a stringer every 16".
Can I use 2×10 for stair stringers?
Yes, 2×10 works for short stairs (under 7 feet rise). For most stairs, use 2×12. Ensure at least 3.5" remains after cutting notches.
What if my rise per step is 8 inches?
8" rise exceeds IRC 2021 maximum of 7.75". Recalculate with more steps to reduce rise, or check local codes (some jurisdictions allow 8").
How much does stair angle matter?
Ideal stair angle is 30-35 degrees. Under 30° is too shallow (wastes space), over 40° is too steep (uncomfortable/unsafe).
Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
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