Calculating stair angle
Calculating stair angles is crucial for building safe and code-compliant staircases. It ensures proper ergonomics, prevents accidents, and meets building regulations. The correct angle (typically 30-40 degrees) affects comfort and safety, influencing riser and tread dimensions. This calculator helps architects, builders, and DIY enthusiasts achieve optimal stair design.
Formula
Angle = arctangent(Rise ÷ Run) × (180 ÷ π). This trigonometric formula calculates the inverse tangent of the vertical rise divided by horizontal run, converting radians to degrees.
Standard Stair Angles Table
| Rise (in) | Run (in) | Angle |
|---|---|---|
| 7.5 | 10 | 36.87° |
| 7 | 11 | 32.47° |
| 8 | 9 | 41.63° |
| 6.5 | 12 | 28.44° |
FAQs
1. Why is stair angle important?
Stair angle affects safety and comfort. Too steep (>50°) becomes dangerous, too shallow (<20°) wastes space. Ideal angles (30-40°) balance these factors while meeting building codes.
2. What's the formula derivation process?
The formula comes from right-triangle trigonometry. Rise and run form vertical and horizontal sides. Tangent(angle) = opposite/adjacent (rise/run), so angle = arctan(rise/run).