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Pythagoras²Equation Solver
Navigationa² + b² = c²
معيار السلامة OSHA 4:1L = √(h² + (h/4)²)

حاسبة أمان السلم وزاوية الميل

Calculate compliant OSHA 4:1 ladder standoff, safe ~75.96° inclination angle, and minimum working reach before climbing. Studying general right-triangle math or missing side problems? Return to our Pythagoras equation solver.

Interactive Pitch Angle Gauge+3 ft / +0.91 m Roof Extension ToggleFeet & Meters Support
Result updated: Base standoff is 4 ft, pitch angle is 76 degrees (Safe OSHA zone), minimum ladder length is 19.49 ft.

حاسبة أمان السلم وزاوية الميل

OSHA 4:1 Rule: base = h / 4 · L = √(h² + base²) · θ ≈ 75.5°–76°

Enter the vertical wall height from ground to the top contact point.
Steeper (>79° Tip Risk)0%: Exact OSHA 4:1Shallower (<71° Slip Risk)
منطقة OSHA الآمنة 4:1
زاوية ميل السلم: 75.96°
76°
المسافة الآمنة للقاعدة
4 ft
الطول الأدنى للسلم
19.49 ft
Reach: 16.49 ft
θ = 76°base = 4 fth=16ftL = 19.49 ft

قائمة التحقق لتثبيت السلم بأمان

  • Set ladder base 4 ft away from wall (OSHA 4:1 rule for 16 ft height).
  • Verify ladder working reach L = √(16² + 4²) ≈ 16.49 ft.
  • Add 3 ft roof landing extension → select ladder ≥ 19.49 ft.
  • Safe OSHA Pitch (75.96°): Balanced against backward tip and base slip.

قائمة التحقق لتثبيت السلم بأمان

01

Measure Eave or Support Height (h)

Determine the vertical contact height. Never guess ladder reach by height alone because angling the base consumes vertical length.

02

Set 4:1 Base Standoff (b = h ÷ 4)

Position feet out 1 ft per 4 ft of wall height (0.25 m per 1 m). This hits ~75.96°, squarely inside the OSHA 72°–78° safe pitch band.

03

Include +3 ft (+0.91 m) Roof Extension

When transitioning onto a roof deck, add 3 feet past the gutter/eave line so your hands maintain three-point grip while stepping off.

04

Perform Elbow & Foot Check

Stand upright with toes touching the ladder rails and extend arms straight ahead—your palms should comfortably touch the rung at shoulder height (~75.5°).