How to use this calculator
Choose what to find. Enter the ladder length and weight, the person’s weight, the friction coefficient at the floor and at the wall (0 for a smooth wall), and the angle or the person’s position. The ladder’s own weight acts at its middle.
Formulas
Slipping about to start at both endsNA = W + Wp1 + μAμB NB = μANA
Moments about the footNBL sin θ + μBNBL cos θ = (W L/2 + Wpd) cos θ
Worked example
5 m, 200 N ladder at 60°, μ = 0.3 at the floor, smooth wall, 800 N person (the default)
- NA = 200 + 800 = 1000 N, and slipping starts when NB = FA = 0.3 × 1000 = 300 N.
- Moments about the foot: 300 × 5 sin 60° = (200 × 2.5 + 800 d) cos 60°.
- 1299.0 = 250 + 400 d, so d = 2.62 m: just over halfway up.
Frequently asked questions
Why does the ladder slip as I climb?
Your weight moves farther from the foot, so its moment about the foot grows. The wall has to push harder to balance it, and the floor friction that resists that push runs out.
What makes a ladder safer?
A steeper angle (the usual rule is about 75°), a grippy floor, or someone holding the foot. A heavier ladder with its weight low also helps.