Climbing Fall Factor & Impact Force Calculator

How it works

fall factor = fall length ÷ rope out = (2 × height above gear + slack) ÷ rope out · peak force F = mg + √( (mg)² + 2 mg k × FF ), k from the rope's rating: F_rated = m₈₀g + √( (m₈₀g)² + 2 m₈₀g k × 1.77 ) · top-piece load ≈ 1.66 × F

What hurts in a fall is not how far you drop but how hard the rope has to stop you, and that depends on the ratio of the fall length to the amount of rope available to stretch — the fall factor. A short fall onto a short length of rope near the belay can be far more violent than a long whipper high on a pitch, because the energy is the same per metre fallen while the rope that absorbs it is a fraction as long. Treating the rope as a spring gives a closed-form peak force in which the fall factor, not the height, appears, and the spring constant can be recovered from the standardised UIAA drop test that rope makers publish. The load then multiplies at the top piece, where the rope changes direction and the belayer's side adds to the climber's, which is why the top runner is the one that fails.

Worked example

Three metres above the last bolt with a metre of slack and 15 m of rope out gives a 7 m fall and a fall factor of 0.47. For an 80 kg climber on a rope rated 8.5 kN, the peak force is about 4.8 kN with a static belay (roughly 6 g), or 3.9 kN with a dynamic belay, and the top bolt sees about 6.4–8 kN — a hard but ordinary catch. The same 7 m fall with only 4 m of rope out would be factor 1.75 and around 8.4 kN.

Frequently asked questions