Climbing Rope Fall Force Calculator (Fall Factor)
See the peak force a climbing fall puts on the rope and gear, from the fall factor, rope length, and climber weight.
Get the result in kN and body weights.
Understanding fall forces is critical for climber safety. The peak impact force depends on the fall factor, climber weight, and rope characteristics. The key concept is the fall factor.
Fall Factor
Fall Factor = Fall Distance / Length of Rope Out
Fall factor ranges from 0 to 2:
- Factor 0: No fall (lowering)
- Factor 0.5: Typical sport climbing fall
- Factor 1.0: Falling to the level of the belayer with no slack
- Factor 2.0: Worst case — falling past the belayer with the full rope length
Impact Force Formula (simplified)
The classic formula from climbing physics:
F = mg + mg × √(1 + 2kf/mg)
Where:
- F = peak impact force (Newtons)
- m = climber mass (kg)
- g = 9.81 m/s²
- k = rope modulus (stiffness) in N
- f = fall factor
A more practical version uses the rope’s stated impact force rating. The UIAA test drops an 80 kg mass with fall factor 1.78 on 2.8 m of rope. Typical dynamic ropes have a rated impact force of 8–10 kN under this test.
Scaled Impact Force
F_actual = F_rated × (Weight / 80) × √(Fall Factor / 1.78)
Worked Example
Climber: 75 kg. Rope rated at 8.5 kN. Fall factor: 1.0. F = 8.5 × (75/80) × √(1.0/1.78) = 8.5 × 0.9375 × 0.7497 = 5.98 kN
Force Reference Table
| Fall Factor | 60 kg Climber | 75 kg Climber | 90 kg Climber |
|---|---|---|---|
| 0.3 | 2.3 kN | 2.9 kN | 3.4 kN |
| 0.5 | 3.0 kN | 3.7 kN | 4.4 kN |
| 1.0 | 4.2 kN | 5.3 kN | 6.3 kN |
| 1.5 | 5.2 kN | 6.5 kN | 7.7 kN |
| 2.0 | 6.0 kN | 7.5 kN | 9.0 kN |
Safety Thresholds
- UIAA maximum: 12 kN (rope must not exceed this)
- Human tolerance: Serious injury risk above 12 kN on the body
- Typical sport climbing fall: 3–6 kN
- Carabiner strength: 20–24 kN (major axis)
Rope drag, dynamic belaying, and belay device slippage all reduce the actual force experienced by the climber. These calculations represent a worst-case static scenario.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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