Climbing Fall Factor and Impact Force Calculator
Fall factor of a lead fall and an idealised estimate of the peak force on the climber, from the fall length, the rope out and the rope's rated impact force.
Results
What this tool does
In climbing it is not the length of a fall that hurts but the fall factor, the distance fallen divided by the rope available to absorb it. A 4 m fall on 6 m of rope (factor 0.67) is gentler than a 2 m fall onto the anchor on 1 m of rope (factor 2, the worst a normal lead fall can be). The force comes from treating the rope as a spring, with the stiffness worked out from the impact force on its label, which the standard drop test measures with an 80 kg mass at a fall factor of about 1.77. Real falls are softer because of belayer movement, rope slipping through the device, friction in the quickdraws and the body itself, and ropes get stiffer with age and after big falls; this is a teaching tool, not a safety calculation.
Formula
f = fall length ÷ rope out · F = mg + √((mg)² + 2 mg f EA)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
fl | Length of the fall | m |
rl | Rope paid out between climber and belayer | m |
m | Climber with gear | kg |
fr | Rope's rated impact force (on the label) | kN |
FF | Fall factor | — |
IF | Peak force on the climber (ideal rope) | kN |
GL | Peak deceleration | g |
ST | Rope stretch at that moment | m |
EA | Rope stiffness implied by the rating (EA) | kN |
Worked example
- Length of the fall4 m
- Rope paid out between climber and belayer6 m
- Climber with gear80 kg
- Rope's rated impact force (on the label)8.5 kN
- Fall factor0.67
- Peak force on the climber (ideal rope)5.56 kN
- Peak deceleration7.1 g
- Rope stretch at that moment1.57 m
- Rope stiffness implied by the rating (EA)21.2 kN
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.