What the fall factor is
In lead climbing, the fall factor measures how severe a fall is for the rope and the climber:
Fall factor = fall distance ÷ length of rope paid out
The force on the climber depends on the fall factor, not on the fall length alone. A long fall with lots of rope out can be softer than a short fall close to the belay, because more rope stretches to absorb the energy.
- Under 0.5: a soft fall, typical of falls high on a single-pitch route.
- 0.5 to 1: a moderate to hard fall.
- 1 to 2: a severe fall, typical of a multi-pitch fall onto the anchor before the first piece is clipped. A factor of 2 is the theoretical maximum for a lead fall.
The impact force estimate
Dynamic ropes are tested under the UIAA standard: an 80 kg mass dropped with a fall factor of about 1.77 on a fixed belay. The peak force is the rope’s rated impact force, often 8 to 9.5 kN for single ropes. Treating the rope as a spring, the force for another fall is:
F = mg + √((mg)² + 2 × mg × M × FF)
where M is the rope’s modulus derived from its rated impact force. The calculator uses this classic model.
Example
A 175 lb climber falls 13 ft with 20 ft of rope out, on a rope rated at 8.8 kN:
- fall factor: 13 ÷ 20 = 0.65;
- peak force on the climber: about 5.7 kN, a deceleration of about 7 g;
- load on the top piece: about 9.4 kN, since it holds both the climber’s side and the belayer’s side of the rope;
- force on the belayer: about 3.7 kN.
Why the real force is lower
The model assumes a fixed belay and no friction. In practice:
- a dynamic belay (the belayer moving or letting some rope slip) cuts the force noticeably;
- belay devices slip slightly;
- harness, knots and the climber’s body absorb energy;
- rope drag through carabiners reduces the length of rope that stretches, which can make the force higher.
Practical lessons
- Clip a solid first piece soon after leaving a multi-pitch belay to avoid a factor-2 fall onto the anchor.
- Old ropes and ropes that have held several hard falls lose elasticity; the impact force rises.
- Gear is rated in kN: a typical carabiner holds 20 to 25 kN along its major axis, but much less when cross-loaded or with the gate open. Small cams and nuts in poor rock hold far less.
Climbing is dangerous. This estimate is for education; learn to place and test protection from qualified instructors.