How to use this calculator
Choose what to solve for, the belt type and how the wrap is given (turns or an angle of contact). T₂ is the larger, tight-side tension, on the side toward which the belt slips or would slip; T₁ is the smaller one. Add the drum radius or belt speed to get the torque or power the belt can transmit before slipping.
Formulas
Flat belt or ropeT2 = T1 eμβ, β in radians
V-belt, groove angle αT2 = T1 eμβ / sin(α/2)
Torque and powerM = (T2 − T1) r P = (T2 − T1) v
Worked example
A rope wrapped 1.5 turns around a post, μ = 0.3, held with 50 N (the default)
- β = 1.5 × 2π = 9.425 rad.
- T₂ = 50 e0.3 × 9.425 = 50 × 16.90 = 845 N: the largest load the 50 N pull can hold.
Frequently asked questions
Which side is T₂?
The side the rope or belt is trying to slide toward, which is always the larger tension. When a person holds a load with a rope over a post, the load side is T₂ and the hand is T₁; when hoisting, the pull is T₂.
Why don’t the drum’s radius matter?
The ratio depends only on the friction and the angle wrapped. The radius changes the torque, not the tensions.