Enter the net tangential belt force (tight-side minus slack-side tension), the radius of the drive pulley, and the efficiency of the drive into the calculator to determine the pulley torque.
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Pulley Torque Formula
The pulley torque calculator uses different formulas depending on the tab you choose. In all modes, the internal calculation is based on SI units, then the result is converted back to the selected display unit.
Force and radius
T = F*r*(E/100)
- T = pulley torque
- F = applied tangential force
- r = pulley radius
- E = drive efficiency as a percent
This mode can solve for torque, force, radius, or efficiency when you enter the other three values.
Power and RPM
omega = 2*pi*RPM/60 T = P*(E/100)/omega
- T = torque
- P = power
- RPM = rotational speed in revolutions per minute
- omega = angular speed in radians per second
- E = transmission efficiency as a percent
This mode converts motor power and speed into shaft torque. If efficiency is left blank, the calculator uses 100% efficiency.
Belt drive ratio
Ratio = D1/D2 N2 = N1*(D1/D2)*(1 - Slip/100) v = pi*D1*N1/60 T2 = T1*(D2/D1)*(E/100) L = 2*C + (pi/2)*(D1 + D2) + ((D2 - D1)^2)/(4*C)
- D1 = driver pulley diameter
- D2 = driven pulley diameter
- N1 = driver speed in RPM
- N2 = driven speed in RPM
- Slip = belt slip percentage
- v = belt speed
- T1 = driver shaft torque
- T2 = driven shaft torque
- C = center distance between pulley shafts
- L = approximate open belt length
- E = transmission efficiency as a percent
This mode calculates speed ratio, driven RPM, belt speed, approximate belt length when center distance is entered, and driven torque when driver torque is entered.
Belt tension
DeltaT = T/r Flat belt: Ttight/Tslack = e^(mu*theta) V-belt: Ttight/Tslack = e^((mu/sin(beta))*theta)
- DeltaT = tension difference between tight side and slack side
- T = pulley torque
- r = pulley radius
- Ttight = tight-side belt tension
- Tslack = slack-side belt tension
- mu = coefficient of friction
- theta = wrap angle in radians
- beta = V-groove half-angle
This mode finds the tight-side and slack-side belt tensions needed to transmit a given torque without exceeding the friction relationship.
Common Pulley Torque Units and Conversions
| Quantity | Common units | Useful conversion |
|---|---|---|
| Torque | N·m, lb-ft | 1 lb-ft = 1.35582 N·m |
| Force | N, lbf, kp | 1 lbf = 4.44822 N |
| Power | W, kW, HP | 1 HP = 745.7 W |
| Angular speed | RPM, rad/s | rad/s = 2*pi*RPM/60 |
Typical Belt Friction and Efficiency Values
| Input | Typical range | Notes |
|---|---|---|
| Flat belt coefficient of friction | 0.20 to 0.35 | Depends on belt material, pulley material, surface condition, and contamination. |
| V-belt coefficient of friction | 0.25 to 0.40 | The groove increases effective grip compared with a flat belt. |
| Good belt drive efficiency | 90% to 98% | Lower values may indicate slip, misalignment, worn belts, or poor tensioning. |
| Small belt slip | 0% to 3% | Slip lowers the driven pulley speed from the ideal speed ratio. |
Example Problems
Example 1: Torque from force and radius
You apply 500 N of tangential force to a pulley with a radius of 0.15 m. The drive efficiency is 90%.
T = F*r*(E/100) T = 500*0.15*(90/100) T = 67.5 Nm
The pulley torque is 67.5 N·m.
Example 2: Torque from power and RPM
A motor delivers 2 kW at 1750 RPM through a drive with 95% efficiency.
omega = 2*pi*1750/60 = 183.26 rad/s T = 2000*(95/100)/183.26 T = 10.37 Nm
The transmitted torque is about 10.37 N·m.
FAQ
What is pulley torque?
Pulley torque is the twisting effect applied to a pulley shaft. It depends on the tangential force at the pulley rim and the pulley radius. For a simple force calculation, doubling the force doubles the torque, and doubling the radius also doubles the torque.
Should pulley radius or diameter be used for torque?
Use radius when calculating torque from force, because torque equals force times radius. Use diameter when calculating belt drive speed ratio, because both pulleys are compared by diameter. If you only have diameter and need torque, divide the diameter by 2 to get radius.
Why does efficiency reduce the torque result?
Efficiency accounts for losses from belt flexing, bearing friction, slip, heat, and misalignment. A 90% efficient drive transmits 90% of the ideal torque or power. If you are calculating the input torque required to produce a certain output torque, you need to account for efficiency in the opposite direction.