Calculate pulley torque from motor power and RPM or belt tensions, and find driven pulley speed (RPM) and ratio from the two pulley diameters.

Efficiency and result unit
Blank uses 100%. Output power divided by input power; includes slip losses.

Pulley Torque Formula

The calculator has three solve modes: torque from measured belt tensions, torque from input power and actual target-shaft RPM, and driven speed and torque from a two-pulley drive. Calculations use SI units internally before conversion to the selected display units. In the power and drive modes, efficiency means overall output power divided by input power, including the losses being modelled.

Force and radius

T = (Ttight - Tslack)×r
  • T = net pulley torque
  • Ttight = measured tight-side belt tension
  • Tslack = measured slack-side belt tension
  • r = pulley pitch/effective radius

In Torque from belt tension, enter both tensions and the pulley pitch/effective radius. The calculator finds net torque from their difference; it does not solve inverse force, radius or efficiency problems. The result does not establish allowable belt tension, traction capacity or a safe working load.

Power and RPM

omega = 2×π×RPM/60; Pout = Pin×(E/100); T = Pout/omega
  • T = torque
  • Pin = input power before the specified losses
  • Pout = delivered power after those losses
  • RPM = rotational speed in revolutions per minute
  • omega = angular speed in radians per second
  • E = transmission efficiency as a percent

In Torque from power and RPM, enter input power before the specified losses, the actual RPM of the shaft whose delivered torque is required, and overall power efficiency. Delivered torque is output power divided by that shaft's angular speed. If the entered power is already delivered power at that shaft, use 100% efficiency to avoid counting the same losses twice. This mode does not infer a different output speed.

Belt drive ratio

ReductionRatio = D2/D1; s = Slip/100; eta = E/100; N2 = N1×(D1/D2)×(1 - s); P1 = T1×2×π×N1/60; P2 = eta×P1; T2 = eta×T1×N1/N2; vsurface = π×D1×N1/60
  • D1 = driver pulley pitch/effective diameter
  • D2 = driven pulley pitch/effective diameter
  • N1 = driver speed in RPM
  • N2 = driven speed in RPM
  • Slip = percentage reduction of driven RPM from the ideal no-slip speed
  • vsurface = driver pitch-line surface speed; actual belt speed is not determined when the slip distribution is unknown
  • T1 = driver shaft torque
  • T2 = driven shaft torque
  • P1 = driver shaft input power
  • P2 = driven shaft output power
  • eta = E/100, the overall power efficiency fraction
  • E = transmission efficiency as a percent

In Driven pulley speed and torque, enter driver torque and RPM, both pitch/effective diameters, the slip percentage and overall power efficiency for the same operating point. The calculator determines driven RPM and torque, reduction ratio, output power and driver pitch-line surface speed. Efficiency already includes the specified drive's power losses; slip separately describes its speed shortfall and is not applied again as an extra power-loss factor. Belt length is not calculated here. For background only, approximate open-belt pitch length is L ≈ 2C + (π/2)(D1 + D2) + (D2 - D1)²/(4C), with shaft centre distance C and all lengths in one unit; use the linked Belt Length Calculator for that separate task.

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

These are background relationships, not an additional calculator mode. DeltaT = T/r gives only the tension difference; torque and radius alone do not determine both individual tensions. The flat- and V-belt exponential equalities describe the limiting tension ratio at impending slip in a simplified friction model. Here theta is wrap angle in radians and beta is the groove half-angle. They assume suitable continuous contact and negligible centrifugal/bending effects; below the limit, the operating ratio need not equal the limiting value. The calculator accepts measured tensions to compute torque and does not solve or verify this traction model. Use product-specific design data for belt selection.

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, kgf 1 lbf ≈ 4.44822 N
Power W, kW, mechanical hp 1 mechanical hp ≈ 745.7 W
Angular speed RPM, rad/s rad/s = 2*pi*RPM/60

Belt Friction and Efficiency Checks

Input Input basis Notes
Flat belt coefficient of friction Product/material-specific data Friction depends on the contacting materials and conditions; it is background information, not a calculator input.
V-belt coefficient of friction Product and groove-specific data Groove geometry and the applicable friction model must match the selected product; no universal coefficient is assumed.
Overall power efficiency Output power ÷ input power Use a measured or manufacturer-supported value for the operating point, including the losses being modelled.
Speed shortfall Measured driven RPM versus ideal RPM Slip (%) = 100 × (1 - actual driven RPM ÷ ideal driven RPM). Use a value consistent with the same operating point as efficiency.

Example Problems

Example 1: Torque from force and radius

The measured tight-side tension is 500 N and slack-side tension is 50 N on a pulley with a 0.15 m pitch radius.

T = (Ttight - Tslack)×r; T = (500 - 50)×0.15; T = 67.5 N·m

The pulley torque is 67.5 N·m.

Example 2: Torque from power and RPM

Input power before the specified losses is 2 kW. Overall power efficiency is 95%, so delivered power is 1.9 kW. The actual target-shaft speed is 1750 RPM.

omega = 2×π×1750/60 ≈ 183.26 rad/s; Pout = 2000×0.95 = 1900 W; T = 1900/(2×π×1750/60) ≈ 10.37 N·m

The delivered torque at 1750 RPM is about 10.37 N·m.

FAQ

What is pulley torque?

Pulley torque is the twisting effect at a pulley shaft. In the belt-tension mode it is the measured tangential tension difference multiplied by the pitch/effective radius. Doubling that tension difference or radius doubles the calculated torque when the other value is fixed.

Should pulley radius or diameter be used for torque?

Use pitch/effective radius for torque from the belt tension difference. Use consistent pitch/effective diameters for the two-pulley speed ratio. If the appropriate diameter is known, its radius is half that diameter; an outside diameter may use a different manufacturer-defined basis.

Why does efficiency reduce the torque result?

Overall efficiency is output power divided by input power. At a specified actual output RPM, 90% efficiency gives 90% of the lossless torque at that same RPM. In drive mode, torque also depends on the actual speed ratio: T2 = (E/100) × T1 × N1/N2. Because slip changes N2, multiplying only by the diameter ratio and overall efficiency would count the speed loss again in output power. Enter consistent efficiency and slip measurements for one operating point; this calculation does not predict belt traction, allowable load or efficiency from slip.