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Belt and Pulley Drive Calculator

Enter driver and driven pulley diameters, input speed, and power to calculate speed ratios, torque at each shaft, belt velocity, belt length, and more. The animated SVG shows both pulleys connected by a belt rotating at the correct relative speeds.

Belt and Pulley System(Speed Reduction)

T\u2081 (tight)T\u2082 (slack)v = 11.4 m/sDriver⌀150 mm1450 RPMDriven⌀300 mm725 RPMC = 600 mm
DriverDrivenTight sideSlack sideBelt velocity

Belt Type

Parameters

mm
mm
RPM
mm
kW

Presets

Results

Speed Ratio
1:2.0
Reduction
Driven RPM
725
RPM
Driver Torque
32.93
N\u00b7m
Driven Torque
63.22
N\u00b7m

Belt and Power

Belt Velocity11.39 m/s
Belt Length1916 mm (1.92 m)
Effective Pull (T\u2081\u2212T\u2082)439.05 N
Contact Angle (small pulley)2.891 rad (165.6\u00b0)
Power Transmitted4.800 kW
Torque Ratio2.000

Step-by-Step Solution

1
Speed ratio=D1D2=150300=0.5\text{Speed ratio} = \frac{D_1}{D_2} = \frac{150}{300} = 0.5
2
N2=N1×D1D2=1450×0.5=725 RPMN_2 = N_1 \times \frac{D_1}{D_2} = 1450 \times 0.5 = 725 \text{ RPM}
3
v=πD1N160=π×0.15×145060=11.3883 m/sv = \frac{\pi D_1 N_1}{60} = \frac{\pi \times 0.15 \times 1450}{60} = 11.3883 \text{ m/s}
4
τ1=Pω1=5×10002π×145060=32.9286 N\cdotm\tau_1 = \frac{P}{\omega_1} = \frac{5 \times 1000}{\frac{2\pi \times 1450}{60}} = 32.9286 \text{ N\cdot m}
5
τ2=τ1×D2D1×η=32.9286×2×0.96=63.2229 N\cdotm\tau_2 = \tau_1 \times \frac{D_2}{D_1} \times \eta = 32.9286 \times 2 \times 0.96 = 63.2229 \text{ N\cdot m}
6
L=2C+π(D1+D2)2+(D1−D2)24C=1916.2333 mmL = 2C + \frac{\pi(D_1+D_2)}{2} + \frac{(D_1-D_2)^2}{4C} = 1916.2333 \text{ mm}
7
θ=π−2sin⁡−1 ⁣(∣D1−D2∣2C)=2.8909 rad≈165.6385°\theta = \pi - 2\sin^{-1}\!\left(\frac{|D_1-D_2|}{2C}\right) = 2.8909 \text{ rad} \approx 165.6385°
8
Feff=Pv=500011.3883=439.0481 NF_{\text{eff}} = \frac{P}{v} = \frac{5000}{11.3883} = 439.0481 \text{ N}
9
Pout=Pin×η=5×0.96=4.8 kWP_{\text{out}} = P_{\text{in}} \times \eta = 5 \times 0.96 = 4.8 \text{ kW}

Reference Guide

Belt Drive Fundamentals

A belt and pulley system transmits rotational motion between two shafts using a flexible belt wrapped around pulleys. The belt maintains the same linear velocity at both pulleys.

Key principle

vbelt=ω1r1=ω2r2v_{\text{belt}} = \omega_1 r_1 = \omega_2 r_2

The driver pulley is connected to the motor. The driven pulley is connected to the load. Belt drives are used in drill presses, lathes, conveyors, compressors, and many other machines.

Speed and Torque Ratios

The speed ratio depends only on pulley diameters. A smaller driver and larger driven pulley gives speed reduction with torque multiplication.

Speed ratio
N2N1=D1D2\frac{N_2}{N_1} = \frac{D_1}{D_2}
Torque ratio (inverse)
τ2τ1=D2D1×η\frac{\tau_2}{\tau_1} = \frac{D_2}{D_1} \times \eta

Power is conserved (minus efficiency losses). Speeding up the driven shaft reduces its torque, and slowing it down increases torque.

Belt Tension and Power

The belt has a tight side (high tension T\u2081) and a slack side (lower tension T\u2082). The difference is the effective pull that transmits power.

Belt velocity
v=πD1N160v = \frac{\pi D_1 N_1}{60}
Power transmitted
P=(T1−T2)×v=Feff×vP = (T_1 - T_2) \times v = F_{\text{eff}} \times v
Open belt length
L=2C+π(D1+D2)2+(D1−D2)24CL = 2C + \frac{\pi(D_1+D_2)}{2} + \frac{(D_1-D_2)^2}{4C}

Belt Types

Flat belts are the simplest type, running on flat-crowned pulleys. They are quiet, tolerate misalignment well, and are typically 95-98% efficient.

V-belts sit in a V-shaped groove, wedging deeper under tension. This gives higher grip than flat belts for the same tension, making them the most common type in industrial drives.

Timing (synchronous) belts have teeth that mesh with grooves on the pulleys. They eliminate slip entirely, maintaining exact speed ratios. Used in engine camshafts, 3D printers, and robotics.

Typical belt drive efficiency ranges from 92% to 98%, depending on belt type, alignment, and tension.