The Length of a Belt calculator computes the length of a belt that goes around two pulleys Belt length around two pulleys. based on the pulley diameters (D_D and D_d) and the distance between the axles (L).

INSTRUCTIONS:  Choose units and enter the following:

• (D_D) Diameter of First Pulley
• (D_d) Diameter of Second Ppulley
• (L) Distance between Axles

Belt Length (BL): The calculator return the belt length (BL) in inches.  However, this can be automatically converted to other length units via the pull-down menu.

The Math

The length of a belt on two pulleys formula is: 

`BL =  (D_D+D_d)*pi/2 +(L*2)+ ( (D_D-D_d)^2 / (L*4) )`

where:

• BL is the belt length
• D_D is the diameter of the first pulley.
• D_d is the diameter of the second pulley.
• L is the distance between the axles. 

Simple Machine Calculators

• Lever Beam Length:  Computes the length of a lever (beam) on one side of a fulcrum needed to lift an object based on the objects weight and the length of the beam on the other side of the fulcrum.
• Leverage Lift Weight:  Computes the weight that can be lifted using a lever based on the downward force and the length of the lever on either side of the fulcrum.
• Fulcrum Position (x): Computes the position of the fulcrum needed in a lever to lift a weight (W) with a downward force (F) with a beam of length (L), where L = x + y.
• Belt Length:  Computes the length of a belt that goes around two pulleys of different diameters separated by a specific distance.two pulley system
• Belt Speed: Computes the speed a belt travels based on the diameter of the pulley and the RPMs.
• Pulley RPMs: Computes the RPMs of a pulley based on the speed of the belt and the diameter of the pulley.
• 2nd Pulley RPMs: Computes the RPMs of a second pulley in a two pulley system when the RPM and Diameter are known for one pulley and the diameter of the second pulley is also known.
• 2nd Pulley Diameter:- Computes the diameter of a second pulley in a two pulley system based on diameter and RPM of one pulley and the RPMs of the second.
• RPM of 4th pulley on three shafts: Computes the RPMs of a fourth pulley on a three shaft system when the RMPs of the first shaft is known and the four diameters.
• 2nd Gear RPM:  Computes the RPMs of a second gear when the RPM and number of teeth are known for the first gear, and the number of teeth are known for the second gear.
• Pulley RPMs: Computes pulley RPMs from belt speed and pulley diameter.
• Sum of Two Lengths: Computes the sum of two lengths (useful with lever calculations).
• Second Gear Torque: Calculates the torque of a second gear when the torque and number of teeth are known for the first gear and the number of teeth of the second gear is known.
• Leadscrew Torque (lift): Computes the torque required to lift a load with a square thread power screw assembly.

References

• Handyman In~Your~Pocket page 42 :(Young and Glover)2012 published by Sequoia Publishing Inc of Littleton, Colorado, U.S.A.