Belt Length

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

$(D_D) "Diameter of Pulley 1"$

$(D_d) "Diameter of Pulley 2"$

$(L) "Distance between Axles"$

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.