The **RPMs of the 4**^{th} pulley on 3 shafts equation calculates the RPMs (rotation rate) of a pulley when the RPM and Diameters are known for a series of pulleys on three axles (see diagram).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**RPM**_{1}) Rotation Rate of the first pulley / axle.
- (
**D**_{1}) Diameter of the first pulley.
- (
**D**_{2}) Diameter of the second pulley.
- (
**D**_{3}) Diameter of the third pulley.
- (
**D**_{4}) Diameter of the fourth pulley.

**RPMs of the 4**^{th} Pulley on axle 3(RPM_{4}): The calculator returns the rotation rate of the 4^{th} pulley (3^{rd} axle) in Revolutions Per Minute (rpm). However, this can be automatically converted to compatible unit via the pull down menu. The rotation rate of the second axle (2^{nd }and 3^{rd}) pullies are also returned.

#### The Math / Science

The formula to compute the rotation rate of a fourth pulley on a three axle system is:

`RPM_4 = (RPM_1 * (D1 * D3))/(D2*D4)`

where:

- RPM
_{4} = Rotation on the fourth pulley on the third axle
- RPM
_{1} = Rotation rate on the first axle
- D1 = Diameter of first pulley on axle 1
- D2 = Diameter of second pulley on axle 2
- D3 = Diameter of third pulley also on axle 2
- D4 = Diameter of the fourth pulley