`RPM_4 = ( RPM_1 * ( D_1 * D_3 ))/( D_2 * D_4 )`

Enter a value for all fields

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:

• (RPM₁) Rotation Rate of the first pulley / axle.
• (D₁)  Diameter of the first pulley.
• (D₂)  Diameter of the second pulley.
• (D₃)  Diameter of the third pulley.
• (D₄)  Diameter of the fourth pulley.

RPMs of the 4^th Pulley on axle 3(RPM₄): 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:

• RPM₄ = Rotation on the fourth pulley on the third axle
• RPM₁ = 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

Simple Machine Calculators

• Lever Beam Length 
• Leverage Lift Weight 
• Fulcrum Position 
• Belt Length 
• Belt Speed
• RPMs to Linear Velocity
• Pulley RPMs 
• 2nd Pulley RPMs
• 2nd Pulley Diameter 
• RPM of 4th pulley on three shafts 
• 2nd Gear RPM 
• Sum of Two Lengths