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# What Is the Formula for RPM?

by Pauline Gill

RPM, defined as revolutions per minute, is an internationally accepted expression of rotational velocity. It refers to the number of revolutions a rotating object makes on its own axis in one minute. Determining RPM is relevant for virtually every rotating entity known to man. RPM is used with many key parameters such as diameter, mass and torque in fixed engineering formulas to calculate horsepower, linear velocity, gear ratios and tangential velocity. Conversely, a number of measurements can be made in any given system to calculate RPM. Since there is no one formula, several examples are provided below.

### Wheel RPM

Calculating RPM of a wheel on a vehicle: An automobile is traveling in a straight line at 60 miles per hour. The outside diameter of each wheel is 27 inches. What is the RPM of the wheels? RPM formula = linear distance traveled divided by linear distance per wheel RPM. 60 miles per hour = one mile per minute = 5,280 feet per minute linear velocity. Wheel circumference in feet = diameter times pi = 27inches/12 inches per foot times 3.1416 = 7.068 feet wheel circumference. RPM = 5,280 feet per minute traveled divided by 7.068 feet per revolution = 747 RPM

### Horsepower RPM

A small diesel engine produces 3 horsepower with 6 pound-feet of torque at what RPM? RPM formula = Horsepower times 5,252 constant (33,000 divided by 3.1416 times 2) divided by torque RPM = 3 HP times 5,252 divided by 6 foot pounds RPM = 15,756 divided by 6 equals 2,626 RPM

### Reduction Gear RPM

Output RPM formula = Input RPM times number of driving gear teeth divided by number of driven gear teeth. A small transmission in a mixer has a 12-tooth gear on the motor shaft driving a 72-tooth gear on the mixer blade. The motor is turning at 1,800 RPM. What is the mixer blade speed? Mixer blade RPM = 1,800 RPM motor speed times 12 teeth divided by 72 teeth on mixer gear = 1,800 times 12 divided by 72 = 300 RPM mixer blade speed

### Tachometer RPM

A tachometer has a magnetic pulse sensor next to an iron gear on a motor shaft. There are 30 teeth on the gear. The pulse readout indicates 90 pulses per second. What is the RPM of the motor shaft? RPM = Pulses per second times 60 seconds per minute divided by number of gear teeth. Motor shaft RPM = 90 times 60 divided by 30 = 180 RPM

### Earth RPM

The Earth spins on its own axis one revolution each 24 hour day. What is the Earth's RPM? Earth RPM = 1 revolution per day divided by minutes per day 24 hours times 60 minutes per hour = 1,440 minutes per day Earth RPM = 1 divided by 1,440 equals 0.00069 RPM