# How to Find Speed From Radius and Revolutions

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Whether you're building a racing robot or making up for a defunct speedometer, finding the speed of a wheel or wheeled object in miles per hour -- or feet per second, depending on the size of the wheels -- from the wheel's radius and the speed in revolutions per minute (rpm) is straightforward. While the calculations for a wheel with a tire are slightly more complex than those used for one without a tire, they are still relatively simple.

• Find the diameter (d) of the wheel by multiplying the radius (r) by two: 2 * r = d.

• Find the circumference (C) of the wheel by multiplying the diameter by pi, which is approximately 3.14159: d * pi = C.

• Multiply C by the rpm to get the velocity (v) in units per minute. For example, if the value of C is in inches, v will be in inches per minute: C * rpm = v.

• If desired, convert v from inches per minute to miles per hour by multiplying by 60/63,360, or 0.00095.

• To find the speed of a motor vehicle with tires using the wheel radius and the rpm, find out the transmission gear ratio -- how many engine revolutions there are for each driveshaft revolution -- and the differential gear ratio -- how many driveshaft revolutions for each axle revolution. Call these R1 and R2. Multiply C by the rpm, and divide this number by R1 multiplied by R2: (C rpm)/(R1 R2) = v.

## References

• Photo Credit wheel image by Dusan Radivojevic from Fotolia.com
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