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