RPM to MPH calculator

How do I calculate speed from RPM?

mph = RPM × tire diameter (in) ÷ (transmission gear ratio × axle ratio × 336). The wheels turn RPM ÷ (gear × axle) times a minute, and each turn covers π × the tire diameter.

Where does 336 come from?

Inches in a mile divided by minutes in an hour times π: 63,360 ÷ (60 × π) = 336.14. The calculator uses the exact value.

Example

At 2,000 RPM with a 26-inch tire, a 1.00 : 1 gear and a 3.73 axle ratio, the car goes 2,000 × 26 ÷ (1 × 3.73 × 336.14) = 41.5 mph. In a 0.70 overdrive it is 59.2 mph.

How do I find the tire diameter?

Type a tire size such as 225/65R17 and the calculator works out the diameter (28.5 in), or enter the diameter in inches. The tire size calculator shows the details.

Why might my real speed differ?

The formula assumes no slip. A tire flattens a little under load and wears down over time, and an automatic transmission’s torque converter can slip until it locks up.

What RPM will I turn at 70 mph?

It depends on the tire diameter and the gearing. With a 265/70R17 tire (31.6 inches), a 0.75 overdrive and a 3.73 axle, 70 mph takes 2,083 RPM.

Where the formula comes from

The engine turns RPM times a minute. The transmission and the axle divide that by the gear ratio and the axle ratio, so the wheels turn RPM ÷ (gear × axle) times a minute. Each turn rolls the tire out by its circumference, π × diameter. Multiply by 60 minutes and divide by 63,360 inches per mile and you get mph = RPM × diameter ÷ (gear × axle × 336.14), where 336.14 is 63,360 ÷ (60π). The formula assumes the tire does not slip and that the diameter you enter is the loaded rolling diameter.

A worked example with tire size

A 265/70R17 tire is about 31.6 inches tall. In a 0.75 overdrive gear with a 3.73 axle ratio, 2,200 RPM gives 73.9 mph. Fitting a 285/70R17 tire (32.7 inches) at the same 2,083 RPM raises the real speed to 72.4 mph, so a speedometer calibrated for the smaller tire would read about 3.5% low at 70 mph. Larger tires also lower the RPM at any given speed, which acts like a taller gear.

Common mistakes

Using the radius instead of the diameter halves the answer. Entering the nominal rim size plus a guess for the tire, rather than the tire’s real height, is the second; the calculator can parse a size such as 265/70R17 for you. Mixing the gear ratio with its inverse is the third: a ratio of 3.73 means the driveshaft turns 3.73 times per wheel turn, and overdrive gears are below 1. Finally, tires wear and flatten, and an automatic transmission can slip, so the real figure is usually a little different.

Sources: the unit arithmetic (63,360 inches per mile, 60 minutes per hour) from NIST SP 811; the tire-size code (section width in mm, aspect ratio in percent, rim diameter in inches) as defined in tire standards such as ISO 4000 and the Tire and Rim Association. Related: tire size calculator, speed calculator, horsepower calculator and bike gear calculator.