RPM Calculator - Revs, Radians, Hertz, and Rim Speed

An rpm calculator converts rotational speed between revolutions per minute and the related units rad/s and hertz, and derives the linear or tangential speed at the rim of a wheel, pulley, or tool of a given diameter. Use it when you know the rotation rate but need the SI coherent angular velocity, when a tachometer only reads RPM and you need a frequency in hertz, or when you know a rim speed in m/s and want the matching rotation rate.

• • Engine and motor work: Convert a tachometer reading in RPM into rad/s for an engineering calculation, or check a fan's rated frequency in hertz.
• • Wheel and tire sizing: Estimate the linear speed at the rim of a tire, pulley, or wheel given its diameter and rotation rate.
• • Spindle feeds: Convert a feed rate in m/s into the rotation rate a motor needs, given a roller or pulley diameter.
• • Workshop tooling: Match a router, lathe, or grinding wheel speed to a recommended surface speed in m/s or ft/s.

RPM, short for revolutions per minute, is the most familiar unit for how fast something spins. Engineering work often needs the same motion in rad/s or in hertz, so keeping those conversions in one place prevents the factor-of-60 and factor-of-2π mistakes.

If you also know the wheel or pulley diameter, this calculator returns the rim speed in the unit that matches your input. Leave the diameter at 0 if you only need the rad/s and Hz conversions.

When the rotation rate matters because the engine is making boost, Boost Horsepower Calculator turns the same RPM and pressure into a flywheel horsepower figure you can compare with a dyno sheet.

The calculator uses the SI definitions of the radian and the second, plus a linear speed formula for a rotating wheel. Every output traces back to a fixed constant or your inputs.

• RPM: Revolutions per minute entered in the calculator.
• rad/s: Radians per second, the SI unit of angular velocity.
• Hz: Hertz, equal to revolutions per second.
• d: Diameter of the rotating wheel, pulley, or tool, converted to meters before use.
• v: Linear or tangential speed at the rim in the same length unit as the diameter input.

The factor 2π converts revolutions into radians, and 60 converts minutes into seconds. The linear speed formula multiplies π by the diameter, then divides by 60 to land in m/s.

If you supply a linear speed and a diameter, the calculator inverts the rim speed formula to give back the matching RPM, useful for conveyor setups without a tachometer.

According to NIST Special Publication 811, the radian is the coherent SI unit of angular measure and the hertz equals one cycle per second

Once you have the rad/s output, Horsepower Calculator accepts the angular velocity along with torque to give back a power figure, which is the natural next step after the conversion here.

These four concepts cover the difference between rotational frequency and angular velocity, the geometry of rim speed, and the SI conversions behind them.

Keeping the four concepts separate matters because the labels are often used loosely. A data sheet that lists 'speed' in RPM and a control loop that asks for rad/s describe the same shaft, but the numbers differ by 2π/60.

Geometry also matters. Doubling the diameter doubles the rim speed at the same RPM, which is why large-diameter pulleys feed material faster than small ones at the same motor speed.

The same combustion engine that runs at a chosen RPM is sized in part by its compression ratio, and Compression Ratio Calculator explains how the static and dynamic ratios differ and how to estimate them from measured cylinder pressure.

Start with the rotational speed and the diameter, then read off the SI units and the rim speed. The linear speed field is only needed for the reverse workflow.

1. 1 Enter the rotation rate: Type the rotational speed in revolutions per minute. The default of 1800 covers a typical four-pole induction motor; use 0 to start from a measured linear speed.
2. 2 Add the wheel or pulley diameter: Set the diameter and pick its unit. The calculator converts to meters internally, so the rim speed output uses the same length unit you selected.
3. 3 Optionally provide a linear speed: If you know a rim speed in m/s, cm/s, mm/s, in/s, or ft/s, type it here and the calculator returns the matching RPM.
4. 4 Set the time window: Enter the number of minutes to count revolutions across. One minute matches RPM; longer windows work for trip meters and motor counters.
5. 5 Read the results panel: The results card lists rad/s, hertz, rim speed, the inverse RPM (when applicable), and the total revolution count. Reset returns every field to the defaults.

A bench grinder running at 3450 RPM with a 6 inch (0.1524 m) wheel returns about 361.3 rad/s, 57.5 Hz, and 27.5 m/s rim speed, which is in the safe operating range for a general-purpose grinding wheel.

For propeller work, the rim speed at the blade tip is a critical safety number, and Boat Speed Calculator pairs that result with hull speed and slip estimates to size a prop for a given boat.

Doing the conversion in one place avoids the factor-of-60 and factor-of-2π mistakes that show up in handwritten work.

• • Cuts arithmetic errors: The rad/s, Hz, and rim speed values come from the same fixed factors, so you do not have to remember whether to multiply or divide by 60 or 2π.
• • Works in both directions: Enter RPM to get rim speed, or enter a measured rim speed plus a diameter to back out the rotation rate you need to set on a motor.
• • Matches the units you already have: The diameter selector covers m, cm, mm, in, and ft, and the rim speed output uses the same length unit, so you do not have to pre-convert values.
• • Useful across many fields: Engineers, machinists, automotive hobbyists, drone builders, and appliance repair technicians all measure rotation in RPM but usually need a different output unit.
• • Includes a total revolution count: The time-window field turns RPM into a count, which is handy for trip meters and conveyor counters.

In practice the calculator is most useful when you are staring at a nameplate or a tachometer and need to feed a different unit into a formula or simulation. The inverse workflow is the part most people forget to do by hand.

It is also a sanity check for cut recommendations: surface speed charts list a target in m/s or ft/s, and the calculator turns a chosen wheel diameter and target surface speed into a recommended RPM on the spot.

For engine work, the recommended RPM pairs naturally with cylinder pressure, and Compression Ratio to PSI Calculator converts the static compression ratio into peak PSI for the same operating point.

The math is exact, but the answer is only as good as the diameter and rotation rate you put in.

• • It assumes a rigid circular path and a fixed diameter. A tire under load flattens and a flexible shaft can change effective diameter, all of which the linear speed formula ignores.
• • It does not correct for gear ratios, gearbox slip, or motor controller frequency scaling. If you are reading RPM at a motor shaft, multiply by the gear ratio yourself.
• • It is a conversion tool, not a safety tool. Spinning a wheel or grinding wheel faster than its rated speed is dangerous regardless of what the calculator says; respect the manufacturer's maximum RPM.

A good rule of thumb is to treat the calculator as exact for unit conversion and to treat the inputs as estimates. The math behind rad/s, Hz, and rim speed does not change, but the diameter you measure is rarely identical to the diameter the part was manufactured to.

When the rim speed matters for safety, such as grinding wheels, bandsaw blades, or bike tires, the manufacturer's maximum speed is the binding limit.

According to NIST SP 330, Section 2, the radian is the coherent unit of plane angle and the phase angle increases by 2π rad per period, so rad/s and Hz differ by 2π

Engine efficiency varies with RPM and load, and BSFC Calculator takes a measured fuel flow and RPM reading to estimate brake specific fuel consumption, which is the metric most engine tuning comparisons use.