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Angular Velocity Converter

Science

Convert angular velocity between RPM, radians per second, degrees per second, and revolutions per second — used for motors, engines, and rotating machinery.

Reviewed by the thecalcu.com team · Last updated July 30, 2026

From
To
All conversionsfor 1 Revolutions per Minute (RPM)
Radians per Second (rad/s)0.10471975
Degrees per Second (°/s)5.9999998
Revolutions per Minute (RPM)1
Revolutions per Second (RPS)0.016666667
Revolutions per Hour (RPH)60.000009

What is a Angular Velocity?

The Angular Velocity Converter converts rotational speed between radians per second, degrees per second, revolutions per minute (RPM), revolutions per second (RPS), and revolutions per hour (RPH). Angular velocity describes how fast something rotates, and different fields default to different units, RPM is standard for engines and motors, while radians per second is the SI unit used directly in physics and engineering formulas.

Enter a value in any supported unit and the converter calculates the equivalent instantly. For related rotational quantities, see the Torque Converter for rotational force and the Acceleration Converter for linear acceleration units.

Why Use an Angular Velocity Converter?

A motor's datasheet specifies RPM, but a physics formula for rotational kinetic energy or angular momentum needs radians per second, converting between them by hand (multiplying or dividing by 2π ÷ 60) is a small but easy-to-fumble step, especially mid-calculation. This converter handles that instantly, whether you're moving from consumer-facing RPM to SI-standard rad/s or checking a slow industrial process rated in revolutions per hour.

Who Should Use This Converter?

  • Mechanical and electrical engineering students converting between RPM and rad/s for physics and dynamics coursework.
  • Automotive and motor enthusiasts working with engine or motor speed specifications across different unit conventions.
  • Robotics and hobbyist engineers calculating motor power or torque requirements that need angular velocity in SI units.
  • Industrial engineers working with slow-rotation equipment specified in revolutions per hour.

What Insights Does the Angular Velocity Converter Give You?

The main output is the converted value in your chosen target unit, calculated precisely from the fixed multiplier relationship between units. Because angular velocity spans a wide practical range, from slow industrial equipment (RPH) to high-speed motors (thousands of RPM), the converter also implicitly shows you the relative scale between two units for a given rotating system.

How to use this Angular Velocity calculator

  1. Choose your starting unit from the source dropdown, for example, "Revolutions per Minute (RPM)".
  2. Enter the numeric value you want to convert in the input field.
  3. Choose your target unit from the destination dropdown, for example, "Radians per Second (rad/s)".
  4. Read the converted result, which updates instantly as you type or change units.
  5. Use the swap (⇅) button if you need to reverse the conversion direction.
  6. Use the copy button to grab the result for a physics calculation, motor spec sheet, or engineering report.
Show formula & methodology ↓Show less ↑

Formula & Methodology

The converter's base unit is radians per second (rad/s). Every supported unit has a fixed multiplier to rad/s:

- 1 degree per second (°/s) = 0.017453 rad/s (π ÷ 180)
- 1 revolution per minute (RPM) = 0.104720 rad/s (2π ÷ 60)
- 1 revolution per second (RPS) = 6.283185 rad/s (2π)
- 1 revolution per hour (RPH) = 0.001745 rad/s (2π ÷ 3600)

Any conversion follows:

Result = Input × (toBase of source unit ÷ toBase of target unit)

Worked example, converting 3,000 RPM (a typical car engine cruising speed) to radians per second:

Result = 3,000 × 0.104720 = 314.16 rad/s

This is the value you'd use directly in a formula for rotational kinetic energy or power output from torque.

Related Tools

You may also find these useful: Frequency Converter.

Frequently Asked Questions

How do I convert RPM to radians per second?
Multiply the RPM value by 0.10472 (which is 2π ÷ 60), since one revolution per minute equals approximately 0.10472 radians per second. Enter your value with 'Revolutions per Minute (RPM)' as the source and 'Radians per Second (rad/s)' as the target and the converter applies this automatically.
Why do engineers use radians per second instead of RPM in physics formulas?
Radians per second is the SI unit of angular velocity and integrates directly into physics formulas involving angular momentum, torque, and rotational kinetic energy without needing an extra conversion factor, while RPM is more intuitive for everyday mechanical contexts like engine speed or spindle speed.
What is the difference between RPM and RPS?
RPM (revolutions per minute) and RPS (revolutions per second) measure the same thing, rotational speed, at different time scales; one RPS equals 60 RPM. RPS is more common in physics and scientific contexts, while RPM is standard for engines, motors, and consumer machinery.
How do I convert degrees per second to RPM?
Divide the degrees-per-second value by 6, since one revolution (360°) per minute corresponds to 6 degrees per second. Enter your value with 'Degrees per Second (°/s)' as the source and 'Revolutions per Minute (RPM)' as the target to see this applied automatically.
What RPM range is typical for a car engine at idle versus highway speed?
A typical car engine idles around 600 to 1,000 RPM and can reach 2,000 to 3,000 RPM or more at highway cruising speed, depending on the vehicle and gear, this converter can translate those values into rad/s for engineering calculations involving engine torque or power.
How does angular velocity relate to linear speed?
Linear speed at a point on a rotating object equals angular velocity (in rad/s) multiplied by the radius from the axis of rotation, this is why a point farther from the centre of a spinning disc moves faster in linear terms even though the whole disc has the same angular velocity.
What is angular velocity used for in torque and power calculations?
Power output of a rotating shaft equals torque multiplied by angular velocity (in rad/s), so converting RPM to rad/s is a necessary step when calculating mechanical power from a motor or engine's torque and speed rating. See the [Torque Converter](/torque-converter/) for torque unit conversions.
Why is revolutions per hour included as a unit?
Revolutions per hour (RPH) is useful for very slow rotational processes, such as industrial mixing equipment, clock mechanisms, or geological/astronomical rotation rates, where RPM or rad/s would produce impractically small decimal values.
Can I use this converter for wheel or motor speed calculations?
Yes, entering a motor or wheel's RPM rating and converting to rad/s is a common first step in calculations involving rotational kinetic energy, centripetal acceleration, or linear speed at the wheel's edge.
Is angular velocity the same as angular acceleration?
No, angular velocity measures how fast something is rotating (radians or degrees per unit time), while angular acceleration measures how quickly that rotational speed is changing (radians per second squared). This converter handles angular velocity only.
Also known as
rpm to rad/s converterrpm to radians per secondangular velocity converterdegrees per second to rpmrevolutions per minute converter