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Angular Velocity Converter: Convert RPM, rad/s, Degrees per Second and More

Angular velocity is used whenever something rotates. From an electric motor and car engine to a ceiling fan, turbine, flywheel, hard drive, or rotating machine, engineers and students often need to express the same rotational speed in different units.

The most common units are radians per second (rad/s), revolutions per minute (RPM), degrees per second (°/s), revolutions per second (rev/s), and hertz (Hz). Converting between them manually can be inconvenient because the calculations involve 2π, 60 seconds per minute, and the relationship between revolutions, radians, and degrees.

The Angular Velocity Converter makes these conversions quick and straightforward. Enter a value, select the original unit, choose the unit you need, and the converted result is calculated instantly.

What Is Angular Velocity?

Angular velocity describes how quickly an object changes its angular position as it rotates around an axis. It tells you the rate of rotation rather than the linear distance traveled.

Angular velocity is commonly represented by the Greek letter ω (omega).

The SI unit of angular velocity is radian per second (rad/s). The Bureau International des Poids et Mesures (BIPM) lists rad/s as the SI derived unit for angular velocity.

For example, if a rotating shaft has an angular velocity of 10 rad/s, its angular position changes by 10 radians every second.

Angular velocity is especially useful when analyzing rotating machinery because rotational systems naturally involve angles, revolutions, and rotational periods.

What Is an Angular Velocity Converter?

An Angular Velocity Converter is a tool that changes an angular velocity value from one unit into another while keeping the physical quantity unchanged.

For example:

1 rad/s = 9.5493 RPM

So a shaft rotating at 1 rad/s is rotating at approximately 9.5493 revolutions per minute.

The CalculatorKits Angular Velocity Converter supports more than 25 angular velocity units, including rad/s, RPM, degrees per second, revolutions per second, hertz, radians per hour, degrees per minute, arcminutes per second, and other rotational units.

This is useful when a technical specification gives rotational speed in one unit while your calculation requires another.

Angular Velocity vs Rotational Speed

The terms angular velocity and rotational speed are often used interchangeably in everyday engineering discussions, but there is an important distinction.

Rotational speed generally describes how fast something rotates.

Angular velocity describes the rate of change of angular position and can include direction. In physics, angular velocity is therefore a vector quantity.

For simple unit conversion, however, you are usually working with the magnitude of the angular velocity.

For example:

Rotational value	Meaning
3000 RPM	3000 revolutions per minute
50 rev/s	50 complete revolutions each second
314.16 rad/s	Equivalent angular velocity
18,000 °/s	Equivalent angular velocity

These values describe the same rotational rate using different units.

How to Use the Angular Velocity Converter

Using the Angular Velocity Converter requires only a few steps.

1. Enter the angular velocity value.
2. Select the unit of the value you entered.
3. Select the unit you want as the result.
4. View the converted value instantly.
5. Use the result in your calculation or engineering work.

For example, to convert 100 RPM to rad/s, enter 100, select RPM as the input unit, and select rad/s as the output unit.

The result is approximately:

100 RPM = 10.472 rad/s

The converter performs the calculation automatically, so you do not have to remember the conversion factor.

Angular Velocity Conversion Formula

The relationship between revolutions and radians is fundamental to angular velocity conversion.

One complete revolution equals:

1 revolution = 2π radians

Since one minute contains 60 seconds:

1 RPM = 2π/60 rad/s

Therefore:

1 RPM ≈ 0.1047198 rad/s

The reverse conversion is:

1 rad/s ≈ 9.5493 RPM

The CalculatorKits converter uses rad/s as its base unit and converts between the selected units using their corresponding conversion factors.

RPM to rad/s

Use:

rad/s = RPM × 2π ÷ 60

For example:

3000 RPM × 2π ÷ 60 = 314.159 rad/s

Therefore:

3000 RPM ≈ 314.16 rad/s

rad/s to RPM

Use:

RPM = rad/s × 60 ÷ 2π

For example:

100 rad/s × 60 ÷ 2π = 954.93 RPM

Therefore:

100 rad/s ≈ 954.93 RPM

The Relationship Between Angular Velocity and Frequency

Angular velocity and ordinary frequency are closely related, but they are not numerically identical.

Frequency tells you how many cycles or revolutions occur per second. It is commonly expressed in hertz.

Angular velocity expressed in rad/s is related to frequency by:

ω = 2πf

where:

ω = angular velocity in rad/s

f = frequency in Hz

This factor of 2π is important. BIPM specifically notes that frequency and angular frequency must be distinguished because their numerical values differ by a factor of 2π.

For example, if a rotating object completes 10 revolutions per second:

f = 10 Hz

Then:

ω = 2π × 10

ω ≈ 62.832 rad/s

So:

10 Hz = 62.832 rad/s

This relationship is particularly important in vibration analysis, electrical engineering, wave motion, motors, and rotating machinery.

Common Angular Velocity Units

Different industries use different angular velocity units depending on the application.

Unit	Symbol	Approximate value in rad/s	Common use
Radian per second	rad/s	1	Physics and engineering
Revolution per minute	RPM or r/min	0.10472	Motors and engines
Degree per second	°/s	0.0174533	Navigation and motion
Revolution per second	rev/s	6.28319	Rotating machinery
Hertz	Hz	6.28319	Frequency and periodic motion
Radian per hour	rad/h	0.000277778	Slow rotational motion
Degree per minute	°/min	0.000290888	Instrumentation
Arcminute per second	′/s	0.000290888	Navigation and astronomy
Gradian per second	gon/s	0.015708	Surveying

The CalculatorKits converter provides a much broader selection of units than this basic table.

Most Common Angular Velocity Conversions

Some conversions appear much more frequently than others.

RPM to rad/s

rad/s = RPM × 0.1047198

Examples:

RPM	rad/s
10 RPM	1.0472 rad/s
100 RPM	10.472 rad/s
500 RPM	52.3599 rad/s
1000 RPM	104.72 rad/s
1500 RPM	157.08 rad/s
3000 RPM	314.16 rad/s
6000 RPM	628.32 rad/s
10,000 RPM	1047.20 rad/s

rad/s to RPM

RPM = rad/s × 9.5493

Examples:

rad/s	RPM
1 rad/s	9.549 RPM
5 rad/s	47.746 RPM
10 rad/s	95.493 RPM
25 rad/s	238.732 RPM
50 rad/s	477.465 RPM
100 rad/s	954.930 RPM
250 rad/s	2387.32 RPM
500 rad/s	4774.65 RPM

RPM to Degrees per Second

Another useful conversion is between RPM and degrees per second.

One revolution contains 360 degrees, so:

1 RPM = 360 ÷ 60 °/s

Therefore:

1 RPM = 6 °/s

The formula is:

°/s = RPM × 6

For example:

3000 RPM × 6 = 18,000 °/s

So a shaft rotating at 3000 RPM changes its angular position at a rate of 18,000 degrees per second.

This conversion can be useful when working with motors, rotary sensors, servo systems, robotics, and motion control.

RPM to Revolutions per Second

Converting RPM to revolutions per second is straightforward because one minute contains 60 seconds.

rev/s = RPM ÷ 60

For example:

3600 RPM ÷ 60 = 60 rev/s

Therefore:

3600 RPM = 60 rev/s

The reverse calculation is:

RPM = rev/s × 60

So:

25 rev/s = 1500 RPM

Angular Velocity Conversion Examples

Example 1: Convert 1500 RPM to rad/s

Start with:

1500 RPM

Use:

rad/s = RPM × 2π ÷ 60

Therefore:

1500 × 2π ÷ 60 = 157.08 rad/s

Answer:

1500 RPM ≈ 157.08 rad/s

This is a common conversion for motor and rotating machinery calculations.

Example 2: Convert 50 rad/s to RPM

Use:

RPM = rad/s × 60 ÷ 2π

Therefore:

50 × 60 ÷ 2π = 477.46 RPM

Answer:

50 rad/s ≈ 477.46 RPM

Example 3: Convert 20 rev/s to rad/s

One revolution equals 2π radians.

Therefore:

20 × 2π = 125.66 rad/s

Answer:

20 rev/s ≈ 125.66 rad/s

Example 4: Convert 1200 RPM to degrees per second

Use:

°/s = RPM × 6

Therefore:

1200 × 6 = 7200 °/s

Answer:

1200 RPM = 7200 °/s

Example 5: Convert 5 Hz to rad/s

Use:

ω = 2πf

Therefore:

ω = 2π × 5

ω ≈ 31.416 rad/s

Answer:

5 Hz ≈ 31.416 rad/s

Real World Examples of Angular Velocity

Angular velocity appears in many everyday and industrial systems.

Electric Motors

Motor specifications are frequently given in RPM. Engineering calculations may require rad/s, particularly when working with torque, power, or rotational dynamics.

For example, a motor running at 3000 RPM has an angular velocity of approximately:

314.16 rad/s

Vehicle Engines

Engine speed is commonly displayed in RPM. A car engine running at 3000 RPM therefore rotates at approximately 314.16 rad/s.

This conversion can be useful when combining engine speed with torque and power equations.

Ceiling Fans

A fan running at 1200 RPM has an angular velocity of approximately:

125.66 rad/s

CalculatorKits uses this type of rotating equipment example to demonstrate practical angular velocity conversion.

Flywheels

Flywheels can rotate at high speeds, and engineers may need to move between RPM and rad/s when analyzing rotational kinetic energy or dynamic behavior.

Gyroscopes

Gyroscopes are another example where angular velocity is important. Their rotational speed may be specified in RPM while physics calculations use rad/s.

Angular Velocity and Linear Velocity

Angular velocity can also be connected to the linear velocity of a point moving around a circular path.

The relationship is:

v = rω

where:

v = tangential or linear velocity

r = radius of the circular path

ω = angular velocity in rad/s

For example, suppose a wheel has a radius of 0.25 m and rotates at 20 rad/s.

Then:

v = 0.25 × 20

v = 5 m/s

So a point on the outer edge of the wheel has a tangential speed of 5 m/s.

This relationship is important because it connects rotational motion with the linear motion of gears, wheels, pulleys, belts, and other mechanical systems.

Angular Velocity, Angular Acceleration and Torque

Angular velocity is often only one part of a larger rotational mechanics calculation.

Angular velocity describes how quickly an object is rotating.

Angular acceleration describes how quickly angular velocity changes.

Torque describes the turning effect of a force.

For example, when an electric motor starts from rest, its angular velocity increases over time. The rate of this increase is angular acceleration. The motor’s torque contributes to producing that rotational motion.

The SI unit of angular acceleration is rad/s², while torque is expressed in newton metres. BIPM lists rad/s² as the SI derived unit for angular acceleration.

This makes angular velocity conversion particularly useful as part of a broader engineering workflow.

Common Mistakes When Converting Angular Velocity

Even simple rotational conversions can produce incorrect results if the units are mixed up.

1. Forgetting the factor of 2π

One revolution is 2π radians, not 1 radian.

For example:

1 rev/s = 2π rad/s

not 1 rad/s.

2. Confusing RPM with rad/s

RPM and rad/s measure the same type of physical quantity but have different numerical values.

For example:

1000 RPM ≠ 1000 rad/s

Instead:

1000 RPM ≈ 104.72 rad/s

3. Confusing Hz with rad/s

A frequency of 1 Hz means one cycle per second. Angular velocity corresponding to 1 Hz is:

2π rad/s

BIPM warns that confusing frequency with angular frequency can introduce a factor of 2π error.

4. Mixing minutes and seconds

RPM is revolutions per minute, while rad/s is radians per second.

The 60 seconds per minute factor must be included when converting between them.

5. Rounding too early

If you are performing several calculations in sequence, rounding intermediate values can introduce unnecessary error.

For engineering work, it is better to keep additional decimal places during intermediate calculations and round the final result to an appropriate number of significant figures.

Why Use the CalculatorKits Angular Velocity Converter?

The CalculatorKits Angular Velocity Converter is designed for quick rotational unit conversions without requiring manual calculations.

Its main advantages include:

1. 25+ angular velocity units for a wide range of applications.
2. Instant conversion as values are entered.
3. rad/s as the base unit, making the conversion structure easy to understand.
4. Common rotational units such as RPM, °/s, rev/s and Hz.
5. Browser based calculations without requiring software installation.
6. No registration required for normal use.
7. Local calculation processing, according to the tool’s current page.

For quick checks, homework, engineering calculations, and unit verification, an online converter can be much faster than repeatedly applying manual conversion formulas.

Angular Velocity Converter FAQs

What is the SI unit of angular velocity?

The SI unit of angular velocity is radian per second (rad/s). BIPM identifies rad/s as the SI derived unit for angular velocity.

How many RPM is 1 rad/s?

1 rad/s ≈ 9.5493 RPM.

How do I convert RPM to rad/s?

Multiply RPM by 2π and divide by 60.

rad/s = RPM × 2π ÷ 60

A convenient approximate factor is:

rad/s = RPM × 0.1047198

How do I convert rad/s to RPM?

Multiply rad/s by 60 and divide by 2π.

RPM = rad/s × 60 ÷ 2π

Or approximately:

RPM = rad/s × 9.5493

Is RPM the same as Hz?

No. RPM measures revolutions per minute, while Hz measures cycles per second.

The relationship is:

1 RPM = 1/60 Hz

For angular velocity:

ω = 2πf

How many rad/s is 3000 RPM?

3000 RPM ≈ 314.16 rad/s.

How many degrees per second is 100 RPM?

Since 1 RPM equals 6 °/s:

100 RPM = 600 °/s

What is the difference between angular velocity and angular acceleration?

Angular velocity describes the rate of rotation, while angular acceleration describes the rate at which angular velocity changes.

Angular velocity uses rad/s, while angular acceleration uses rad/s².

Can angular velocity be negative?

Yes. In physics, angular velocity can be positive or negative depending on the chosen direction of rotation. A negative value generally indicates rotation in the opposite direction from the defined positive direction.

For simple unit conversion, the magnitude can be converted in the same way regardless of direction.

Is the CalculatorKits Angular Velocity Converter free?

Yes. The CalculatorKits tool is available for free and does not require registration. Its current page states that calculations are performed locally in the browser.

Related CalculatorKits Tools

If you are working with rotational mechanics, these CalculatorKits tools can complement angular velocity calculations:

1. Acceleration Converter
   Convert acceleration values between different units for motion and engineering calculations.
2. Angular Acceleration Converter
   Convert angular acceleration between rad/s², rev/s², RPM/s, degrees/s², and other units.
3. Torque Converter
   Convert torque values between commonly used metric and imperial units.
4. Moment of Inertia Calculator
   Work with rotational inertia values used in mechanical and rotational motion calculations.

Conclusion

Angular velocity is a fundamental quantity in rotational mechanics, and converting between units such as RPM, rad/s, degrees per second, revolutions per second, and hertz is common in physics, engineering, automotive applications, robotics, machinery, and motion control.

The most important relationship to remember is that one complete revolution equals 2π radians. From that relationship, common conversions such as RPM to rad/s and rad/s to RPM become straightforward.

For example:

1 RPM ≈ 0.1047198 rad/s

1 rad/s ≈ 9.5493 RPM

When you need a quick result, the CalculatorKits Angular Velocity Converter removes the need for manual calculations. Enter the value, select the source and target units, and get the converted result instantly.

For technical or safety critical work, conversion results should still be checked against the applicable engineering specifications, standards, or measurement requirements.

References

1. BIPM, The International System of Units, SI Brochure
2. NIST, Guide for the Use of the International System of Units
3. ISO, Quantities and units standards
4. Encyclopaedia Britannica, Angular velocity

• Written and reviewed by the CalculatorKits Editorial Team
• Last Updated: September 10, 2026