Angular Velocity Online Calculator

Example data table

Formula used

Angular velocity (ω) measures how fast an object rotates. This tool supports multiple real-world input sets, then converts everything into a single standard output in radians per second.

• ω = θ / t (angle divided by time)
• ω = 2π × RPM / 60 (from revolutions per minute)
• ω = 2πf (from frequency in hertz)
• ω = v / r (from linear speed and radius)
• ω = 2π / T (from rotational period)

How to use this calculator

1. Select the method that matches your known values.
2. Enter the numbers and choose the correct units.
3. Press Calculate to view results above the form.
4. Use the download buttons to export your latest result.
5. For comparisons, switch methods and re-calculate.

Angular velocity in practical motion

Angular velocity, written as ω, describes rotational speed as angle covered per unit time. In engineering and physics it links circular motion to linear behavior through v = ωr. This calculator lets you compute ω from different inputs and then compares outputs in rad/s, deg/s, rev/s, and RPM.

1) Why radians per second is the standard

Radians are dimensionless, so rad/s fits cleanly into formulas for centripetal acceleration a = ω²r and rotational kinetic energy E = ½Iω². Converting everything to seconds avoids mistakes when values are entered in minutes or hours.

2) Common unit conversions

One revolution equals 2π radians and 360 degrees. RPM is convenient for motors, but rad/s is preferred for calculations. For reference: 1 RPM ≈ 0.10472 rad/s and 1 rad/s ≈ 9.5493 RPM.

3) Using angle and time

If you measure an angle sweep with a sensor or video analysis, use ω = θ/t. Example: 180° in 2 seconds gives about 1.5708 rad/s, which is roughly 15.0 RPM.

4) Using speed and radius

For wheels, belts, and turntables, linear speed can be easier to measure than angle. With ω = v/r, a rim speed of 12 m/s at a radius of 0.5 m produces 24 rad/s (about 229 RPM).

5) Frequency and period methods

When rotation is periodic, frequency f in hertz maps to angular velocity by ω = 2πf. If you know the period T, use ω = 2π/T. These are useful for rotating machinery, oscillators, and repeated cycles.

6) Accuracy and measurement tips

Use consistent units, and confirm the radius is the distance from the rotation axis to the point where speed is measured. For noisy data, average several readings. Small radii amplify uncertainty in ω = v/r, so measure r carefully.

7) Where this calculator helps most

Typical use cases include motor selection, pulley sizing, conveyor design, robotics joints, and lab experiments. Exporting results to CSV supports reports, while the PDF summary is handy for documentation and sharing calculated ω values with teammates.

FAQs

1) What is angular velocity?

Angular velocity is the rate of rotation. It tells how fast an object turns by measuring angle change per time, commonly reported in rad/s, deg/s, rev/s, or RPM.

2) Why does this tool show multiple outputs?

Different fields prefer different units. Engineers often compute in rad/s, technicians read RPM, and classrooms use degrees. Showing all formats helps cross-check and communicate results clearly.

3) When should I use the RPM method?

Use RPM when you have motor speed from a datasheet, tachometer, or controller display. The calculator converts RPM to rad/s using ω = 2π·RPM/60.

4) Can angular velocity be negative?

Yes. A negative value indicates the opposite rotation direction based on your sign convention. If direction matters, keep a consistent reference for clockwise versus counterclockwise.

5) What radius should I enter for ω = v/r?

Enter the distance from the rotation axis to the point where the linear speed is measured. For a wheel rim speed, that is the wheel radius to the rim.

6) How do CSV and PDF downloads work?

After you calculate, the latest result is stored for this session. The download buttons export that stored result, including inputs, method, and converted outputs for easy reporting.