Angular Velocity Calculator

Enter RPM to calculate angular velocity, rotational frequency, and period.

Rotational speed (RPM)

—rad/s

—rev/s (Hz)

—deg/s

—period s/rev

—ω = 2π × RPM / 60

These are idealized classical-physics calculations. Real systems can differ because of air resistance, friction, deformation, measurement uncertainty, non-constant forces, or other effects not included in the selected model.

Physics model preflight

Check the governing model before trusting the number

steady rotational rate

ω = 2π·RPM / 60

Reading the current native inputs…

Rotational speed conversion; signed RPM preserves rotation direction while period uses speed magnitude. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

Angular Velocity Calculator: RPM, rad/s, Hz & Radius

Convert RPM to rad/s, Hz, deg/s and period, then calculate tangential speed and centripetal acceleration from radius.

Radius

Radius unit

Reference RPM

Use the tool above, then refresh this verification workspace.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

ω = 2π·RPM / 60 — steady rotational rate.

How to verify the result

For RPM input, 60 RPM must equal 1 revolution per second, 2π rad/s, and a 1 s period.

Domain and assumption boundary

Rotational speed conversion; signed RPM preserves rotation direction while period uses speed magnitude. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.

Practical guide and verification

Keep rotational units explicit

RPM, revolutions per second, hertz and radians per second describe related rates with different scale factors. Record the unit with every value so a correct number is not later interpreted in the wrong unit.

Use 2π radians per revolution as the round-trip

Convert revolutions per second to radians per second by multiplying by 2π. Dividing the result by 2π should recover the original revolutions per second and provides a direct unit check.

Radius is only needed for tangential speed

Angular velocity alone does not depend on radius. Radius becomes necessary when converting rotation into linear rim or surface speed, where v = ωr assumes a point at that radius from the axis.

Do not infer load or safety from speed alone

The same angular velocity can correspond to very different forces depending on radius, mass distribution and acceleration. This calculator does not establish bearing limits, rotor safety, tire ratings or machine operating limits.

Match reference RPM values to the real device

Preset comparisons are useful orientation, but actual motors, turntables, wheels and shafts can have slip, control error or changing speed. Use measured RPM when validating a physical system.