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RPM to Radians Per Second Calculator

Enter a rotational speed in RPM or radians per second and instantly see it converted, along with degrees per second and Hz.

Rotational speed converter

Enter a rotational speed and choose its unit.

Radians per second—Enter a value above.
RPM—
Degrees per second—
Frequency (Hz)—
Quick insight

RPM to Radians Per Second Calculator

Enter a rotational speed to see it converted between RPM and radians per second.

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What Is an RPM to Radians Per Second Calculator?

Rotational speed is measured two main ways: RPM (revolutions per minute), the familiar unit on tachometers and motor spec sheets, and radians per second (rad/s), the SI unit for angular velocity used directly in physics and engineering formulas. This calculator converts between them instantly, and also shows degrees per second and frequency in Hz.

If you're working through a rotational dynamics problem, sizing a motor, or converting a manufacturer's RPM spec into the angular velocity your engineering formula needs, this tool bridges the gap without manual unit algebra.

How to Read Your Results

Radians Per Second (rad/s)

This is angular velocity in the SI unit, ready to plug directly into formulas like linear velocity (v = ω × r) or centripetal acceleration (a = ω² × r).

RPM

Revolutions per minute — the everyday, human-scale way of describing how fast something spins.

Degrees Per Second

Another angular velocity unit, more intuitive for some applications since a full circle is a familiar 360°.

Frequency (Hz)

Revolutions per second — useful when working with rotational systems in the context of vibration or signal frequency.

Real-World Example

A car engine is spinning at 3,000 RPM. What is that in radians per second?

UnitValue
RPM3,000 RPM
Radians per second≈314.16 rad/s
Degrees per second18,000 °/s
Frequency50 Hz

Using ω = 3,000 × 2π ÷ 60 gives about 314.16 rad/s — the value you'd plug directly into a torque or centripetal force equation.

Tips for Working With Angular Velocity

  • Always use rad/s, not RPM, in formulas that call for angular velocity (ω) — mixing units silently gives wrong answers.
  • One revolution is always 2π radians, regardless of the size of the rotating object.
  • Frequency in Hz and RPM are related by a simple factor of 60 (Hz = RPM ÷ 60).
  • For linear speed at a radius r, multiply angular velocity in rad/s by r: v = ω × r.

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Note: This calculator performs a direct unit conversion for steady-state rotational speed. It does not account for angular acceleration, variable speed over time, or mechanical losses in a rotating system.

Last updated: August 2026 · Reviewed by: Simple Calculator Tools Editorial Team