Angular Velocity Calculator: rpm to rad/s, Frequency, Period and Speed at a Radius

Rotation rate in any unit.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose what you know, such as the speed in rpm.

Enter the value and a radius.

The calculator gives omega in rad/s, rpm, Hz, the period and the speed at the radius.

Formulas used

  • \omega = \frac{2\pi N}{60} = 2\pi f = \frac{2\pi}{T}
  • v = \omega r
  • a = \omega^2 r

Worked example

With the default numbers in the calculator above:

  1. Angular velocity: 157.08 rad/s
  2. Speed in revolutions per minute: 1500 rpm
  3. Frequency: 25 Hz
  4. Period of one turn: 0.04 s
  5. Linear speed at the radius: 15.708 m/s (56.549 km/h)
  6. Centripetal acceleration at the radius: 2467.4 m/s2 (251.6 g)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you know? The angle turned and the time; Angle turned 720 deg; Time taken 2 s.

  1. Angular velocity: 6.28319 rad/s
  2. Speed in revolutions per minute: 60 rpm
  3. Frequency: 1 Hz
  4. Period of one turn: 1 s
  5. Linear speed at the radius: 0.628319 m/s (2.2619 km/h)
  6. Centripetal acceleration at the radius: 3.94784 m/s2 (0.40257 g)

Common questions

How do I convert rpm to rad/s?

Multiply by 2 pi and divide by 60. So 1 rpm is 0.1047 rad/s.

What is the relationship between omega and linear speed?

The speed of a point is omega times its distance from the axis.

What is the difference between frequency and angular frequency?

Frequency counts turns per second. Angular frequency counts radians per second, which is 2 pi times as much.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics or dynamics text (rotational motion).

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