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Angular Velocity Calculator

Convert between rotational speed, angular velocity and the linear speed at a radius.

About Angular Velocity Calculator

Angular velocity is radius-independent, but the linear speed it produces grows directly with radius. That is why the tip of a long blade moves far faster than one near the hub at the same rpm. Tip speed rather than rpm is what limits turbine and fan design, because it drives both stress and noise.

Formula

Angular Velocity

ω = 2π × rpm ÷ 60; tangential speed v = ω r

ω
Angular velocity in radians per second
v
Linear speed at radius r

Worked example

With the default values below, Angular Velocity Calculator returns Angular Velocity of 157.0796. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rotational speedminimum 0 rpm
1,500 rpm
Radiusminimum 0 m
0.25 m

Results

Angular Velocity
157.0796 rad/s
Tangential Speed at That Radius
39.270 m/s
Revolutions per Second
25.0000 rev/s
Time for One Revolution
0.04000 s
Angular Speed
9,000.00 deg/s

Step by step

  1. 1Values used
  2. 2Angular Velocity
  3. 3Angular Velocity= 157.0796 rad/s
  4. 4Tangential Speed at That Radius= 39.270 m/s
  5. 5Revolutions per Second= 25.0000 rev/s
  6. 6Time for One Revolution= 0.04000 s
  7. 7Angular Speed= 9,000.00 deg/s

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Angular Velocity calculated?

ω = 2π × rpm ÷ 60; tangential speed v = ω r Angular velocity is radius-independent, but the linear speed it produces grows directly with radius. That is why the tip of a long blade moves far faster than one near the hub at the same rpm.

Why does Angular Velocity matter?

Tip speed rather than rpm is what limits turbine and fan design, because it drives both stress and noise.

What values do I need to enter?

This calculator takes 2 inputs: Rotational speed, Radius. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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Angular Velocity Calculator – Calculate Angular Velocity