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Angular Acceleration Calculator

Calculate angular acceleration from a change in rotational speed, and the torque it needs.

About Angular Acceleration Calculator

Angular acceleration is the rotational analogue of linear acceleration, and torque plays the role of force. Peak power is highest at the end of the spin-up, because power is torque times the instantaneous speed. Motor selection is usually governed by the peak power at the end of acceleration rather than by the torque alone.

Formula

Angular Acceleration

α = (ω₁ − ω₀) ÷ t; torque τ = I α

α
Angular acceleration in radians per second squared
I
Moment of inertia of the rotating assembly

Worked example

With the default values below, Angular Acceleration Calculator returns Angular Acceleration of 62.8319. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial rotational speedminimum 0 rpm
0 rpm
Final rotational speedminimum 0 rpm
3,000 rpm
Time takenminimum 0.01 s
5 s
Moment of inertiaminimum 0 kg m2
0.5 kg m2

Results

Angular Acceleration
62.8319 rad/s2
Torque Required
31.4159 N m
Revolutions During the Change
125.00 rev
Final Angular Velocity
314.159 rad/s
Peak Power Required
9,869.60 W

Step by step

  1. 1Values used
  2. 2Angular Acceleration
  3. 3Angular Acceleration= 62.8319 rad/s2
  4. 4Torque Required= 31.4159 N m
  5. 5Revolutions During the Change= 125.00 rev
  6. 6Final Angular Velocity= 314.159 rad/s
  7. 7Peak Power Required= 9,869.60 W

Assumptions and limits

  • The result is derived only from the 4 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 4 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 Acceleration calculated?

α = (ω₁ − ω₀) ÷ t; torque τ = I α Angular acceleration is the rotational analogue of linear acceleration, and torque plays the role of force. Peak power is highest at the end of the spin-up, because power is torque times the instantaneous speed.

Why does Angular Acceleration matter?

Motor selection is usually governed by the peak power at the end of acceleration rather than by the torque alone.

What values do I need to enter?

This calculator takes 4 inputs: Initial rotational speed, Final rotational speed, Time taken, Moment of inertia. 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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