Angular Acceleration Calculator
Angular acceleration from a spin-up or spin-down in rpm over a time, or from a torque acting on a known moment of inertia — with the revolutions turned during the change.
Angular acceleration is the rate of change of angular velocity: convert the two rpm figures to radians per second, take the difference and divide by the time.
How the angular acceleration calculator works
Angular acceleration is the rate of change of angular velocity: convert the two rpm figures to radians per second, take the difference and divide by the time. The rotational form of Newton’s second law gives the same quantity from cause instead of effect — torque divided by moment of inertia. A point at radius r accelerates tangentially at α × r.
Formula: α = (ω₂ − ω₁) ÷ t with ω = 2π × rpm ÷ 60; or α = τ ÷ I
Worked examples
| Inputs | Angular acceleration (rad/s²) | Note |
|---|---|---|
| 0 to 3,000 rpm in 5 seconds | 62.832 | 62.83 rad/s² |
| 10 N·m on 0.5 kg·m² | 20 | 20 rad/s² |
| Braking from 1,500 rpm to rest in 3 s | -52.36 | −52.36 rad/s² |
FAQFrequently asked questions
What is the difference between angular velocity and angular acceleration?
Angular velocity is how fast something spins (radians per second); angular acceleration is how fast that spin is changing. A motor at a steady 3,000 rpm has angular velocity but zero angular acceleration.
Why radians rather than rpm?
Radians per second is the SI unit and the one that makes v = ωr and a = αr work without conversion factors. The calculator also shows rpm per second because that is how a spin-up is usually described.
How do torque and moment of inertia come in?
They are the rotational versions of force and mass: α = τ ÷ I, so the same torque spins a light flywheel up faster than a heavy one. Moment of inertia depends on how the mass is spread, not just how much there is.
What is the revolutions row?
The angle turned during the change, from the average angular velocity times the time — the rotational equivalent of distance = average speed × time — expressed in revolutions.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.