Angular Acceleration Calculator
Angular acceleration measures how quickly a rotating object changes its spin rate. It is the rotational analogue of linear acceleration and is central to the design of motors, flywheels, turbines, and any spinning machinery. Given the starting and ending angular velocities and the time over which the change occurs, the angular acceleration follows directly. Enter the initial and final angular velocity in radians per second, the elapsed time, and optionally a radius; this calculator returns the angular acceleration, the equivalent change in revolutions per minute, and the tangential acceleration at the radius.
Angular acceleration formula
Change in velocity = omega_final - omega_initial
Angular acceleration = (omega_final - omega_initial) / t
Tangential acceleration = angular acceleration * radius
RPM change per second = angular acceleration * 60 / (2 * pi)
Angular velocities are in radians per second and time in seconds, giving angular acceleration in radians per second squared. Tangential acceleration applies to a point at the entered radius from the axis.
Rotational motion context
- Angular acceleration is the rotational counterpart of linear acceleration; the kinematic equations have identical forms.
- Convert revolutions per minute to radians per second by multiplying by 2 pi and dividing by 60.
- Net torque equals moment of inertia times angular acceleration (tau = I x alpha), the rotational form of Newton's second law.
- A point on a rotating body also has centripetal acceleration omega^2 times r directed toward the axis, separate from tangential acceleration.
- A negative result indicates deceleration relative to the chosen positive direction of rotation.
Angular acceleration: frequently asked questions
What is angular acceleration?
Angular acceleration is the rate of change of angular velocity over time. It equals the change in angular velocity divided by the elapsed time: alpha = (omega_final - omega_initial) / t. The SI unit is radians per second squared (rad/s^2).
How do I convert RPM to angular velocity?
Angular velocity in radians per second equals revolutions per minute times 2 pi divided by 60. So 60 RPM equals 2 pi radians per second, about 6.28 rad/s. This calculator accepts angular velocity directly in radians per second.
What is the relationship to torque?
Newton's second law for rotation states that net torque equals moment of inertia times angular acceleration (tau = I x alpha). If you know the angular acceleration and the moment of inertia, you can find the required torque, and vice versa.
What is tangential acceleration?
Tangential acceleration is the linear acceleration of a point on a rotating body along its circular path. It equals the angular acceleration times the radius (a_t = alpha x r). This calculator reports tangential acceleration when you enter a radius.
Can angular acceleration be negative?
Yes. A negative angular acceleration means the rotation is slowing down (decelerating) if the angular velocity is positive, or speeding up in the negative direction. The sign follows the chosen positive direction of rotation.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.