Torque and Angular Acceleration Calculator
The rotational form of Newton's second law links torque, moment of inertia, and angular acceleration through tau = I * alpha. Enter any two of the three and this calculator returns the third, along with all three rearrangements. Torque is the rotational equivalent of force, moment of inertia is the rotational equivalent of mass, and angular acceleration is the rate of change of angular velocity. The relationship is exact for a rigid body rotating about a fixed axis.
Leave torque blank to solve for it from I and alpha. Enter torque and one other value to solve for the missing one.
Rotational dynamics formula
tau = I * alpha
alpha = tau / I
I = tau / alpha
where tau = torque (N.m), I = moment of inertia (kg.m2), alpha = angular acceleration (rad/s2)
This is the rotational analogue of F = m * a. A net torque produces angular acceleration in proportion to the inverse of the body's moment of inertia.
Worked example
A flywheel has a moment of inertia of 5 kg.m2 and accelerates at 4 rad/s2. The required net torque is tau = 5 * 4 = 20.00 N.m. If instead a 20 N.m torque is applied to the same flywheel, its angular acceleration is alpha = 20 / 5 = 4.00 rad/s2.
Torque and angular acceleration: frequently asked questions
What is the rotational form of Newton's second law?
It is tau = I * alpha, where tau is net torque, I is the moment of inertia, and alpha is the angular acceleration. It is the rotational analogue of F = m * a: torque replaces force, moment of inertia replaces mass, and angular acceleration replaces linear acceleration.
What units are used?
Torque is in newton-metres (N.m), moment of inertia is in kilogram-metre-squared (kg.m2), and angular acceleration is in radians per second squared (rad/s2).
How do I find moment of inertia?
Moment of inertia depends on the mass distribution and rotation axis. For a solid disc about its centre, I = (1/2) m r2. For a point mass on a rod, I = m r2. Enter the value for your specific body; this calculator does not assume a shape.
Can I solve for angular acceleration instead of torque?
Yes. The calculator returns all three relationships. Given torque and moment of inertia, angular acceleration is alpha = tau / I. Given torque and angular acceleration, moment of inertia is I = tau / alpha.
Sources
- NIST: SI units (newton-metre, radian).
- The relation tau = I * alpha is the standard rotational form of Newton's second law.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.