Angular Acceleration Calculator

Related Calculators

Angular acceleration: The rate of change of angular velocity with time. In this calculator, the main SI form is rad/s^2. [2]

Change in angular velocity: Final angular velocity minus initial angular velocity, often written as delta omega. [2]

Angular velocity: How fast something rotates. You can enter it here in rad/s, deg/s, or rpm, and the calculator converts it internally to rad/s.

Tangential acceleration: The linear acceleration along the tangent to the circular path at the point of interest. [2]

Torque: A twisting effect that changes rotational motion. In this calculator it is used with moment of inertia and angular acceleration.

Moment of inertia: A measure of how hard it is to change an object's rotational speed about a chosen axis.

Negative result: A negative sign means the quantity points opposite your chosen positive rotation direction. For angular acceleration, that often means the object is slowing down in the positive direction.

Mistake: Entering rpm values in Initial angular velocity (selected unit) or Final angular velocity (selected unit) while Angular velocity unit is left on rad/s.
Fix: Set Angular velocity unit to rpm before calculating, or re-enter the values in rad/s.

Mistake: Using 0 for Time interval (selected unit) in a mode that divides by time.
Fix: Enter a time greater than 0, and make sure Time unit matches your homework values.

Mistake: Using 0 or a negative number for Radius (selected unit) when solving with alpha = a_t / r.
Fix: Enter a radius greater than 0 and check Length unit (for radius) so the size is interpreted correctly.

Mistake: Typing a negative value into Moment of inertia (kg*m^2) for a rigid-body problem.
Fix: Use a positive Moment of inertia (kg*m^2) ; if you want direction, put the sign on Torque (N*m) or angular quantities instead.

Mistake: Confusing slowing down with a calculation error when Angular acceleration comes out negative.
Fix: Keep the sign. A negative Angular acceleration or negative Change in angular velocity means the change points opposite your chosen positive direction.

Mistake: Turning on Also compute angular displacement (constant alpha) and expecting a value in every mode.
Fix: That output needs omega1, alpha, and time together. If one of those is missing in the current Solve for mode, the angular displacement result will show N/A.

• The angular-velocity-over-time mode gives average angular acceleration over the entered time interval, not a full instantaneous calculus-based result.
• The formulas for Final angular velocity and optional angular displacement assume angular acceleration stays constant during the time interval.
• For torque modes, the calculator uses the simplified rigid-body relation tau = I alpha about a fixed axis and does not model changing moment of inertia or multiple torques separately.
• Time interval (selected unit) must be greater than 0 in modes that divide by time, Radius (selected unit) must be greater than 0 in modes that divide by radius, and Moment of inertia (kg*m^2) must be greater than 0 in modes that divide by inertia.
• If solving for time and angular acceleration is 0, there is no single numeric answer: time is not uniquely determined when initial and final angular velocity are equal, and it is impossible when they are different.
• Optional angular displacement is shown only when omega1, alpha, and time are all available in the current mode.
• Unit conversions are built in, but results can still be wrong if the chosen unit selectors do not match the numbers you typed.

Core method

This calculator first converts entered values to SI units, then applies the formula that matches the selected mode. Angular velocity is converted to rad/s, time to seconds, radius to meters, and tangential acceleration to m/s^2.

α (angular acceleration) = (ω2 - ω1) / t

ω2 (final angular velocity) = ω1 + α * t

t (time interval) = (ω2 - ω1) / α

α = a_t / r

a_t = α * r

τ = I * α

α = τ / I

I = τ / α

The angular acceleration definition used here is change in angular velocity divided by time. [1][2] The calculator keeps the sign, so a negative answer means the change is opposite your chosen positive direction.

Unit conversions used

rad/s = rpm * (2π / 60)

rad/s = deg/s * (π / 180)

s = min * 60

m = ft * 0.3048

m = in * 0.0254

After solving in SI units, the calculator also shows equivalent displays such as deg/s^2 and rpm/s when useful.

Optional angular displacement

If you turn on the extra displacement output, the calculator uses the constant-angular-acceleration kinematics equation below when omega1, alpha, and time are all available.

θ (angular displacement) = ω1 * t + 0.5 * α * t^2

Mini example

Suppose Initial angular velocity (selected unit) = 0 rad/s, Final angular velocity (selected unit) = 10 rad/s, and Time interval (selected unit) = 5 s.

α = (10 - 0) / 5 = 2 rad/s^2

So the object speeds up by 2 rad/s each second. If the final angular velocity were 10 rad/s and the initial angular velocity were 20 rad/s over 4 s, the result would be -2.5 rad/s^2, which means the rotation is changing opposite the positive direction you chose.

Error handling and special cases

If time, radius, or moment of inertia would cause division by zero, the calculator blocks the result and shows an error instead. In time-solving mode, if α = 0 and ω2 = ω1, there is no single time value; if α = 0 and the two angular velocities differ, that situation is impossible under the formula.

What can make real answers differ

Real systems may have changing torque, friction, slipping, changing radius, or non-constant angular acceleration. In those cases, this calculator is still useful for homework-style average or constant-alpha problems, but a lab result or engineering model may differ.