Kinematics
The basic definition of angular acceleration.
α = Δω / t
Angular Acceleration Calculator
Calculate angular acceleration from angular velocity change, torque and inertia, or tangential acceleration and radius.
Angular Acceleration
Calculate rotational acceleration using Kinematics, Torque (Newton's 2nd Law), or Tangential Force.
Physics Formula
α = Δω / t
Understanding Angular Acceleration
Angular acceleration (alpha, $\alpha$) is the rate of change of angular velocity over time. It explains how quickly an object speeds up or slows down its rotation.
Dynamics (Torque)
Newton's Second Law for rotation. Torque ($\tau$) causes acceleration based on rotational mass ($I$).
τ = I · α
Tangential Acceleration
The linear acceleration of a point on the edge of the rotating object.
at = r · α
angular acceleration formulas and interpretation
Angular acceleration measures how quickly angular velocity changes with time.
The calculator supports rotational kinematics, torque dynamics, and the tangential-to-angular acceleration relationship.
How to use the angular acceleration calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Average angular acceleration equals angular velocity change divided by elapsed time.
α = Δω / Δt- α — Angular acceleration
- Rate of angular velocity change (rad/s²)
- Δω — Angular velocity change
- Final minus initial angular velocity (rad/s)
- Δt — Time
- Elapsed interval (s)
Rotor speed-up example
A rotor changes speed by 30 rad/s in 5 seconds.
- Velocity change
- 30 rad/s
- Time
- 5 s
- α = 30 / 5
- α = 6 rad/s²
Result: Angular acceleration is 6 rad/s².
Angular velocity increases by 6 rad/s each second.
Understanding your results
Interpreting the result
Positive angular acceleration increases angular velocity in the chosen positive rotational direction.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.
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