Rotational Motion Calculator — Angular Acceleration & Required Torque
Calculate angular acceleration and required torque using angular speed, time or acceleration, moment of inertia, and available drive input.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Angular motion
Time or angular acceleration
Inertia
Available drive
Geometry
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Angular acceleration formula:
If time is provided:
α = (ω − ω₀) / t
If angular acceleration is provided directly:
α = α
Required torque formula:
Treq = J · α
where:
- α — angular acceleration (rad/s²)
- ω₀ — initial angular speed (rad/s)
- ω — final angular speed (rad/s)
- t — time (s)
- J — moment of inertia (kg·m²)
- Treq — required torque (Nm)
When to use this calculator
When to use this calculator:
- Check the torque required to accelerate a rotating load from an initial angular speed to a final angular speed.
- Calculate angular acceleration when the acceleration time is known.
- Determine required torque from moment of inertia and angular acceleration.
- Compare required torque with available drive torque or torque derived from available power.
- Calculate equivalent linear velocity and linear acceleration when a radius is provided.
How to interpret the result
Angular acceleration is defined as the change in angular speed over the acceleration time, or as the directly provided acceleration input.
Required torque is defined as the torque needed to accelerate the given moment of inertia at the calculated angular acceleration.
The result depends on speed change, acceleration time, and moment of inertia. Increasing the speed change increases angular acceleration and required torque. Increasing the acceleration time decreases angular acceleration and required torque. Increasing moment of inertia increases required torque.
- Safe — available drive torque divided by absolute required torque is greater than or equal to 1.5.
- Limit — available drive torque divided by absolute required torque is greater than or equal to 1.1 and lower than 1.5.
- Unsafe — available drive torque divided by absolute required torque is lower than 1.1.
- Invalid — the input set is rejected when required motion, inertia, drive input, calculated time, calculated torque, average speed, or available torque cannot be calculated according to the JS validation rules.
The result is used to evaluate whether the available drive input provides enough torque margin for the requested rotational acceleration.
Calculation example
Example:
A user wants to accelerate a rotating load from standstill to a defined angular speed and check whether the selected drive has enough torque.
- ω₀ — Initial angular speed = 0 rad/s
- ω — Final angular speed = 100 rad/s
- t — Time = 2 s
- J — Moment of inertia = 0.05 kg·m²
- T — Available torque = 4 Nm
α = 50 rad/s² and Treq = 2.5 Nm.
Assumptions and limitations
- Angular acceleration is constant between the initial and final angular speed.
- Required torque is calculated only from moment of inertia and angular acceleration.
- Moment of inertia is treated as positive and constant.
- The user must provide either acceleration time or angular acceleration, but not both.
- The user must provide either available torque or available power, but not both.
- When available power is used, available torque is calculated from available power and average angular speed.