Skip to content
engineering

Angular Acceleration Calculator

Calculate angular acceleration from initial and final RPM over a time interval in rad/s².

Angular acceleration
31.4159 rad/s²
α = Δω ÷ Δt where ω = 2πN ÷ 60. Speed changed from 0 to 157.08 rad/s over 5 s.
Δω — Change in angular velocity
157.08 rad/s
Time interval
5 s

How it works

  1. 1Enter the initial rotational speed in RPM and the final rotational speed in RPM.
  2. 2Enter the time interval in seconds over which the speed change occurs.
  3. 3The calculator applies α = Δω ÷ Δt (where ω = 2πN ÷ 60) and shows the angular acceleration plus the change in angular velocity.

Use cases

  • Motor and drive design — determining how quickly a motor reaches operating speed.
  • Robotics and servo tuning — calculating joint angular acceleration for trajectory planning.
  • Mechanical engineering coursework — verifying rotational dynamics problems.

Frequently asked questions

What is angular acceleration?

Angular acceleration (α) is the rate of change of angular velocity over time, measured in rad/s². It is α = Δω ÷ Δt, where Δω is the change in angular velocity and Δt is the elapsed time.

How do I convert RPM to rad/s?

Multiply RPM by 2π and divide by 60: ω (rad/s) = RPM × 2π ÷ 60. For example, 1500 rpm equals 1500 × 2π ÷ 60 ≈ 157.08 rad/s.

What is the angular acceleration from 0 to 1500 rpm in 5 s?

Δω = 157.08 − 0 = 157.08 rad/s. α = 157.08 ÷ 5 ≈ 31.42 rad/s². Enter those values above to confirm the result instantly.

Related tools

See all →
Gear Ratio Calculator

Find the gear ratio, output speed, torque, and mechanical advantage of a gear pair, in metric or imperial.

Gear Train Calculator

Calculate the overall ratio and output speed of a multi-stage compound gear train.

Torque Calculator

Calculate shaft torque from power and rotational speed in metric or imperial units.

Power Transmission Calculator

Calculate the mechanical power transmitted by a rotating shaft from torque and shaft speed.