How this calculator works
Angular displacement tracks the total signed rotation and is not wrapped to one turn. An arc must follow the circular path, rather than the straight chord between endpoints. The steady-speed mode assumes unchanged angular velocity; the accelerated mode includes the starting angular speed and assumes constant angular acceleration.
Formula
theta = s/r; theta = omega t; theta = omega_0 t + alpha t²/2. Angles in these equations are radians.
Worked example
Travelling 12 m along a circle of radius 3 m turns through 4 rad. Starting at 2 rad/s and accelerating at 4 rad/s² for 3 s gives 24 rad.
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Frequently asked questions
Can the result exceed 360 degrees?
Yes. Displacement can include many complete turns.
Can I use chord length?
No. Arc length follows the circumference. A chord requires a different trigonometric relationship.
What does a negative angle mean?
It means motion opposite to the positive direction you chose.