Free · Physics models
Angular Travel from Radius, Speed or Acceleration
Calculate angular displacement using circular travel or constant angular kinematics.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
angular displacement radius = 5.0000. This worked example uses the displayed units and declared assumptions.
angular_displacement_radius = distance_traveled / radius ; angular_displacement_velocity = velocity * time ; angular_displacement_acceleration = velocity * time + (1 / 2 * (acceleration * (time * time )))
Worked example
Enter these known values and leave the other values blank.
- I know the:
- 1
- Distance traveled (s)
- 10 m
- Radius of the circular path (r)
- 2 m
- Angular displacement (θ)
- 5 rad
Assumptions and limitations
- Angles are radians internally. Angular acceleration units are the selected angle unit per second squared; the authored /s² suffix restores this dimension. Angular-velocity and acceleration modes assume constant rates over elapsed time.
- Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.
Common questions
What assumptions apply?
Angles are radians internally. Angular acceleration units are the selected angle unit per second squared; the authored /s² suffix restores this dimension. Angular-velocity and acceleration modes assume constant rates over elapsed time.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Angles are radians internally. Angular acceleration units are the selected angle unit per second squared; the authored /s² suffix restores this dimension. Angular-velocity and acceleration modes assume constant rates over elapsed time. Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.