Angular Displacement Calculator
Work out angular displacement instantly with clear inputs, formula shown and shareable results.
About Angular Displacement Calculator
Rotational kinematics mirrors the linear case with angle replacing distance: theta = omega.t + alpha.t^2/2. Spinning up from 10 rad/s at 2 rad/s2 for 5 s sweeps 75 rad, which is just under 12 full turns, and ends at 20 rad/s. Dividing by 2 pi converts radians into revolutions.
Formulas
Angular displacement
theta = omega x t + 0.5 alpha t^2
Revolutions
revolutions = theta / (2 pi)
Worked example
With the default values below, Angular Displacement Calculator returns Angular Displacement of 75.000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Initial angular velocity
- 10 rad/s
- Angular acceleration
- 2 rad/s2
- Time elapsedminimum 0 s
- 5 s
Results
- Angular Displacement
- 75.000 rad
- Complete Revolutions
- 11.9366
- Final Angular Velocity
- 20.000 rad/s
- Same Displacement In Degrees
- 4,297.2
Step by step
- 1Values used
- 2Angular displacement
- 3Revolutions
- 4Angular Displacement= 75.000 rad
- 5Complete Revolutions= 11.9366
- 6Final Angular Velocity= 20.000 rad/s
- 7Same Displacement In Degrees= 4,297.2
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why use radians rather than degrees?
Because arc length is simply r.theta in radians. Degrees would inject a conversion factor into every formula.
How do I get the distance a point on the rim travels?
Multiply the angular displacement in radians by the radius.