Angle and Arc Simulation
Radians look arbitrary until you see where they come from. This simulation ties an angle at the centre of a circle to the arc it cuts, showing that the ratio of arc to radius is the angle itself.
How to use this simulation
- Sweep the central angle and watch the arc grow
- Change the radius of the circle
- Switch the readout between degrees and radians
What to look for
- An angle of one radian always cuts an arc exactly as long as the radius
- Doubling the radius doubles the arc for the same angle
- A full circle is 2π radians, a little over six radii of arc
The physics behind it
Arc length is s = rθ when θ is measured in radians, which is exactly why radians are defined that way — one radian is the angle subtending an arc equal in length to the radius. A full turn wraps the circumference 2πr around the circle, giving 2π radians. The same relation gives sector area as ½r²θ.