Radians

Measuring angles with the radius

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• 1 radian: the arc length equals the radius. $2\pi$ rad $= 360°$ and $\pi$ rad $= 180°$.
• Arc length $s = r\theta$, and speed on a circle $v = r\omega$ (with $\theta$ in radians).
• Radians make the formulas of calculus and physics simple.

Steps

1. How many radii?
2. The radian
3. Convert to radians
4. Convert to degrees
5. Arc length
6. Why bother?
7. Spinning wheel