Conversion between degrees and radians

Since the length of a circle is $2\pi R$, a full angle measures $2\pi$ radians. From this all the conversions follow.

Property — Degree ↔ radian conversion

A full angle measures $2\pi$ radians. Therefore: $180° = \pi \text{ rad},\qquad 90° = \frac{\pi}{2} \text{ rad},\qquad 60° = \frac{\pi}{3} \text{ rad},\qquad 45° = \frac{\pi}{4} \text{ rad},\qquad 30° = \frac{\pi}{6} \text{ rad}.$ The general formula is $\alpha_{\text{rad}} = \frac{\pi}{180°}\cdot \alpha_{\text{gradi}},\qquad \alpha_{\text{gradi}} = \frac{180°}{\pi}\cdot \alpha_{\text{rad}}.$

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Topics: Trigonometry
Concepts: Angle · Radian
Skills: Calculating · Using formulae