Grade 12 · Mathematics
Radians
Why it matters
Angle measure.
Advanced20m readingPrerequisite: None
What is a radian?
Short answer
A radian is a unit of angle measure based on the radius of a circle: one radian is the angle subtended at the centre by an arc equal in length to the radius. A full circle is 2π radians, so 180° equals π radians. Radians are the natural unit for calculus and for the arc-length and area formulas of circles.
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Frequently asked questions
- How do you convert between degrees and radians?
- Multiply degrees by π/180 to get radians, or radians by 180/π to get degrees.
- Why use radians instead of degrees?
- Radians make calculus formulas and arc-length and area relationships clean, because the measure is tied directly to the radius.