Pre-Calculus 12 · Mathematics · Lesson 5.1
Radians
- Level
- Grade 12
- Reading time
- 4 min reading
- Review
- Last reviewed 2026-09-03
- Standard
- Accuracy standard
- Errata
Abstract
Angle measure.
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.
Concept preview
What you will be able to do
- 01Convert between degrees and radians and find coterminal and reference angles
- 02Use arc length s = rθ and sector area A = ½r²θ
- 03Read exact trigonometric values from the unit circle
A radian measures an angle by the arc it cuts off: one radian is the angle for which the arc length equals the radius. Since a full circle has circumference , going all the way around is radians. So rad , rad . Radians are 'natural' because they tie angle directly to length, which is why every formula in calculus uses them.
School Plan
Radians
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Related topics
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.