Go to content
How to convert degrees to radians. Use the interactive display. Change the value of the angle in degrees and then this will be converted to radians.

## Summary/Background

Radians and degrees are two alternative units for measuring angle. There are 360 degrees or 2 \pi radians in a full turn. The radian measure is used at advanced level and beyond in mathematics through out calculus (differentiation and integration).
360 \text{ degrees} = 2\pi \text{ radians}

1 \text{ degree} = \displaystyle \frac{\pi}{180} \text{ radians}

1 \text{ radian} = \displaystyle \frac{180}{\pi} \text{ degrees}

## Software/Applets used on this page

This page uses jsMath
You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## Glossary

### calculus

the study of change; a major branch of mathematics that includes the study of limits, derivatives, rates of change, gradient, integrals, area, summation, and infinite series. Historically, it has been referred to as "the calculus of infinitesimals", or "infinitesimal calculus".
There are widespread applications in science, economics, and engineering.

### radian

a measure of angle equal to the size of the angle subtended at the center of a circle of radius r by an arc of length r.

### union

The union of two sets A and B is the set containing all the elements of A and B.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)1TrigonometryRadians-
AP Calculus BC (USA)1TrigonometryRadians-
AQA A-Level (UK - Pre-2017)C2TrigonometryRadians-
AQA A2 Maths 2017Pure MathsTrigonometry and RadiansRadians-
AQA AS/A2 Maths 2017Pure MathsTrigonometry and RadiansRadians-
CBSE XI (India)Sets and FunctionsTrigonometric FunctionsRadians-
CCEA A-Level (NI)C2TrigonometryRadians-
CIE A-Level (UK)P1TrigonometryRadians-
Edexcel A-Level (UK - Pre-2017)C2TrigonometryRadians-
Edexcel A2 Maths 2017Pure MathsUsing RadiansRadians-
Edexcel AS/A2 Maths 2017Pure MathsUsing RadiansRadians-
I.B. Higher Level3TrigonometryRadians-
I.B. Standard Level3TrigonometryRadians-
Methods (UK)M2TrigonometryRadians-
OCR A-Level (UK - Pre-2017)C2TrigonometryRadians-
OCR A2 Maths 2017Pure MathsRadiansRadians-
OCR MEI A2 Maths 2017Pure MathsRadiansRadians-
OCR-MEI A-Level (UK - Pre-2017)C2TrigonometryRadians-
Pre-Calculus (US)C4TrigonometryRadians-
Pre-U A-Level (UK)2TrigonometryRadians-
Scottish (Highers + Advanced)HM1TrigonometryRadians-
Scottish HighersM1TrigonometryRadians-
Universal (all site questions)TTrigonometryRadians-
WJEC A-Level (Wales)C2TrigonometryRadians-