Degrees to Radians Converter Formula

Understand the math behind the degrees to radians converter. Each variable explained with a worked example.

Use the Degrees to Radians Converter

Formulas Used

Radians

radians = deg * pi / 180

Turns

turns = deg / 360

Variables

VariableDescriptionDefault
degDegrees(deg)180

How It Works

How to Convert Degrees to Radians

Formula

Radians = Degrees × (pi / 180)

A full circle is 360 degrees or 2pi radians. So 1 degree = pi/180 radians, which is approximately 0.01745329 radians.

Worked Example

Convert 180 degrees to radians.

deg = 180
  1. 01Radians = 180 × (pi / 180)
  2. 02= 180 × 0.017453
  3. 03= pi
  4. 04= 3.141593 rad

Frequently Asked Questions

Why do we use radians?

Radians are the natural unit for measuring angles in calculus and higher mathematics. Many formulas (like arc length s = r * theta) work directly when the angle is in radians.

How many radians in a full circle?

A full circle is 2pi radians, approximately 6.283185 radians.

What is 90 degrees in radians?

90 degrees equals pi/2 radians, approximately 1.5708 radians.

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Open Degrees to Radians Converter