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Intermediate ∿ Trigonometry Topic 3 of 98

Converting Degrees and Radians

Multiply by π/180 or 180/π.

Key idea

Multiply by π/180 or 180/π.

In depth

Since 180° = π rad, multiply degrees by π/180 to get radians, and radians by 180/π to get degrees. The conversion factor is just a ratio equal to 1 in different units.

Worked example

60° = 60 × π/180 = π/3. And 3π/4 rad = 3π/4 × 180/π = 135°.

Formula

180° = π rad

Real-world uses

Common mistake

Using the factor upside down. Check that the units cancel.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Converting Degrees and Radians?

Multiply by π/180 or 180/π. It is a topic at the intermediate level in Trigonometry.

What is the formula for Converting Degrees and Radians?

The key formula is 180° = π rad.

Where is Converting Degrees and Radians used in real life?

Real-world examples: Switching between calculator modes and programming languages that expect radians.

What should I learn before Converting Degrees and Radians?

Make sure you are comfortable with Radians, the previous topic in Trigonometry.

What is a common mistake with Converting Degrees and Radians?

Using the factor upside down. Check that the units cancel.

How can I practise Converting Degrees and Radians?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Converting Degrees and Radians?

Move on to Right Triangle Terminology next.

Related intermediate topics in Trigonometry