Degrees to Radians Calculator

Published on: January 19, 2025
Final Answer: Free • Full Steps: Plus

This Degrees to Radians Calculator helps you convert an angle from degrees to radians. It uses the formula radians = degrees × π / 180, which changes the angle into radian form used in trigonometry. Multiply the degree value by π, then divide by 180 to get the answer in radians. It is a simple way to check answers, understand angle conversion, and practise basic trigonometry step by step.

Step-by-step method

  1. Identify the angle in degrees.
  2. Use the conversion formula.
  3. Substitute the value.
  4. Simplify the result (if possible).

Formula:

\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)

Example 1:

\(180^{\circ}\)

Step 1 - Identify the angle in degrees.

In this problem: The given angle is \(180^{\circ}\).

\(\theta = 180^{\circ}\)

Step 2 - Use the conversion formula.

In this problem: Use the conversion formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)

Step 3 - Substitute the value.

In this problem: Substitute: \(\text{radians} = 180 \times \frac{\pi}{180}\).

\(\text{radians} = 180 \times \frac{\pi}{180}\)

Step 4 - Simplify the result (if possible).

In this problem: Simplify to a \(\pi\) value: \(\pi\).

\(\text{radians} = \pi\)

Final answer:

\(\text{radians} = \pi\)

Example 2:

\(45^{\circ}\)

Step 1 - Identify the angle in degrees.

In this problem: The given angle is \(45^{\circ}\).

\(\theta = 45^{\circ}\)

Step 2 - Use the conversion formula.

In this problem: Use the conversion formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)

Step 3 - Substitute the value.

In this problem: Substitute: \(\text{radians} = 45 \times \frac{\pi}{180}\).

\(\text{radians} = 45 \times \frac{\pi}{180}\)

Step 4 - Simplify the result (if possible).

In this problem: Simplify to a \(\pi\) value: \(\frac{\pi}{4}\).

\(\text{radians} = \frac{\pi}{4}\)

Final answer:

\(\text{radians} = \frac{\pi}{4}\)
See Example 1 Hide Example 1

Problem

\(180^{\circ}\)

Approach

Step-by-step method

  1. Identify the angle in degrees.
  2. Use the conversion formula.
  3. Substitute the value.
  4. Simplify the result (if possible).

Step 1

Step 1 - Identify the angle in degrees.

In this problem: The given angle is \(180^{\circ}\).

\(\theta = 180^{\circ}\)

Step 2

Step 2 - Use the conversion formula.

In this problem: Use the conversion formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)

Step 3

Step 3 - Substitute the value.

In this problem: Substitute: \(\text{radians} = 180 \times \frac{\pi}{180}\).

\(\text{radians} = 180 \times \frac{\pi}{180}\)

Step 4

Step 4 - Simplify the result (if possible).

In this problem: Simplify to a \(\pi\) value: \(\pi\).

\(\text{radians} = \pi\)

Final Answer

\(\text{radians} = \pi\)
See Example 2 Hide Example 2

Problem

\(45^{\circ}\)

Approach

Step-by-step method

  1. Identify the angle in degrees.
  2. Use the conversion formula.
  3. Substitute the value.
  4. Simplify the result (if possible).

Step 1

Step 1 - Identify the angle in degrees.

In this problem: The given angle is \(45^{\circ}\).

\(\theta = 45^{\circ}\)

Step 2

Step 2 - Use the conversion formula.

In this problem: Use the conversion formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

\(\text{radians} = \text{degrees} \times \frac{\pi}{180}\)

Step 3

Step 3 - Substitute the value.

In this problem: Substitute: \(\text{radians} = 45 \times \frac{\pi}{180}\).

\(\text{radians} = 45 \times \frac{\pi}{180}\)

Step 4

Step 4 - Simplify the result (if possible).

In this problem: Simplify to a \(\pi\) value: \(\frac{\pi}{4}\).

\(\text{radians} = \frac{\pi}{4}\)

Final Answer

\(\text{radians} = \frac{\pi}{4}\)