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Degrees to Radians Converter

Convert degrees to radians and radians to degrees instantly. Bidirectional angle converter with formula and common values.

°

Radians

0.785399

rad

45 ° = 0.785399 rad

rad = ° × 0.0174533

Degrees to Radians: 1 ° equals 0.017453 rad. To convert degrees to radians, multiply by 0.017453 (rad = ° × 0.0174533). For example, 10 ° = 0.174533 rad.

How to Convert Degrees to Radians

To convert from degrees to radians, multiply the value by 0.017453. The conversion is linear, meaning doubling the input doubles the output.

Conversion Formula

  • Degrees to Radians: rad = ° × 0.0174533
  • Radians to Degrees: ° = rad ÷ 0.0174533

Degrees to Radians Conversion Chart

Degrees (°)Radians (rad)
0.10.001745
0.250.004363
0.50.008727
10.017453
20.034907
30.05236
50.087267
100.174533
200.349066
250.436333
500.872665
1001.74533
2504.363325
100017.4533

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FAQ

How many radians are in one degree?

One degree equals approximately 0.0174533 radians. This comes from dividing pi by 180.

Why do mathematicians prefer radians over degrees?

Radians simplify calculus and trigonometric formulas. Derivatives of sine and cosine only work cleanly when the angle is in radians.

What is 180 degrees in radians?

180 degrees equals exactly pi radians, approximately 3.14159. This is the fundamental relationship between the two units.

When should I use degrees instead of radians?

Degrees are more intuitive for everyday measurements like navigation, construction, and geographic coordinates. Radians are preferred in pure mathematics and physics equations.

How many radians are in 1 degre?

1 ° equals 0.017453 rad.

How do you convert degrees to radians?

Multiply the degre value by 0.017453. Formula: rad = ° × 0.0174533.

How many radians are in 5 degrees?

5 ° = 0.087267 rad.

How do you convert radians back to degrees?

Use the inverse formula: ° = rad ÷ 0.0174533. For example, 1 rad = 57.295755 °.