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Convert Degrees to Radians

Seamlessly convert values from Degrees (deg) to Radians (rad). Includes the exact formula, a quick reference table, and real-world context.

Conversion Formula

Radians = Degrees × 0.017453

Degrees to Radians Conversion Table

Degrees (deg)Radians (rad)
1 deg0.017453 rad
2 deg0.034907 rad
5 deg0.087266 rad
10 deg0.174533 rad
15 deg0.261799 rad
20 deg0.349066 rad
25 deg0.436332 rad
50 deg0.872665 rad
100 deg1.7453 rad
500 deg8.7266 rad

About Degrees

The degree is the most common unit for measuring angles. A full circle contains 360 degrees. It is used in geometry, navigation, geography (latitude/longitude), and everyday angle measurements.

Real-World Examples

  • A right angle is exactly 90 degrees
  • The leaning Tower of Pisa leans at about 3.97 degrees from vertical
  • A perfect slam dunk requires a release angle of about 52 degrees

💡 Did you know? The choice of 360 degrees in a circle dates back to ancient Babylon, where a base-60 (sexagesimal) number system was used. 360 was chosen because it has many divisors (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180).

About Radians

The radian is the SI unit for measuring angles. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle equals 2π radians (approximately 6.2832 radians).

Real-World Examples

  • A right angle equals π/2 radians (approximately 1.5708)
  • A full rotation equals 2π radians (approximately 6.2832)
  • In calculus, trigonometric functions use radians by default

💡 Did you know? Radians are considered 'dimensionless' units because they represent a ratio of two lengths (arc length to radius). This is why they are preferred in physics and higher mathematics.

Frequently Asked Questions

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