Convert angles between degrees and radians instantly. Includes π notation, revolutions, and gradians - type in either field for instant conversion
Conversion Formula
radians = degrees × (π/180)
degrees = radians × (180/π)
Example: 90, 180, 360
Example: 1.5708, 3.1416, 6.2832
Degrees
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Radians (decimal)
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Radians (π notation)
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Revolutions
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Gradians
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Angles can be measured in multiple units, with degrees and radians being the most common in mathematics and science. Understanding both systems and converting between them is essential for trigonometry, calculus, physics, and engineering applications.
Degrees are the most intuitive angle measurement for most people. A full circle is divided into 360 degrees, possibly originating from ancient Babylonian astronomy which used a base-60 number system. Common angles include 90° (right angle), 180° (straight line), and 360° (full rotation). Degrees are ideal for everyday applications, navigation, and introductory mathematics. For more on understanding degrees and radians conversion, check out additional resources.
Radians measure angles based on the radius of a circle. One radian is the angle formed when the arc length equals the radius. A full circle contains 2π radians (approximately 6.28). Radians are the natural unit for calculus and physics because they simplify many mathematical formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Learn more about converting between degrees and radians for practical applications.
Key Conversions:
180° = π radians
90° = π/2 radians
360° = 2π radians
1 radian ≈ 57.296°
| Degrees | Radians (π) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.524 |
| 45° | π/4 | 0.785 |
| 60° | π/3 | 1.047 |
| 90° | π/2 | 1.571 |
| 180° | π | 3.142 |
| 360° | 2π | 6.283 |
Use Degrees for: Navigation, construction, everyday measurements, introductory geometry, and when communicating with non-technical audiences. Degrees are more intuitive for most people.
Use Radians for: Calculus, physics, advanced mathematics, computer programming, and any situation involving derivatives or integrals of trigonometric functions. Radians make mathematical formulas simpler and more elegant.
Radians are the "natural" unit for angles in mathematics because they simplify many formulas. In calculus, derivatives and integrals of trig functions work cleanly with radians but require correction factors with degrees.
A full circle contains 2π radians (approximately 6.283 radians), which equals 360 degrees. This comes from the circumference formula C = 2πr.
π/2 radians equals 90 degrees (a right angle). This is one of the most common angle conversions you'll encounter.
Yes! Negative angles indicate rotation in the opposite direction (clockwise instead of counterclockwise). For example, -90° equals 270° measured in the positive direction.
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