Angle Converter
Convert angle units instantly, including degrees, radians, and gradians. Ideal for math, engineering, physics, and navigation calculations.
| Degrees | Radians |
|---|---|
| 0 | 0 |
| 15 | 0.2618 |
| 30 | 0.5236 |
| 45 | 0.7854 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 135 | 2.35619 |
| 150 | 2.61799 |
| 180 | 3.14159 |
| 210 | 3.66519 |
| 225 | 3.92699 |
| 240 | 4.18879 |
| 270 | 4.71239 |
| 300 | 5.23599 |
| 315 | 5.49779 |
| 330 | 5.75959 |
| 360 | 6.28319 |
Understanding Angles π
Angles describe the rotation between two lines around a point. They are fundamental in mathematics, physics, engineering, navigation, and computer graphics.
This converter allows quick and accurate conversions between degrees, radians, and gradians for all practical applications.
Using standard ranges ensures clarity and avoids mistakes in calculations or diagrams.
Key Facts
- A full circle = 360 degrees = 2Ο radians = 400 gradians.
- Radians link an angle directly to the circle's radius, simplifying math and physics formulas.
- Gradians were created to make right angles exactly 100 units, easing percentage-based calculations.
- Degrees are widely used in navigation, surveying, and daily life.
Formulas
radians = degrees Γ (Ο / 180)- Convert degrees to radians.degrees = radians Γ (180 / Ο)- Convert radians to degrees.gradians = degrees Γ (400 / 360)- Convert degrees to gradians.degrees = gradians Γ (360 / 400)- Convert gradians to degrees.
Common Angle Conversions
- 90Β° = Ο/2 radians = 100 gradians
- 180Β° = Ο radians = 200 gradians
- 45Β° = Ο/4 radians = 50 gradians
- 270Β° = 3Ο/2 radians = 300 gradians
FAQs
Why are radians used in math instead of degrees?
Radians simplify formulas involving circles, derivatives, and integrals. Many mathematical functions assume angles are in radians.
When are gradians useful?
Gradians are convenient in engineering and surveying because right angles are exactly 100 gradians, making fractions easy to work with.
Can I mix degrees and radians in calculations?
Mixing units can lead to errors. Always convert all angles to the same unit before calculating.