What are Radians and Degrees?
Radians and degrees are two units for measuring angles:
- Degrees are the more familiar unit, where a full circle is 360°
- Radians are based on the radius of a circle, where a full circle is 2π radians (about 6.283)
- Radians are often used in higher mathematics and physics because they simplify many formulas
How to Convert Radians to Degrees
The conversion between radians and degrees is based on the mathematical calculation between the circumference of a circle and its angles. A full circle has 360 degrees, which is equal to 2π radians. Therefore, a half of a circle is 180 degrees, which is equal to π radians. This ratio 180° = π radians and it allows to convert between these two units of angle measurement.
180° = π radians
This means a full half circle is equal to 180 degrees or π radians.
To convert radians to degrees:
Use the formula:
Degrees = Radians × (180 / π)
Example: Convert 2 radians to degrees:
Degrees = 2 × (180 / π) = 114.59°
To convert degrees to radians:
Use the formula:
Radians = Degrees × (π / 180)
Example: Convert 90° to radians:
Radians = 90 × (π / 180) = π/2 = 1.57 radians
Note: Use a calculator with a π (pi) value, that is 3.1416.
This conversion is important in mathematics, physics, or engineering, where angles are measured in radians.
Degree to Angle Conversions
- 0° = 0 radians
- 30° = 0.5236 radians
- 45° = 0.7854 radians
- 60° = 1.0472 radians
- 90° = 1.5708 radians
- 180° = 3.1416 radians (π)
- 360° = 6.2832 radians (2π)
Use Cases
- Trigonometry: Converting between units for trigonometric functions
- Physics: Working with angular velocity or rotational motion
- Engineering: Calculations involving circular motion or rotations
- Computer Graphics: Working with rotation transformations
Therefore, this angle tool helps you convert between degrees and radians, saving you time and giving error-free results when working with angle measurements.
