What are Degrees and Radians?
Degrees and radians are two units of measuring angles, both units are explained in detail below:
- 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, which is around 6.283
- Radians are used in higher mathematics and physics calculations, as they simplify many formulas
How to Convert Degrees to Radians
The conversion between degrees and radians 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 degrees to radians:
Use the formula:
Radians = Degrees × (π / 180)
Example: Convert 90° to radians:
Radians = 90 × (π / 180) = π/2 = 1.57 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°
Note: Use a calculator with a π (pi) value, that is 3.1416.
This conversion is essential in physics, engineering, or any mathematic calculation where angles are measured in radians.
Degree to Radian 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)
Where You Can Use This
- Trigonometry: Changing angle units for solving math problems
- Physics: Using angles for things like spinning objects
- Engineering: Working with machines parts that rotate
- Computer Graphics: Rotating shapes in design and animation
Therefore, this tool accurately converts degrees to radians, and even radians to degrees, and is perfect for math, science, or engineering tasks when angle measurements are required.
