Rad Degrees Calculator
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Reviewed by Calculator Editorial Team
Convert between radians and degrees with this precise rad degrees calculator. Learn the conversion formula, see examples, and understand when to use each unit.
What is rad degrees?
Radians and degrees are two different units for measuring angles. Degrees are commonly used in everyday contexts, while radians are more common in advanced mathematics and physics.
The degree is a unit of angle measurement that is based on the full circle being divided into 360 equal parts. A full circle is therefore 360 degrees. The radian is a unit of angle measurement that is based on the radius of a circle. A full circle is 2π radians (approximately 6.283 radians).
Key Difference
Degrees are more intuitive for everyday use because they divide a circle into familiar 360 parts. Radians are more natural for mathematical calculations because they relate directly to the radius of a circle.
Conversion formula
The relationship between radians and degrees is defined by the following formulas:
Degrees to Radians
radians = degrees × (π/180)
Radians to Degrees
degrees = radians × (180/π)
Where π (pi) is approximately 3.141592653589793.
Example Conversion
Convert 90 degrees to radians:
90° × (π/180) ≈ 1.5708 radians
How to use this calculator
- Enter the value you want to convert in the input field.
- Select whether you're converting from degrees to radians or radians to degrees.
- Click the "Calculate" button to see the result.
- Use the "Reset" button to clear the calculator.
The calculator will display the converted value and show a visual representation of the angle on a circle.
Common uses
Radians and degrees are used in various fields:
- Mathematics: Calculus and trigonometry often use radians.
- Physics: Many physical laws use radians for angular measurements.
- Engineering: Some engineering calculations use radians.
- Everyday life: Degrees are more common for simple angle measurements.
FAQ
Why do we need both radians and degrees?
Degrees are more intuitive for everyday use because they divide a circle into familiar 360 parts. Radians are more natural for mathematical calculations because they relate directly to the radius of a circle.
Which unit is more precise?
Both units are equally precise. The choice between them depends on the context and the conventions of the field you're working in.
Can I convert radians to degrees without a calculator?
Yes, you can use the conversion formulas (π/180 for degrees to radians and 180/π for radians to degrees) to perform manual conversions.