Degrees to Radians Converter
How It Works
This degrees to radians converter uses established formulas to provide accurate results.
The basic rule:
- Radians = Degrees × (π/180)
- Degrees = Radians × (180/π)
- Full circle = 360° = 2π radians
- 1 radian ≈ 57.2958°
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by π/180. For example, 90° × π/180 = π/2 radians. Common conversions: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.
How do I convert radians to degrees?
Multiply the radian value by 180/π. For example, π/3 × 180/π = 60°.
Why do we use radians in math?
Radians are the natural unit for angles in calculus and higher math because they simplify formulas. For instance, the derivative of sin(x) is cos(x) only when x is in radians. Arc length also simplifies to s = rθ.
What is a radian?
A radian is the angle subtended at the center of a circle by an arc whose length equals the radius. One full revolution = 2π radians ≈ 6.2832 radians.