🎓 Mathematics • Trigonometry
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Degree / Radian Converter
Converts angles between Degrees and Radians with exact fractional π multiples and decimal representations.
Unit Circle Angles:
Trigonometric Functions & Unit Circle Calculator
Angle = 45° = 0.7854 rad (≈ 0.25π)
Trigonometric Ratios & Unit Circle Coordinates
(cos θ, sin θ) = (0.7071, 0.7071)
Sinesin(θ) = 0.7071Exact: √2/2
Cosinecos(θ) = 0.7071Exact: √2/2
Tangenttan(θ) = 1Exact: 1
Cosecant (1/sin)csc(θ) = 1.4142
Secant (1/cos)sec(θ) = 1.4142
Cotangent (1/tan)cot(θ) = 1
Degrees vs. Radians
A degree divides a full circle into 360 equal parts. A radian measures the angle where arc length equals radius (2π rad = 360°).
Formula & Step-by-Step Calculation
rad = deg × (π / 180), deg = rad × (180 / π)
180 degrees exactly equals π radians.
Worked Step-by-Step Examples
Example 1
Convert 180° to radians
Solution: π rad (≈ 3.14159)
• 180 × (π / 180) = π rad
Common Real-World & Academic Use Cases
- ✓ Calculus trigonometric derivatives
- ✓ Physics rotational velocity (rad/s)
- ✓ Computer graphics angles
How to Use the Degree / Radian Converter
1
Select Input Unit
Choose Degrees or Radians.
2
Enter Value
Input angle.
3
Read Conversion
Inspect exact π fraction and decimal.
Frequently Asked Questions
Q: How many degrees is 1 radian?
1 radian ≈ 57.2958 degrees.