Enter Radian Values
Use decimal values, fractions, π multiples, or expressions. Parentheses and scientific notation are supported.
Degrees = Radians × 180 ÷ π
The inverse conversion is Radians = Degrees × π ÷ 180.
How to Use This Calculator
- Select the input format matching your radian value.
- Enter one value or a supported mathematical expression.
- Choose precision, rounding, normalization, and π settings.
- Add optional batch values for several simultaneous conversions.
- Press the conversion button to view detailed results.
- Copy, download CSV, or print results as PDF.
Radians and Degrees Explained
A radian measures an angle using a circle’s radius. One complete rotation contains 2π radians. The same rotation contains exactly 360 degrees.
Therefore, π radians equals 180 degrees. Multiply radians by 180 and divide by π. This relationship handles positive, negative, and oversized angles.
Normalized angles show equivalent positions within one rotation. Reference angles describe the acute angle to the x-axis. Coterminal angles differ by complete 360-degree rotations.
Common Radians to Degrees Table
| Radians | Degrees | Unit-circle point |
|---|---|---|
| 0 | 0° | (1, 0) |
| π/6 | 30° | (√3/2, 1/2) |
| π/4 | 45° | (√2/2, √2/2) |
| π/3 | 60° | (1/2, √3/2) |
| π/2 | 90° | (0, 1) |
| 2π/3 | 120° | (−1/2, √3/2) |
| 3π/4 | 135° | (−√2/2, √2/2) |
| π | 180° | (−1, 0) |
| 3π/2 | 270° | (0, −1) |
| 2π | 360° | (1, 0) |
Worked Examples
Example 1: Convert π/3 radians
Multiply π/3 by 180 and divide by π. The π values cancel from the fraction. The result is exactly 60 degrees.
Example 2: Convert 2.5 radians
Multiply 2.5 by 180 and divide by π. The decimal result is approximately 143.239449 degrees. Its position lies within Quadrant II.
Example 3: Convert −3π/2 radians
The direct result equals −270 degrees. A positive coterminal angle equals 90 degrees. Both angles share the same terminal side.
Frequently Asked Questions
How do I convert radians to degrees?
Multiply the radian value by 180. Then divide the product by π. The result is the angle in degrees.
Why does π radians equal 180 degrees?
A full circle contains 2π radians. A full circle also contains 360 degrees. Dividing both values by two gives equality.
Can I enter π-based expressions?
Yes, expressions like pi/6 work directly. You may also enter 3*pi/4. The calculator recognizes the π symbol too.
What is a coterminal angle?
Coterminal angles share the same terminal side. They differ by complete 360-degree rotations. Positive and negative versions are displayed automatically.
What is a reference angle?
A reference angle is always nonnegative and acute. It measures the terminal side from the x-axis. Axis angles can have zero reference angles.
Why is tangent sometimes undefined?
Tangent equals sine divided by cosine. It is undefined when cosine equals zero. This occurs at odd multiples of π/2.
Can negative radians be converted?
Yes, negative radians represent clockwise rotation. Their degree results are negative before normalization. Equivalent positive coterminal angles are also shown.
What does angle normalization do?
Normalization places angles inside a selected interval. It does not change their terminal position. Common intervals include 0–360 and −180–180 degrees.
Can I export multiple conversions?
Yes, enter multiple expressions in the batch field. Separate values using commas or new lines. The CSV export includes every displayed batch result.