Radian to Degree Calculator
Use decimal radians or a fraction of π. The calculator can also normalize the degree output and show decimal plus DMS results.
Plotly Conversion Graph
The line shows the linear relationship between radians and degrees. Your calculated point is highlighted on the chart.
Example Data Table
| Radian Input | Degree Output | DMS Output |
|---|---|---|
| π/12 | 15.0000° | 15° 0' 0.0000" |
| π/6 | 30.0000° | 30° 0' 0.0000" |
| π/4 | 45.0000° | 45° 0' 0.0000" |
| π/3 | 60.0000° | 60° 0' 0.0000" |
| π/2 | 90.0000° | 90° 0' 0.0000" |
| π | 180.0000° | 180° 0' 0.0000" |
| 3π/2 | 270.0000° | 270° 0' 0.0000" |
| 2π | 360.0000° | 360° 0' 0.0000" |
Formula Used
Main conversion formula:
Degrees = Radians × 180 / π
This formula scales a radian measure by 180 divided by π, because π radians equals 180 degrees. The calculator applies this formula first, then it optionally normalizes the result and formats it as decimal degrees and DMS.
Reverse reference formula:
Radians = Degrees × π / 180
This reverse formula helps when you want to convert a degree angle into radians. It is included here because several common angle questions use the opposite direction.
How to Use This Calculator
- Select Decimal Radians or π Fraction as your input mode.
- Enter the angle value. For π fractions, type the numerator and denominator.
- Choose the number of decimal places for rounding.
- Pick whether you want no normalization, 0° to 360°, or -180° to 180°.
- Choose the output format you want to see.
- Press Calculate to show the result above the form.
- Review the conversion table, steps, and graph.
- Use the CSV or PDF buttons to export the current result.
Answers to Requested Questions
Convert the given angle measure from degrees to radians: 135°
Use radians = degrees × π / 180. So, 135 × π / 180 = 3π / 4. Therefore, 135° equals 3π/4 radians.
Degrees to radians formula
The formula is radians = degrees × π / 180. Multiply the degree value by π, then divide by 180 to get the radian measure.
π/10 radians to degrees
Use degrees = radians × 180 / π. For π/10, the π cancels, leaving 180 / 10 = 18°.
3π radians to degrees
Apply degrees = radians × 180 / π. For 3π, the π cancels, giving 3 × 180 = 540°.
360 degree to radian
Use radians = degrees × π / 180. So, 360 × π / 180 = 2π radians.
1 radian to degrees
Use degrees = 1 × 180 / π. This equals about 57.2958°. One radian is slightly less than 60 degrees.
330 degrees to radians
Use radians = degrees × π / 180. So, 330 × π / 180 simplifies to 11π/6 radians.
6 radians to degrees
Use degrees = 6 × 180 / π. That gives about 343.7747°. The exact value is 1080 / π degrees.
FAQs
1. What is the fastest way to convert radians to degrees?
Multiply the radian value by 180 and divide by π. This is the standard formula and works for decimals, fractions of π, positive angles, and negative angles.
2. Why does the formula use 180 divided by π?
Because π radians is exactly equal to 180 degrees. The ratio 180/π converts the angle from the radian scale to the degree scale.
3. Can this calculator handle π fractions like 3π/4?
Yes. Choose the π fraction mode, enter the numerator and denominator, and the calculator converts the fraction into radians before computing the degree result.
4. What does normalization mean in angle conversion?
Normalization rewrites the degree answer into a preferred interval, such as 0° to 360° or -180° to 180°, without changing the angle’s direction.
5. What is DMS output?
DMS stands for degrees, minutes, and seconds. It is another way to display angular measurements and is useful in surveying, navigation, and geometry problems.
6. Can I convert negative radians to degrees?
Yes. The same formula applies. A negative radian value produces a negative degree value unless you choose a normalization option to rewrite it.
7. Is 1 radian equal to 60 degrees?
No. One radian is approximately 57.2958 degrees. It is close to 60 degrees, but not exact.
8. Can I export the result for reports or homework?
Yes. After calculation, use the CSV button for spreadsheet-style data or the PDF button for a clean summary you can save or share.