Convert from Radians to Degrees
Conversion Calculator
Welcome to our Convert from Radians to Degrees Calculator.
This math calculator will help you to convert between angles in radians to angles in degrees.
You can also choose your own degree of accuracy.
Convert from Radians to Degrees Conversion Calculator
How It Works
- Select the angle in radians you want to convert.
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your desired accuracy (default is 2 decimal places)
- Click the Convert button
- You will be shown the angle in degrees to the required number of decimal places and also the working out along the way.
Convert From Radians to Degrees Formula
We can see the relationship between radians and degrees by looking at the angles in one full turn:
- One full turn is equal to 360°
- One full turn is equal to 2π radians
This shows us that 360° = 2π radians.
By dividing both sides of the equation by 2, we get:
180° = π radians
Using this equation, we can deduce the formulas for converting between radians and degrees.
The formula for converting an angle from radians to degrees:
\[ d = {180 \over \pi } r \]
where d is the angle in degrees and r is the angle in radians.
This means that to change an angle from radians to degrees:
- Multiply the number by 180.
- Divide the result by π
Convert Radians to Degrees Examples
1) Convert 2.3 radians into degrees, giving your answer to 1 decimal place.
Step 1) Multiply the number of radians by 180.
- \[ 2.3 \times 180 = 414 \]
Step 2) Divide this result by π
- \[ 414 \div \pi = 131.78029... \]
So 2.3 radians = 131.8° to 1 decimal place.
2) Convert 1 ½ radians into degrees, giving your answer to 1 decimal place.
Step 1) Multiply the number of radians by 180.
- \[ 1 {1 \over 2} \times 180 = 270 \]
Step 2) Divide this result by π
- \[ 270 \div \pi = 85.943669.. \]
So 1 ½ radians = 85.9° to 1 decimal place.
3) Convert π/3 radians into degrees
Step 1) Multiply the number of radians by 180.
- \[ { \pi \over 3} \times 180 = {180 \pi \over 3} = 60 \pi \]
Step 2) Divide this result by π
- \[ 60 \pi \div \pi = 60 \]
So π/3 radians = 60°.
4) Convert 5 ¼ radians into degrees, giving your answer to 2 decimal places.
Step 1) Multiply the number of radians by 180.
- \[ 5 {1 \over 4} \times 180 = 945 \]
Step 2) Divide this result by π
- \[ 945 \div \pi = 300.80284.. \]
So 5 ¼ radians = 300.80° to 2 decimal places.
Common Conversions Facts radians to degrees
Here are some a few quick simple conversion facts from radians to degrees.
| RADIANS | DEGREES |
|---|---|
| \[ 0 \; radians \] | 0° |
| \[ {\pi \over 2} \; radians \] | 90° |
| \[ \pi \; radians \] | 180° |
| \[ {3\pi \over 2} \; radians \] | 270° |
| \[ 2\pi \; radians \] | 360° |
| \[ {\pi \over 4} \; radians \] | 45° |
| \[ {3\pi \over 4} \; radians \] | 135° |
| \[ {\pi \over 6} \; radians \] | 30° |
| \[ {\pi \over 3} \; radians \] | 60° |
| \[ {2\pi \over 3} \; radians \] | 120° |
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