Convert from Degrees to Radians
Conversion Calculator
Welcome to our Convert from Degrees to Radians Calculator.
This math calculator will help you to convert between angles in degrees to angles in radians.
You can also choose your own degree of accuracy.
Convert from Degrees to Radians Conversion Calculator
How It Works
- Select the angle in degrees 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: 32 1/2 (thirty-two and one-half); 100 4/5 (one hundred and four-fifths); 71 1/3 (seventy-one 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 Degrees to Radians Formula
We can see the relationship between degrees and radians 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 degrees to radians:
\[ r = {\pi \over 180 } d \]
where r is the angle in radians and d is the angle in degrees.
This means that to change an angle from degrees to radians:
- Multiply the number by π.
- Divide the result by 180
Convert Degrees to Radians Examples
1) Convert 140 degrees into radians, giving your answer to 2 decimal places.
Step 1) Multiply the number of degrees by π.
- \[ 140 \times \pi = 140 \pi \]
Step 2) Divide this result by 180
- \[ 140 \pi \div 180 = {140 \pi \over 180} = {7 \pi \over 9} \]
- \[ {7 \pi \over 9} = 2.443461 \]
So 140° = 2.44 radians to 2 decimal places.
2) Convert 75 degrees into radians, giving your answer to 1 decimal place.
Step 1) Multiply the number of degrees by π.
- \[ 75 \times \pi = 75 \pi \]
Step 2) Divide this result by 180
- \[ 75 \pi \div 180 = {75 \pi \over 180 } = {5 \pi \over 12} \]
- \[ {5 \pi \over 12} = 1.308997 \]
So 75° = 1.31 radians to 2 decimal places.
3) Convert 243 degrees into radians, giving your answer to 1 decimal place.
Step 1) Multiply the number of degrees by π.
- \[ 243 \times \pi = 243 \pi \]
Step 2) Divide this result by 180
- \[ 243 \pi \div 180 = {243 \pi \over 180} = {27 \pi \over 20} \]
- \[ {27 \pi \over 20 } = 4.2411501 \]
So 243° = 4.2 radians to 1 decimal place.
4) Convert 150 degrees into radians, giving your answer to 2 decimal places.
Step 1) Multiply the number of degrees by π.
- \[ 150 \times \pi = 150 \pi \]
Step 2) Divide this result by 180
- \[ 150 \pi \div 180 = {150 \pi \over 180} = {5 \pi \over 6} \]
- \[ {5 \pi \over 6 } = 2.6179939 \]
So 150° = 2.62 radians to 2 decimal places.
Common Conversions Facts Degrees to Radians
Here are some a few quick simple conversion facts from degrees to radians.
| DEGREES | RADIANS |
|---|---|
| 0° | \[ 0 \; radians \] |
| 90° | \[ {\pi \over 2} \; radians \] |
| 180° | \[ \pi \; radians \] |
| 270° | \[ {3\pi \over 2} \; radians \] |
| 360° | \[ 2\pi \; radians \] |
| 45° | \[ {\pi \over 4} \; radians \] |
| 135° | \[ {3\pi \over 4} \; radians \] |
| 30° | \[ {\pi \over 6} \; radians \] |
| 60° | \[ {\pi \over 3} \; radians \] |
| 120° | \[ {2\pi \over 3} \; radians \] |
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