1 degree equals approximately 0.0175 radians.
To convert degrees into radians, you multiply the degree value by π divided by 180. This is because a full circle contains 360 degrees or 2π radians, so 1 degree is a fraction of that circle measured in radians.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert degrees to radians is:
radians = degrees × (π / 180)
This works because a full circle has 360 degrees and 2π radians. Dividing both sides by 360 gives:
1 degree = (2π radians) / 360 = π / 180 radians
So, multiplying a degree value by π/180 converts it to radians.
For example:
Convert 1 degree to radians:
1 × (π / 180) = 0.0174533 radians (approximately)
Conversion Example
- Convert 45 degrees to radians:
- Multiply 45 × π / 180
- 45 × 0.0174533 ≈ 0.7854 radians
- This means 45 degrees is about 0.7854 radians.
- Convert 90 degrees to radians:
- 90 × π / 180 = 90 × 0.0174533
- = 1.5708 radians
- So, 90 degrees equals roughly 1.5708 radians.
- Convert 180 degrees to radians:
- 180 × π / 180 = π radians
- This is exactly 3.1416 radians.
- Convert 270 degrees to radians:
- 270 × π / 180 = 4.7124 radians
- 270 degrees equals approximately 4.7124 radians.
- Convert 360 degrees to radians:
- 360 × π / 180 = 2π radians
- This is about 6.2832 radians.
Conversion Chart
| Degree | Radian |
|---|---|
| -24.0 | -0.4189 |
| -20.0 | -0.3491 |
| -16.0 | -0.2793 |
| -12.0 | -0.2094 |
| -8.0 | -0.1396 |
| -4.0 | -0.0698 |
| 0.0 | 0.0000 |
| 4.0 | 0.0698 |
| 8.0 | 0.1396 |
| 12.0 | 0.2094 |
| 16.0 | 0.2793 |
| 20.0 | 0.3491 |
| 24.0 | 0.4189 |
| 26.0 | 0.4538 |
Use the chart by finding the degree value on the left column, then read across to see its radian equivalent. This helps quick conversion without calculation.
Related Conversion Questions
- How many radians is 1 degree equal to?
- What is the radian equivalent of 1° angle?
- How do you convert 1 degree into radians?
- Is 1 degree less than 0.02 radians?
- What is the formula for turning 1 degree into radians?
- Can 1° be expressed exactly in radians?
- What angle in radians corresponds to 1 degree?
Conversion Definitions
Degree: A degree is a unit for measuring angles, dividing a full circle into 360 equal parts. Each degree is subdivided into 60 minutes and seconds for precision. Degrees are widely used in geometry, navigation, and everyday angle measurements.
Rad: Short for radian, a rad is the SI unit of angular measure. One radian is the angle created when the radius length of a circle is wrapped along its circumference. There are exactly 2π radians in a full circle, making it fundamental in trigonometry and calculus.
Conversion FAQs
Why use radians instead of degrees?
Radians are natural for mathematical calculations, specially in calculus and trigonometry. They relate angles directly to arc lengths, making formulas simpler. Degrees are easy for everyday use but less convenient for advanced math.
Is 1 degree exactly equal to 0.0175 radians?
Not exactly; 1 degree equals π/180 radians which is approximately 0.0174533 radians. The value 0.0175 is rounded for simplicity but less precise.
Can you convert radians back to degrees?
Yes, to convert radians to degrees, multiply the radian value by 180/π. This reverses the conversion and gives the angle in degrees.
Why does the conversion formula use π?
Because radians are based on the circle’s radius and circumference, and π relates diameter and circumference. Using π connects degrees to the circle’s geometry, enabling direct conversion.
Are there any angles where degree to radian conversion is exact?
Yes, angles like 0°, 90°, 180°, 270°, and 360° convert to exact multiples of π/2 radians. For example, 180° equals π radians exactly.