25 degrees equals approximately 0.4363 radians.
Table of Contents
To convert degrees to radians, the degree value is multiplied by π and divided by 180, because a full circle is 360 degrees or 2π radians. This relationship makes converting any degree measure to radians straightforward.
Conversion Tool
Result in radians:
Conversion Formula
The formula to convert degrees (°) to radians (rad) is:
radians = degrees × (π / 180)
This works because a circle has 360 degrees and 2π radians, so 1 degree equals π/180 radians. Multiplying degrees by π/180 converts the angle to its equivalent length on the radian scale.
For example, converting 25 degrees:
- Start with 25°
- Multiply 25 by π: 25 × π = 25π
- Divide by 180: 25π ÷ 180 = (25/180)π
- Numerical value: (25/180) × 3.1416 ≈ 0.4363 radians
Conversion Example
- Convert 45 degrees to radians:
- 45 × π = 45π
- 45π ÷ 180 = (45/180)π = (1/4)π
- Numerically: 0.7854 radians
- Convert 90 degrees to radians:
- 90 × π = 90π
- 90π ÷ 180 = (90/180)π = (1/2)π
- Numerically: 1.5708 radians
- Convert 60 degrees to radians:
- 60 × π = 60π
- 60π ÷ 180 = (60/180)π = (1/3)π
- Numerically: 1.0472 radians
- Convert 10 degrees to radians:
- 10 × π = 10π
- 10π ÷ 180 = (10/180)π = (1/18)π
- Numerically: 0.1745 radians
Conversion Chart
| Degrees | Radians | Degrees | Radians | Degrees | Radians |
|---|---|---|---|---|---|
| 0.0 | 0.0000 | 10.0 | 0.1745 | 20.0 | 0.3491 |
| 1.0 | 0.0175 | 11.0 | 0.1910 | 21.0 | 0.3665 |
| 2.0 | 0.0349 | 12.0 | 0.2094 | 22.0 | 0.3839 |
| 3.0 | 0.0524 | 13.0 | 0.2269 | 23.0 | 0.4014 |
| 4.0 | 0.0698 | 14.0 | 0.2443 | 24.0 | 0.4189 |
| 5.0 | 0.0873 | 15.0 | 0.2618 | 25.0 | 0.4363 |
| 6.0 | 0.1047 | 16.0 | 0.2793 | 26.0 | 0.4538 |
| 7.0 | 0.1222 | 17.0 | 0.2967 | 27.0 | 0.4712 |
| 8.0 | 0.1396 | 18.0 | 0.3142 | 28.0 | 0.4887 |
| 9.0 | 0.1571 | 19.0 | 0.3316 | 29.0 | 0.5061 |
| 30.0 | 0.5236 | 40.0 | 0.6981 | 50.0 | 0.8727 |
This chart list degrees in increments, beside their radian equivalents. To find a radian value for any degree, look for the closest degree in the table, then read across to see its radian measure.
Related Conversion Questions
- How many radians are in 25 degrees exactly?
- What is the radian value for 25 degrees when calculating angles?
- How do I convert 25 degrees to radians for a trigonometry problem?
- Is 25 degrees more or less than 0.5 radians?
- What formula is used to change 25 degrees into radians?
- How precise is the radian equivalent of 25 degrees?
- Can 25 degrees be converted to radians without a calculator?
Conversion Definitions
Degrees: Degrees is a unit to measure angles, dividing a circle into 360 equal parts. Each part, called one degree, is used in geometry and navigation to describe the size of an angle or rotation, making it easier to express angular measurements on a familiar scale.
Radians: Radians is a unit for measuring angles based on the radius of a circle. One radian is the angle formed when the length of the arc equals the radius, which gives a natural way to relate linear and angular measurements in mathematics and physics.
Conversion FAQs
Why is π divided by 180 in the degree to radian formula?
Because a full circle has 360 degrees and 2π radians, dividing π by 180 converts degrees to radians proportionally. This fraction represents the radian measure of one degree, ensuring the angle corresponds correctly between the two units.
Can radians be greater than 2π?
Yes, radians can be greater than 2π, which represents one full rotation. Angles larger than 360 degrees have radian measures exceeding 2π, useful in describing multiple rotations or angles beyond a single circle.
Is it necessary to convert degrees to radians in calculations?
Many mathematical functions, especially trigonometric functions in programming or calculus, require radians because they work with the radius-based angle measure. Using degrees without conversion can cause incorrect results.
How accurate is converting 25 degrees to radians using decimals?
The decimal approximation, like 0.4363, is usually precise enough for most uses. However, for high-precision calculations, keeping the value as a fraction of π or using more decimal places reduces rounding errors.
What happens if I input a negative degree value in the conversion tool?
Negative degree values convert to negative radians, indicating angles measured in the opposite direction. The tool handles negative inputs correctly, showing the corresponding negative radian value.