10 degrees is equal to approximately 0.1745 radians.
The conversion from degrees to radians involves multiplying the degree value by π and dividing by 180. Since a full circle is 360 degrees or 2π radians, this ratio helps convert angles between these two units.
Conversion Tool
Result in radians:
Conversion Formula
The formula to convert degrees to radians is:
radians = degrees × (π / 180)
This formula works because a full rotation is 360 degrees which equals 2π radians. Dividing both sides by 360 gives 1 degree equals π/180 radians. Multiplying degrees by this factor converts them to radians.
For example, converting 10 degrees:
- Start with 10 degrees
- Multiply by π/180: 10 × (π/180)
- Calculate: 10 × 0.0174533 ≈ 0.174533 radians
Conversion Example
- Convert 45 degrees to radians:
- 45 × (π/180) = 45 × 0.0174533 = 0.7854 radians
- Convert 90 degrees to radians:
- 90 × (π/180) = 90 × 0.0174533 = 1.5708 radians
- Convert 180 degrees to radians:
- 180 × (π/180) = 180 × 0.0174533 = 3.1416 radians
- Convert 270 degrees to radians:
- 270 × (π/180) = 270 × 0.0174533 = 4.7124 radians
- Convert 360 degrees to radians:
- 360 × (π/180) = 360 × 0.0174533 = 6.2832 radians
Conversion Chart
The chart below shows degree values from -15.0 to 35.0 and their equivalent radians. You can use this chart to quickly find radians for common degree values without calculations.
| Degrees | Radians |
|---|---|
| -15.0 | -0.2618 |
| -10.0 | -0.1745 |
| -5.0 | -0.0873 |
| 0.0 | 0.0000 |
| 5.0 | 0.0873 |
| 10.0 | 0.1745 |
| 15.0 | 0.2618 |
| 20.0 | 0.3491 |
| 25.0 | 0.4363 |
| 30.0 | 0.5236 |
| 35.0 | 0.6109 |
Related Conversion Questions
- How many radians are in 10 degrees exactly?
- What is the formula to convert 10 degrees to radians?
- Can you convert 10 degrees to radians without a calculator?
- Why does 10 degrees equal about 0.1745 radians?
- How to use the degree to radians conversion tool for 10 degrees?
- Are radians and degrees interchangeable when measuring 10 degrees?
- What angle in radians corresponds to 10 degrees in a circle?
Conversion Definitions
Degree: A degree is a unit of angular measurement equal to 1/360 of a full circle. It is divided into 60 minutes and each minute into 60 seconds. Degrees are commonly used in geometry, navigation, and everyday angle measurements due to its simple division of circles into parts.
Radians: A radian is the angle created when the length of the arc of a circle equals the radius of that circle. It represents the standard unit of angular measure in mathematics and science, where one full rotation equals 2π radians, about 6.283 radians.
Conversion FAQs
Why is π divided by 180 in the degree to radians formula?
The division by 180 in the formula comes from the relationship between degrees and radians. Since 180 degrees equals π radians, multiplying degrees by π/180 converts the angle to radians. This factor adjusts the scale from the degree system to the radian system.
Can I convert radians back to degrees easily?
Yes, converting radians to degrees is reversing the process. You multiply radians by 180 divided by π. This switches the angle measurement from radians back into degrees, useful for understanding or communication in degrees.
Is the conversion exact or approximate?
The conversion uses π, which is an irrational number with infinite decimals. Because of this, the result is an approximation when rounded for practical use. The formula itself is exact, but decimals may be rounded in calculations.
Why use radians instead of degrees in some calculations?
Radians simplify many mathematical formulas, especially in calculus and trigonometry, because they relate angles directly to the radius and arc length. This makes derivatives and integrals of trigonometric functions cleaner and more natural in radians.
Can negative degrees be converted to radians?
Yes, negative degrees represent rotation in the opposite direction and convert normally using the same formula. Negative degree values produce negative radian results, indicating direction but the conversion method stays consistent.