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The result of converting 150 degrees to radian is approximately 2.6179 radians.
To convert degrees into radian, we multiply the degree value by π divided by 180. So, for 150 degrees, the calculation is 150 × π / 180, which simplifies to 5π / 6, giving us about 2.6179 radians.
Conversion Result and Explanation
Conversion Tool
Result in radian:
Conversion Formula
The conversion from degrees to radian is based on the relationship that 180 degrees equals π radians. The formula is degrees × π / 180. Since π radians equals 180 degrees, multiplying degrees by π/180 gives us the equivalent in radians. For example, converting 150 degrees:
- Start with the degree value: 150
- Multiply by π: 150 × π
- Divide by 180: (150 × π) / 180
- Simplify: (5 × π) / 6
- Approximate: 2.6179 radians
Conversion Example
- Convert 90 degrees to radian:
- Start with 90 degrees
- Multiply 90 by π: 90 × π
- Divide by 180: (90 × π) / 180
- Simplify: π / 2
- Result: approximately 1.5708 radians
- Convert 45 degrees:
- Start with 45 degrees
- Multiply by π: 45 × π
- Divide by 180: (45 × π) / 180
- Simplify: π / 4
- Result: about 0.7854 radians
- Convert 180 degrees:
- Start with 180 degrees
- Multiply by π: 180 × π
- Divide by 180: (180 × π) / 180
- Simplify: π
- Result: approximately 3.1416 radians
Conversion Chart
| Degrees | Radians |
|---|---|
| 125.0 | 2.1817 |
| 130.0 | 2.2689 |
| 135.0 | 2.3562 |
| 140.0 | 2.4435 |
| 145.0 | 2.5307 |
| 150.0 | 2.6179 |
| 155.0 | 2.7053 |
| 160.0 | 2.7925 |
| 165.0 | 2.8798 |
| 170.0 | 2.9671 |
| 175.0 | 3.0543 |
This chart helps to quickly find the radian equivalent for selected degree values. To use, locate your degree value in the first column and read across to see the radian conversion.
Related Conversion Questions
- How many radians are in 150 degrees?
- What is the radian measure of 150 degrees?
- Convert 150 degrees into radians step-by-step?
- Why is 150 degrees equal to about 2.6179 radians?
- How do I convert other degrees to radians using the formula?
- What is the value of 150 degrees in terms of π?
- Is there a quick way to convert 150 degrees to radians without a calculator?
Conversion Definitions
Degrees
Degrees are units used to measure angles, where one full circle equals 360 degrees. It divides a circle into 360 equal parts, making it a common way to express angles in navigation, geometry, and everyday usage.
Radian
Radian is an angle measure based on the radius of a circle, where one radian equals the angle at the center of a circle subtended by an arc equal in length to the radius. A full circle contains 2π radians, linking geometry and calculus.
Conversion FAQs
What is the easiest way to convert 150 degrees into radians?
The simplest method is multiplying the degree value by π and dividing by 180. For 150 degrees, it becomes 150 × π / 180 which simplifies to 5π / 6, roughly 2.6179 radians.
Can I use a calculator instead of the formula?
Yes, many calculators have a built-in radian conversion function. You can enter 150 degrees and select the radian mode, or directly input 150 × π / 180 into a calculator to get the result.
Why does the conversion involve π?
Because a radian relates to the arc length of a circle, and π radians equals 180 degrees, the factor π/180 ensures an accurate conversion from degrees to the radian measure based on circle geometry.
How is the conversion different for other angle measures?
The process remains the same; multiply the degree measure by π and divide by 180. For larger or smaller angles, this formula accurately converts any degree value into radians.
What is the significance of 180 degrees in the conversion?
180 degrees is the measure of a straight angle, which corresponds to π radians. This makes it the fundamental reference point for converting degrees into the radian system.
