150 degrees is approximately 2.61799 radians.
To convert degrees to radians, we multiply the degrees by π divided by 180. For 150 degrees, this calculation is 150 × π/180, which simplifies to 5π/6. Numerically, it equals about 2.61799 radians, because π is approximately 3.14159.
Conversion of Degrees to Radian
Result in radian:
Conversion Formula
The formula to convert degrees to radians is: radians = degrees × π / 180. This works because a full circle has 2π radians, which aligns with 360 degrees. Dividing 2π by 360 gives π/180, the conversion factor. Multiplying degrees by this factor yields radians.
For example, to convert 150 degrees, multiply 150 by π/180: 150 × π/180 = (150/180) × π = (5/6) × π = 5π/6.
Conversion Example
- Convert 90 degrees:
- Step 1: Write formula: radians = degrees × π / 180.
- Step 2: Substitute 90: 90 × π / 180.
- Step 3: Simplify numerator: 90/180 = 1/2.
- Step 4: Result: 1/2 × π = π/2 ≈ 1.5708 radians.
- Convert 45 degrees:
- Step 1: Formula: radians = 45 × π / 180.
- Step 2: Simplify: 45/180 = 1/4.
- Step 3: Result: 1/4 × π = π/4 ≈ 0.7854 radians.
- Convert 180 degrees:
- Step 1: Formula: radians = 180 × π / 180.
- Step 2: Simplify: 180/180 = 1.
- Step 3: Result: 1 × π = π ≈ 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 | 2.61799 |
| 155.0 | 2.7053 |
| 160.0 | 2.7925 |
| 165.0 | 2.8798 |
| 170.0 | 2.9670 |
| 175.0 | 3.0543 |
This chart helps you quickly find the radian equivalents for degrees from 125 to 175. To use, locate the degree value and read across to see the radian measure.
Related Conversion Questions
- How many radians is 150 degrees exactly?
- What is the radian value of 150 degrees in decimal form?
- Can you show me the step-by-step conversion of 150 degrees to radians?
- What is the formula used to convert 150 degrees into radians?
- How do I convert degrees like 150 into radians without a calculator?
- Is 150 degrees equal to 5π/6 radians?
- What is the radian equivalent of 150 degrees in fractions?
Conversion Definitions
Degrees
Degrees are units measuring angles, where a full circle equals 360 degrees. This division makes it easy to specify angles, with each degree representing 1/360th of a complete rotation, widely used in navigation, cooking, and geometry.
Radian
Radian is an angle measurement based on the radius of a circle, where one radian equals the angle at which the arc length equals the radius. It provides a natural measure for angles in mathematics, with a full circle being 2π radians.
Conversion FAQs
Why is π used in converting degrees to radians?
π appears because a circle’s circumference relates to its radius through π. Since radians measure angles based on arc length, π naturally appears in formulas converting degrees to radians, maintaining proportional relationships between the two units.
Can I convert any degrees to radians using the same formula?
Yes, the formula radians = degrees × π / 180 works universally for all degree values, providing a consistent method to convert any angle measurement from degrees to radians accurately.
What is the significance of 180 degrees in radians?
180 degrees equals π radians, as it represents half a circle. This key conversion point helps relate degrees to radians directly, serving as the basis for converting any degree measure into its radian equivalent.