150 degrees is equal to approximately 2.61799 radians.
To convert degrees to radians, you multiply the degree value by π/180. This changes the unit from degrees, which divide a circle into 360 parts, to radians, which measure angles based on the radius of a circle.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert degrees (deg) to radians (rad) is:
radians = degrees × (π / 180)
This works because a full circle is 360 degrees but also equals 2π radians. Dividing both sides by 360 shows that 1 degree equals π/180 radians. So, multiply any degree measure by π/180 to get radians.
For example, converting 150 degrees:
- Start with 150 degrees
- Multiply 150 × π/180
- This simplifies to (150/180) × π = (5/6) × π
- Numerically, 5/6 × 3.14159 ≈ 2.61799 radians
Conversion Example
- Convert 90 degrees to radians:
- Multiply 90 × π/180
- 90/180 = 1/2, so 1/2 × π
- 1/2 × 3.14159 = 1.5708 radians
- Convert 45 degrees to radians:
- Multiply 45 × π/180
- 45/180 = 1/4, so 1/4 × π
- 1/4 × 3.14159 = 0.7854 radians
- Convert 120 degrees to radians:
- Multiply 120 × π/180
- 120/180 = 2/3, so 2/3 × π
- 2/3 × 3.14159 = 2.0944 radians
- Convert 30 degrees to radians:
- Multiply 30 × π/180
- 30/180 = 1/6, so 1/6 × π
- 1/6 × 3.14159 = 0.5236 radians
Conversion Chart
| Degrees (deg) | Radians (rad) |
|---|---|
| 125.0 | 2.1817 |
| 130.0 | 2.2689 |
| 135.0 | 2.3562 |
| 140.0 | 2.4435 |
| 145.0 | 2.5307 |
| 150.0 | 2.6180 |
| 155.0 | 2.7053 |
| 160.0 | 2.7925 |
| 165.0 | 2.8798 |
| 170.0 | 2.9671 |
| 175.0 | 3.0543 |
This chart shows how degree values between 125 and 175 translate to radians. To use, find the degree value in the left column and see the equivalent radian value on the right. Helpful for quick reference without calculation.
Related Conversion Questions
- What is 150 degrees in radians exactly?
- How do you convert 150 deg to rad using a calculator?
- Why does 150 degrees equal about 2.618 radians?
- Can radians be negative if degrees is 150?
- What is the formula to change 150 deg to rad?
- How many radians are in 150 degrees and how to prove it?
- Is 150 degrees more than 2 radians?
Conversion Definitions
deg: The abbreviation “deg” stands for degree, a unit measuring angles. One degree represents 1/360th part of a full rotation or circle. Degrees are widely used in geometry, navigation, and many fields that involve measuring angles in human-friendly values.
rad: “Rad” refers to radian, an angle unit based on radius length. One radian is the angle created when the arc length equals the radius of a circle. Unlike degrees, radians relate directly to circle geometry and are used in higher mathematics and physics.
Conversion FAQs
How precise is the conversion from degrees to radians?
The conversion is exact in the formula form, but decimal approximations introduce slight rounding errors. Using π as 3.14159 or more digits increases accuracy. For many practical purposes, four decimal places are enough, but scientific calculations may require more precision.
Can I convert radians back to degrees from 150 degrees?
Yes, radians can be converted back by multiplying the radian value by 180/π. For example, 2.618 radians × (180/π) returns to 150 degrees. This reversibility makes converting between these units flexible for different applications.
Why do some calculators use radians instead of degrees?
Calculators often use radians because many mathematical functions, like trigonometric functions, are defined more naturally with radians. Radians simplify formulas and calculus operations, so radians are preferred in advanced math, although degrees are easier for everyday angle measures.
Is there any situation where converting 150 degrees to radians is not necessary?
If you’re only working with angles in everyday terms or directions, degrees are fine and conversion isn’t required. But for calculus, physics, or engineering tasks involving angular velocity or waveforms, radians are essential, so conversion becomes necessary.
Does the conversion formula change for angles larger than 360 degrees?
No, the formula for converting degrees to radians stays the same regardless of the angle size. Degrees beyond 360 represent multiple rotations, but their radian equivalents are calculated by multiplying with π/180 the same way.