Convert Degrees to Radians in Terms of Pi Calculator
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Reviewed by Calculator Editorial Team
Convert degrees to radians in terms of π with this precise calculator. Learn the conversion formula, see worked examples, and visualize the relationship between degrees and radians.
Conversion Formula
The relationship between degrees and radians is defined by the fact that a full circle (360°) is equal to 2π radians. This gives us the conversion formula:
Degrees to Radians Formula
radians = degrees × (π / 180)
This formula allows you to express any angle in degrees as a multiple of π radians. For example, 90° becomes π/2 radians, 180° becomes π radians, and 360° becomes 2π radians.
How to Use This Calculator
- Enter the angle in degrees in the input field
- Click the "Calculate" button
- View the result in radians expressed in terms of π
- Use the chart to visualize the relationship between degrees and radians
Note
The calculator automatically simplifies the result to show the angle in terms of π. For example, 120° will be shown as 2π/3 radians.
Worked Example
Let's convert 150° to radians in terms of π:
- Start with the degrees value: 150°
- Multiply by π/180: 150 × (π/180)
- Simplify the fraction: 5π/6
- Final result: 150° = 5π/6 radians
This means 150° is equivalent to 5π/6 radians, or approximately 2.61799 radians.
Common Angle Conversions
Here are some common angle conversions from degrees to radians in terms of π:
| Degrees | Radians (in terms of π) | Decimal Radians |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 120° | 2π/3 | 2.0944 |
| 180° | π | 3.1416 |
| 270° | 3π/2 | 4.7124 |
| 360° | 2π | 6.2832 |
FAQ
Why convert degrees to radians?
Radians are the standard unit of angular measurement in calculus, physics, and engineering. Many mathematical formulas and equations are expressed more simply in radians.
What is the difference between π and 180?
The number 180 comes from the fact that a full circle is 360°, and π radians make up a full circle. Therefore, 180° is equal to π radians.
Can I convert radians back to degrees?
Yes, the inverse formula is degrees = radians × (180/π). Our calculator can perform both conversions.