Degrees to Radians Converter
Convert angles from degrees (°) into radians (rad) instantly with exact Pi (π) fraction notation, step-by-step formula calculations, worked examples, and conversion charts.
To convert any angle from Degrees (°) to Radians (rad), multiply the angle in degrees by π / 180: Angle in Radians = Angle in Degrees × (π / 180)
Example: $180^\circ = \pi \text{ rad} \approx 3.141593 \text{ rad}$, and $90^\circ = \frac{\pi}{2} \text{ rad} \approx 1.570796 \text{ rad}$.
Degrees to Radians Conversion Chart
Standard trigonometry reference table showing common angles in degrees, exact Pi (π) fraction notation, and decimal radian equivalents:
| Degrees (°) | Exact Pi (π) Radians | Decimal Radians (rad) | Action |
|---|---|---|---|
| 0° | 0 rad | 0 rad | |
| 30° | π / 6 rad | 0.523599 rad | |
| 45° | π / 4 rad | 0.785398 rad | |
| 60° | π / 3 rad | 1.047198 rad | |
| 90° | π / 2 rad | 1.570796 rad | |
| 120° | 2π / 3 rad | 2.094395 rad | |
| 135° | 3π / 4 rad | 2.356194 rad | |
| 150° | 5π / 6 rad | 2.617994 rad | |
| 180° | π rad | 3.141593 rad | |
| 210° | 7π / 6 rad | 3.665191 rad | |
| 225° | 5π / 4 rad | 3.926991 rad | |
| 240° | 4π / 3 rad | 4.188790 rad | |
| 270° | 3π / 2 rad | 4.712389 rad | |
| 300° | 5π / 3 rad | 5.235988 rad | |
| 315° | 7π / 4 rad | 5.497787 rad | |
| 330° | 11π / 6 rad | 5.759587 rad | |
| 360° | 2π rad | 6.283185 rad |
How to Convert Degrees to Radians (Step-by-Step)
A degree (°) is a unit of angle measurement defined such that a full circle revolution contains 360 degrees. A radian (rad) is the SI unit of angle measure defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. A full circle revolution equals 2π radians.
The Fundamental Relation:
Since $360^\circ = 2\pi \text{ radians}$, dividing both sides by 2 gives: 180° = π radians
Conversion Formula:
To convert any angle from degrees to radians, multiply by π / 180: Radians = Degrees × (π / 180)
Worked Step-by-Step Examples:
- Multiply 45 by π / 180:
45 × (π/180) - Simplify fraction 45/180:
45/180 = 1/4 - Exact result: π / 4 rad
- Decimal result: 0.785398 rad
- Multiply 120 by π / 180:
120 × (π/180) - Simplify fraction 120/180:
120/180 = 2/3 - Exact result: 2π / 3 rad
- Decimal result: 2.094395 rad
- Multiply 270 by π / 180:
270 × (π/180) - Simplify fraction 270/180:
270/180 = 3/2 - Exact result: 3π / 2 rad
- Decimal result: 4.712389 rad
- Multiply 360 by π / 180:
360 × (π/180) - Simplify fraction 360/180:
360/180 = 2 - Exact result: 2π rad
- Decimal result: 6.283185 rad
Reverse Conversion: How to Convert Radians to Degrees
To convert radians back into degrees, multiply the angle in radians by 180 / π:
Degrees = Radians × (180 / π)Example: Convert π / 3 radians to degrees: (π/3) × (180/π) = 180 / 3 = 60°.
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Angle Unit Conversion Formula Matrix
rad = deg × (π / 180)deg = rad × (180 / π)grad = deg × (10 / 9)How to Use the Degrees to Radians Tool in 4 Steps
Input Degrees
Type your angle in degrees into the input field or click a standard preset chip.
Auto-Calculate
The converter instantly calculates the exact Pi fraction and decimal radian values.
View Formula Step
Check the dynamic formula breakdown explaining the exact simplification.
Copy Result
Click the Copy button to quickly copy the formatted output for your work.
Frequently Asked Questions (FAQs)
π / 180. For example, 180 degrees equals 180 × (π/180) = π radians. π / 180 radians, which is approximately 0.0174533 radians. 2π / 360 gives π / 180.