What Is a Pie Chart Angle?
A pie chart angle (central angle) is the degree measure of a slice in a pie chart. Since a full circle is 360 degrees, each category's angle is proportional to its share of the total. This calculation is fundamental to constructing accurate pie charts manually or programmatically.
For example, if a category represents 25% of the total, its central angle is 25% of 360 degrees = 90 degrees. Understanding these angles helps ensure that pie charts accurately represent the underlying data proportions.
Formula
Percentage to Angle Table
| Percentage | Angle (degrees) | Radians | Fraction of Circle |
|---|---|---|---|
| 10% | 36° | 0.628 | 1/10 |
| 25% | 90° | 1.571 | 1/4 |
| 33.3% | 120° | 2.094 | 1/3 |
| 50% | 180° | 3.142 | 1/2 |
| 75% | 270° | 4.712 | 3/4 |
| 100% | 360° | 6.283 | 1/1 |
Calculation Steps
- Identify the category value and the total sum of all categories.
- Divide the category value by the total to get the proportion.
- Multiply the proportion by 360 to get the central angle in degrees.
- Optionally multiply by 2*pi for radians.
- Verify that all category angles sum to 360 degrees.
Frequently Asked Questions
Why 360 degrees?
A circle contains exactly 360 degrees. This convention dates back to ancient Babylonians who used a base-60 number system. Every pie chart represents a complete circle, so all slice angles must total 360 degrees.
How do I draw a slice by hand?
Use a protractor centered on the circle's center. Mark the starting angle, then measure the calculated central angle clockwise. Draw lines from the center to both marks to create the slice boundaries.
What if my angles do not sum to exactly 360?
Rounding errors can cause small discrepancies. Adjust the largest slice by the rounding difference to ensure the total is exactly 360 degrees. This is standard practice in data visualization.