Hong Life CalculatorsUnderstanding the pie chart calculator — concept and principle
This calculator turns a list of categories and values into the numbers you need for a pie chart: each slice's percentage share and its angle at the centre in degrees. Use it for budgets, survey results, time use, sales mix or any data that splits a whole into parts, and when drawing a pie chart by hand with a protractor.
How it is calculated
- Total = sum of all values
- Share (%) = value ÷ total × 100
- Slice angle (°) = value ÷ total × 360
- Degrees per unit = 360 ÷ total
Enter one category per line with its value. All values must use the same unit. Shares and angles are rounded to one decimal place, so they may not add up exactly.
The principle
A full circle is 360°, and a pie chart gives each category the same fraction of the circle as its fraction of the total. Because the shares of all categories add up to the whole, the slices add up to 100% and 360°. The angle is what you measure with a protractor; the percentage is what readers usually want to see. Pie charts are good at showing "part of a whole" for a small number of categories, but people judge angles less accurately than lengths, so exact comparisons are easier with a bar chart.
Worked example
Default data: Rent 1,200, Food 450, Transport 200, Utilities 150, Savings 300, Other 200.
- Total = 1,200 + 450 + 200 + 150 + 300 + 200 = 2,500.
- Degrees per unit = 360 ÷ 2,500 = 0.144.
- Rent: 1,200 ÷ 2,500 = 48%, angle 1,200 × 0.144 = 172.8°.
- Food 18% (64.8°), Transport 8% (28.8°), Utilities 6% (21.6°), Savings 12% (43.2°), Other 8% (28.8°).
- Six slices; largest Rent (48%), smallest Utilities (6%). The angles add to 360°.
How to read the result
The largest slice shows where most of the total goes; here rent takes almost half of the budget. Small slices under about 5% are hard to see and are often grouped as "Other". If you are comparing two pie charts, compare the percentages, not the visual size, and make sure each chart represents a complete whole.
Common mistakes
- Including a "Total" line in the data, which double-counts everything.
- Mixing units or periods, such as monthly and yearly amounts.
- Using a pie chart for data that do not add up to a meaningful whole.
- Using negative values, which cannot be drawn as slices.
Frequently asked questions
How do I convert a percentage to degrees?
Multiply the percentage by 3.6. For example 25% × 3.6 = 90°.
How many slices should a pie chart have?
There is no strict rule, but a few large slices are far easier to read than many small ones.
When is a bar chart better?
When categories do not form a whole, when there are many of them, or when exact differences matter.
Sources: Arithmetic of proportions: share = value ÷ total × 100%, central angle = share × 360°