Pie Chart
A pie chart is a circular graph divided into slices, each representing a category's share of the whole.
Formula
\text{Slice angle} = \dfrac{\text{category frequency}}{\text{total}} \times 360^\circ
Definition
A pie chart is a circle divided into slices, like a pizza, where each slice represents a category and the bigger the slice, the larger that category's share of the total. It is a circular statistical graphic divided into sectors: each sector's arc length (and area) is proportional to the relative frequency or percentage it represents, with slice angle $= (\text{relative frequency}) \times 360^\circ$, working well for showing part-to-whole relationships with a small number of categories. Formally, a pie chart encodes proportions using angle (and implicitly area); perceptual research shows that humans judge angles and areas less accurately than lengths, making pie charts less precise than bar graphs, and a donut chart (pie chart with center removed) shifts emphasis toward arc length rather than area.
Example
A class voting on a field trip might split $40\%$ zoo, $35\%$ museum, $25\%$ aquarium, with a pie chart showing three slices sized to match. A monthly budget of rent $35\%$ ($126^\circ$), food $20\%$ ($72^\circ$), transportation $15\%$ ($54^\circ$), savings $20\%$ ($72^\circ$), and other $10\%$ ($36^\circ$) has angles summing to $360^\circ$. When two pie chart slices have relative frequencies of $0.31$ and $0.29$, readers struggle to identify which is larger, while a bar graph with labeled heights resolves this immediately, the core critique of pie charts in data visualization.
Key Insight
Pie charts are great for showing parts of a whole, like percentages of a budget or a class vote, but they become hard to read with many categories or when slices are nearly equal, so bar graphs are often more accurate for comparisons. Despite these statistical critiques, pie charts remain effective when there are few categories, one category is clearly dominant, and the goal is part-to-whole communication rather than precise comparison.