Pie Chart

A pie chart is a circular chart divided into sectors whose angles, and therefore areas and arc lengths, are proportional to the relative frequencies of the categories of a variable, so that the whole circle represents 100 percent of the data and each slice shows one category's share. It is the chart most people meet first and most statisticians use sparingly: it is intuitive for a single message of the form "this category makes up about half" and surprisingly weak for nearly anything else, which makes it one of the most debated charts in data visualisation.

A pie chart is built by converting each category's relative frequency to an angle: the share multiplied by 360 degrees gives the slice's angle, so a category making up 25 percent occupies 90 degrees. This requires that the slices be parts of one whole, mutually exclusive and exhaustive, summing to 100 percent; a pie of survey answers where respondents could tick several options, or one that leaves out a category, is misleading by construction. The pie chart's invention is credited to William Playfair, the Scottish engineer who also devised the line and bar charts, in his Statistical Breviary of 1801, and Florence Nightingale's coxcomb diagrams of the 1850s, polar-area charts of monthly deaths in the Crimean War, show how circular layouts could carry persuasive evidence, though those are not pie charts in the strict sense because slice radius as well as angle varies.

The central weakness of the pie chart is perceptual: people judge angles and areas less accurately than they judge positions along a common scale, so small differences between slices are hard to see. Experiments in graphical perception by William Cleveland and Robert McGill in 1984 ranked position along a common scale as the most accurately judged encoding and angle and area as markedly worse, which is the research usually cited against pies. A bar chart of the same relative frequencies places every category on one baseline, so a 22 percent bar and a 25 percent bar are easy to tell apart while two near-equal slices of a pie are not. This is also why ordering matters, since sorting slices by size from 12 o'clock clockwise restores some readability.

Used well, a pie chart serves a narrow but legitimate purpose, which is showing part-to-whole composition for a handful of categories, ideally when one share is dramatically larger or smaller than the others or when it sits near an easily recognised fraction such as a half or a quarter. Typical appropriate uses include a budget split into a few headings, vote share among two or three parties, and the composition of a dataset's missing values by cause. Variants include the donut chart, which cuts out the centre to hold a total or label and makes arc length rather than angle the visual cue, and the exploded pie, which pulls a slice out for emphasis but distorts the picture. Three-dimensional pies are the worst offenders, since perspective makes the slices at the front look larger than identical slices at the back.

The usual pitfalls follow directly from this. Pies with more than five or six slices, many tiny wedges, or percentages that differ by only a few points are difficult to read and are better replaced by a bar chart. Pies cannot show change over time, cannot compare two datasets side by side without careful alignment, and cannot represent negative values at all. Placing several pies of different totals next to each other tempts viewers to compare slice sizes rather than shares. A pie chart is also a display only of a frequency distribution of a categorical variable, using its relative frequencies; it carries no information about centre or spread, and cannot be used for a continuous variable unless it is first grouped into classes, for which the histogram is the correct choice.

Read a pie chart as a picture of relative frequencies as shares of one whole: effective when the message is a single dominant slice among a few, hard to read once slices crowd or differ narrowly, and almost always accompanied by the actual percentages or paired with a bar chart where accurate comparison matters.