Pie charts and percentages

The South held 38.1% of the US population in 2020, so its slice of a pie chart spans 38.1% of 360°, about 137°.

A pie chart shows how one whole is split into parts. The whole is the full circle, 100 percent or 360 degrees, and each part gets a slice in proportion to its share. That makes the pie good at one question, "what fraction of the total is this part?", and poor at most others. Before drawing a pie, check that the parts really add up to a meaningful whole, that nothing is counted twice and that nothing is missing.

From counts to shares to angles

Take the four US regions again. The total is 331,449,281. The South's share is 126,266,107 ÷ 331,449,281 ≈ 0.381, or 38.1%. The West has 23.7%, the Midwest 20.8% and the Northeast 17.4%. Shares like these always add to 100% (up to rounding). To draw a slice, multiply the share by 360°: the South gets 0.381 × 360° ≈ 137.1°, the West about 85.4°, the Midwest about 74.9° and the Northeast about 62.6°. Add the angles and you get back 360°.

When a pie stops working

OpenStax lists the common problems. Too many slices overwhelm the reader; past five or six categories a pie stops showing which part matters most, and small categories are better gathered into "other". A pie cannot show change over time. The trap is two pies side by side for two years: the circles are the same size, but the totals are not, so a slice that shrinks in percentage may stand for more people than before. One more problem is not on the OpenStax list: in experiments by the statisticians William Cleveland and Robert McGill in the 1980s, people judged position and length on a common scale more accurately than angles. Try it in the lab with the West (23.7%) and the Midwest (20.8%).

A pie that means nothing

Some data cannot be a pie at all. The yearly numbers of Korean births from 2015 to 2025 are eleven separate counts, not eleven parts of one total. You could add them, but "share of all births in those eleven years" is not what anyone asks about a single year. Choose the births data and the pie type in the lab and the panel will warn you. The same holds for averages, rates and percentages that each describe a different group: percentages of different wholes do not share a pie.

Percent or percentage point?

Shares invite a common slip. In 2010 the South held 114,555,744 of 308,745,538 people, a share of 37.1%. In 2020 its share was 38.1%. The share rose by 1.0 percentage point, which is a relative rise of about 1.0 ÷ 37.1 ≈ 2.7%. Both statements are correct, but they are different numbers, and mixing them up can make a change look about 2.7 times bigger or smaller than it is. When you compare two shares, say "percentage points" for the difference and "percent" only for a relative change.