Simple Pie Charts — Fundamental Concepts

Fundamental Concepts

One-whole toolkit

Full circle: 360 degrees = 100 percent = the stated total.
Fraction from angle: θ/360.
Percentage from angle: θ/3.6.
Angle from percentage: percentage × 3.6.
Amount: total × fraction.
Total from a known part: part / fraction.

Missing sector

Subtract known percentages from 100 or known angles from 360. Keep the two systems separate. A remainder can be assigned to one category only when that category is the sole missing part of the partition.

Ratios

Within one pie, amount ratios equal angle ratios and percentage ratios. Category-to-rest uses the complementary share. Category-to-whole uses the full 360 degrees or 100 percent. Read the denominator named in the question before reducing the ratio.

Useful anchors

180 degrees is one half; 120 is one third; 90 is one quarter; 72 is one fifth; 60 is one sixth; 36 is one tenth. These anchors check scale and simplify arithmetic.

Limits and verification

An absolute amount needs a total or a known part-to-share relationship. Relative comparisons within the same pie may not. Labels rounded from actual observations can have small sum discrepancies; exact exercises should remain internally consistent. Check a recovered total by reconstructing the known part, and check a recovered sector by summing all sectors back to the whole.