Pie Charts

At a glance 10 rules

1. 1Degrees and percent$100\% = 360^\circ,\quad 1\% = 3.6^\circ$$x^\circ = \dfrac{x}{3.6}\,\% = \dfrac{5x}{18}\,\%$
2. 2Angle to percent

   $18^\circ$

   5%

   $36^\circ$

   10%

   $45^\circ$

   12.5%

   $54^\circ$

   15%

   $60^\circ$

   $16\tfrac{2}{3}$%

   $72^\circ$

   20%

   $81^\circ$

   22.5%

   $90^\circ$

   25%

   $108^\circ$

   30%

   $120^\circ$

   $33\tfrac{1}{3}$%

3. 3Value of a sector$\text{value} = \dfrac{\text{angle}}{360^\circ} \times \text{total}$$= \dfrac{\text{share}\ \%}{100} \times \text{total}$
4. 4Drawing the pie$\text{angle} = \dfrac{\text{value}}{\text{sum of all values}} \times 360^\circ$
5. 5Convert onceAdd or subtract the angles (or the percents) first and turn only the result into a value: one degree is worth the total $\div 360$.
6. 6Ratio of two sectors$\dfrac{\text{value}_A}{\text{value}_B} = \dfrac{\text{angle}_A}{\text{angle}_B}$$\text{the total cancels, so never work it out}$
7. 7Total from a gap$1\% = \dfrac{\text{known gap}}{\text{gap in percentage points}}$$\text{total} = 100 \times (\text{value of } 1\%)$
8. 8Pie within a pie$\text{angle in main pie} = \dfrac{\text{sub-share}\ \%}{100} \times \text{parent angle}$
9. 9When a sector changesA transfer between sectors keeps the total. A new or bigger sector raises it: the untouched sectors keep their values, so their angles shrink in proportion.
10. 10Whole-number sectorsIf every sector counts people, write each angle over 360 in lowest terms: the total must be a multiple of every denominator.