Constructing pie charts: calculating the angles
Maths · Key Stage 3 · The School
The one formula
A pie chart's full circle is 360°, representing the whole data set. Each category's angle = (category's count ÷ total count) × 360°. A category that is half the data gets 180°; a category that is a tenth of the data gets 36°. The circle itself does the fraction-to-angle conversion for you, once you know the formula.
Working through a full data set
40 people were asked their favourite colour: 20 blue, 10 red, 6 green, 4 yellow. Blue: (20 ÷ 40) × 360 = 180°. Red: (10 ÷ 40) × 360 = 90°. Green: (6 ÷ 40) × 360 = 54°. Yellow: (4 ÷ 40) × 360 = 36°. Every angle is calculated the same way, using the same grand total each time.
The check that catches every mistake
All the angles in a pie chart MUST add up to exactly 360°, because together they represent the entire data set. Adding the colours above: 180 + 90 + 54 + 36 = 360. This check catches almost every arithmetic slip before you pick up a protractor, and it is worth doing before drawing a single line.
With the four angles calculated and checked (180°, 90°, 54°, 36°), draw a circle and mark the centre. Draw one radius line as a starting point. Use a protractor from that line to mark 180° for blue, then continue from THAT new line to mark the next 90° for red, and so on round the circle — each angle measured from where the previous one ended, not from the same starting line every time. Label each slice as you go, because an unlabelled pie chart is only half finished, however accurate the angles are.