Constructing a pie chart

The idea

To draw a pie chart, divide 360° in the ratio of the quantities to get each slice's angle, draw a radius, measure each angle in turn from the previous radius, then colour and label the slices.

A pie chart of favourite sports

30 students chose their favourite sport: Cricket 12, Football 9, Kabaddi 6, Hockey 3. We will draw a pie chart for this.

What do we need to find first, before we draw any slice?

• The colour of each slice
• The angle of each slice
• The length of the radius

Draw the pie chart

Follow the steps. First divide 360° in the ratio of the numbers. Then draw the radii one after another, each time measuring from the last radius. At the end, colour and label the slices.

Divide, draw, measure in turn, colour

To draw a pie chart, divide 360° in the ratio of the quantities to get each slice's angle, draw a radius, measure each angle in turn from the previous radius, then colour and label the slices.

For 12 : 9 : 6 : 3: Simplest form: 12 : 9 : 6 : 3 = 4 : 3 : 2 : 1 (÷ 3) 4 + 3 + 2 + 1 = 10 parts, so one part is 360° ÷ 10 = 36°. The angles are 144°, 108°, 72° and 36°.

Measure each angle from the previous radius, not from the first one, or the slices will overlap. The last slice is what is left, so the angles must add up to 360°: 144° + 108° + 72° + 36° = 360°.

Notes

To draw a pie chart, divide 360° in the ratio of the quantities to get each slice's angle, draw a radius, measure each angle in turn from the previous radius, then colour and label the slices.

Check yourself

40 students come to school by cycle 15, bus 10, walking 5 and car 10. In a pie chart, what is the angle of the cycle slice?

Answer: 135 °

15 : 10 : 5 : 10 = 3 : 2 : 1 : 2, which is 8 parts. One part is 360° ÷ 8 = 45°. The cycle slice has 3 parts: 3 × 45° = 135°. (The others are 90°, 45° and 90°.)

Which is the correct order of steps to draw a pie chart?

The angles of a pie chart are 144°, 108°, 72° and 36°. To draw the second slice, where do you measure 108° from?

Five slices of a pie chart have angles 90°, 60°, 45°, 75° and 30°. The pie chart has 6 slices. What is the angle of the sixth slice?

Answer: 60 °

The slices fill the whole circle, 360°. The five angles add up to 90° + 60° + 45° + 75° + 30° = 300°, so the sixth is 360° − 300° = 60°.

• Colour the slices, divide 360°, draw a radius, measure the angles. The colouring comes last. You cannot draw the slices before you know their angles.
• Draw a radius, measure 90° for every slice, divide 360°, colour. The angles must be found first, by dividing 360° in the ratio. They are not all 90°.
• Divide 360° in the ratio, draw a radius, measure each angle in turn, colour and label — correct. Yes! Find the angles, draw the first radius, measure the angles one after another, then colour and label.
• From the start radius again. Then the second slice would lie on top of the first slice. Measure from where the first slice ended.
• From the radius you drew last, the end of the first slice — correct. Yes! Each angle is measured in turn from the previous radius, so the slices sit side by side.
• From the opposite side of the circle. The slices must follow each other round the circle, each starting where the last one ended.