Pie Charts – Grade 8 Maths

Angle Formula

angle = freq/total × 360°

Drawing Pie Charts

Measure each sector accurately

Reading Pie Charts

freq = angle/360 × total

Comparing Pie Charts

Different totals — use fractions

Pie Charts vs Bar Charts

When to use each type

1. The Angle Formula

A pie chart shows how a total is split into categories. Each category becomes a sector (slice). The angle of each sector is proportional to the frequency.

Angle = (Frequency ÷ Total) × 360°

Equivalently: Angle per unit = 360° ÷ Total, then multiply by each frequency.

Example: Total = 40 students. "Football" frequency = 10.
Angle = (10 ÷ 40) × 360° = 0.25 × 360° = 90°

Always check: all sector angles must add up to 360°. Round carefully — rounding errors accumulate.

2. Drawing Pie Charts

Steps to draw a pie chart from a frequency table:

Find the total frequency
Calculate each sector angle using the formula
Draw a circle and mark the centre
Draw a radius line to start
Use a protractor to measure each angle from the previous line
Label each sector with the category name (and/or percentage)

Angles should be whole numbers where possible. If told to round, show your working and note that total ≈ 360° (off by 1° due to rounding is acceptable).

Colour	Frequency	Angle
Red	15	15/60 × 360 = 90°
Blue	20	20/60 × 360 = 120°
Green	12	12/60 × 360 = 72°
Yellow	13	13/60 × 360 = 78°
Total	60	360°

3. Reading Pie Charts

To find the frequency from a sector angle, rearrange the formula:

Frequency = (Angle ÷ 360°) × Total

To find a percentage: Percentage = (Angle ÷ 360°) × 100%

A pie chart has total 200. A sector has angle 45°.
Frequency = (45 ÷ 360) × 200 = 0.125 × 200 = 25

Sometimes only the pie chart is given (no total). You can only find percentages, not actual frequencies, unless the total is stated.

4. Comparing Pie Charts

Two pie charts with different totals cannot be directly compared by angle alone — the same sector angle means different actual frequencies.

Chart A total = 100. Chart B total = 400. Both have a 90° sector for "Sport".
Chart A: Sport = 25 people. Chart B: Sport = 100 people.
But as a proportion: both are 25% — so the fraction is the same.

When comparing, state:

Which category has the largest/smallest proportion in each chart
How the proportions differ between the two groups
Whether the actual number is larger/smaller (state the totals)

5. Pie Charts vs Bar Charts

	Pie Chart	Bar Chart
Best for	Parts of a whole (proportions)	Comparing individual frequencies
Shows	Relative sizes (fractions/percentages)	Actual frequencies clearly
Limitation	Hard to compare similar-sized slices	Harder to see proportions
Data type	Categorical, one survey	Categorical, easy to compare groups

Use a pie chart when you want to emphasise that categories are parts of a total. Use a bar chart when the actual count matters or you're comparing multiple groups.

Example 1 — Calculate Sector Angles

40 students were asked their favourite subject. Draw a pie chart.

Subject	Frequency	Angle
Maths	12	?
Science	8	?
English	10	?
Art	10	?
Total	40	360°

Step 1: Angle per unit = 360 ÷ 40 = 9°

Step 2: Maths: 12 × 9 = 108°

Step 3: Science: 8 × 9 = 72°

Step 4: English: 10 × 9 = 90°

Step 5: Art: 10 × 9 = 90°

Check: 108 + 72 + 90 + 90 = 360° ✓

Example 2 — Read a Pie Chart

A pie chart represents 120 people. The "Walk" sector has an angle of 75°. The "Bus" sector has an angle of 150°.

Walk: (75 ÷ 360) × 120 = 25 people

Bus: (150 ÷ 360) × 120 = 50 people

Walk %: (75 ÷ 360) × 100 = 20.8% ≈ 20.8%

When the total is given, you can find exact frequencies. Without the total, you can only find percentages.

Example 3 — Find a Missing Angle

A pie chart has sectors: Red = 120°, Blue = 95°, Green = ?, Yellow = 80°.

Sum of known angles: 120 + 95 + 80 = 295°

Green: 360 − 295 = 65°

If total = 72, Green frequency = (65 ÷ 360) × 72 = 13

Example 4 — Compare Two Pie Charts

Survey A (50 students): Sport sector = 144°. Survey B (200 students): Sport sector = 108°.

Survey A proportion: 144 ÷ 360 = 40% → 0.40 × 50 = 20 students

Survey B proportion: 108 ÷ 360 = 30% → 0.30 × 200 = 60 students

Comparison: Survey A has a higher proportion choosing Sport (40% vs 30%), but Survey B has more students choosing Sport (60 vs 20).

Always mention both proportion and actual number when comparing pie charts with different totals.

🥧 Pie Chart Builder

Enter up to 6 categories (label:frequency, one per line):

Total:

📐 Sector Angle Calculator

Frequency: Total:

🔄 Reverse: Angle → Frequency

Angle (°): Total:

Exercise 1 — Sector Angles

Calculate the sector angle for each frequency. Total = 60.

1. Frequency = 15. What is the sector angle?

2. Frequency = 20. What is the sector angle?

3. Frequency = 12. What is the sector angle?

4. Frequency = 13. What is the sector angle?

5. If total = 90 and frequency = 30, what is the angle?

6. Total = 72, frequency = 9. Angle?

7. Total = 45, frequency = 15. Angle?

8. Total = 100, frequency = 25. Angle?

9. Total = 120, frequency = 40. Angle?

10. Total = 200, frequency = 50. Angle?

Exercise 2 — Reading Pie Charts

Use Frequency = (Angle ÷ 360) × Total.

1. Angle = 90°, Total = 80. Frequency?

2. Angle = 120°, Total = 180. Frequency?

3. Angle = 45°, Total = 40. Frequency?

4. Angle = 72°, Total = 100. Frequency?

5. Angle = 150°, Total = 60. Frequency?

6. Angle = 60°, Total = 120. Frequency?

7. Angle = 30°, Total = 48. Frequency?

8. Angle = 180°, Total = 50. Frequency?

9. Angle = 36°, Total = 200. Frequency?

10. Angle = 270°, Total = 80. Frequency?

Exercise 3 — Finding Missing Angles

All angles in a pie chart add up to 360°.

1. Angles: 90°, 110°, 80°, ?. Find the missing angle.

2. Angles: 120°, 100°, 95°, ?. Missing angle?

3. Angles: 72°, 108°, 60°, 45°, ?. Missing?

4. Three equal sectors and one sector of 60°. What is each equal sector?

5. Angles: 150°, 90°, ?. Find the missing angle.

6. Five equal sectors. What is each sector angle?

7. Angles: 135°, 45°, 90°, ?. Missing?

8. Angles: 100°, 80°, 60°, 40°, ?. Missing?

9. Total = 50. Sector angle = 144°. Frequency?

10. Frequency = 18, total = 54. Sector angle?

Exercise 4 — Percentages from Pie Charts

Percentage = (Angle ÷ 360) × 100

1. Sector angle = 90°. What percentage?

2. Sector angle = 72°. Percentage?

3. Sector angle = 36°. Percentage?

4. Sector angle = 180°. Percentage?

5. Sector angle = 120°. Percentage?

6. Category is 30% of total. Sector angle?

7. Category is 15% of total. Sector angle?

8. Category is 5% of total. Sector angle?

9. Sector = 45°, total = 500. Frequency?

10. Sector = 54°, total = 200. Frequency?

Exercise 5 — Mixed Questions

1. Total = 120, angle = 90°. Frequency?

2. Frequency = 24, total = 96. Angle (°)?

3. Sector = 45°, total = 160. Frequency?

4. 4 equal sectors. Angle of each?

5. Angles: 100°, 80°, 120°. Find the 4th angle.

6. Frequency = 35, total = 140. Angle?

7. Angle = 108°, total = 150. Frequency?

8. Frequency = 18, total = 72. Percentage?

9. Angle = 144°, total = 75. Frequency?

10. Category = 40% of 250. Sector angle?

🏋️ Practice — 20 Questions

1. Total = 80, freq = 20. Angle?

2. Total = 60, freq = 45. Angle?

3. Angle = 90°, total = 160. Frequency?

4. Angle = 120°, total = 90. Frequency?

5. Angle = 72°. Percentage?

6. 25% of total. Sector angle?

7. Angles: 80°, 110°, 95°, ?. Missing?

8. Total = 360, freq = 45. Angle?

9. Angle = 36°, total = 300. Frequency?

10. Total = 48, freq = 16. Angle?

11. Angle = 135°, total = 80. Frequency?

12. Freq = 7, total = 28. Angle?

13. Angle = 54°. Percentage?

14. 12.5% of total. Angle?

15. 6 equal sectors. Each angle?

16. Angles: 45°, 90°, 135°, ?. Missing?

17. Total = 500, angle = 72°. Frequency?

18. Freq = 60, total = 240. Angle?

19. Angle = 270°, total = 120. Frequency?

20. Category = 37.5% of total. Angle?

🏆 Challenge — 8 Questions

1. A pie chart shows: Red = 80°, Blue = 110°, Green = 95°, Yellow = ?°. Total survey = 144 people. How many chose Green?

2. Pie chart A (total 60): Football sector = 120°. Pie chart B (total 180): Football sector = 80°. Which group has more football fans?

Enter: 1 for Chart A, 2 for Chart B

3. A pie chart represents 240 people. Three sectors have angles 90°, 105°, 75°. The fourth sector represents the remaining people. How many people are in the fourth sector?

4. Sector angles are in ratio 1:2:3:6. What is the angle of the largest sector?

5. A pie chart has 5 sectors. Four have angles 84°, 72°, 96°, 48°. The fifth sector represents 15% of the total. Find the fifth sector's angle. (Check it's consistent.)

6. Total = 200. A sector has angle 54°. Another sector has angle 126°. What is the ratio of the two frequencies (first:second, as a simple ratio)? Enter as a single number: first value of ratio when second = 7.

7. 60 students chose subjects. Maths:English:Science:Art = 3:2:4:1. What is the sector angle for Science?

8. A pie chart shows data for 150 people. The "Other" sector has angle 24°. How many people chose "Other"?

🥧 Pie Charts