Calculating pie-chart angles Revision Card

AI generatedStatisticsKS3 / GCSE

Calculating pie-chart angles.

A whole circle is 360°. Each sector represents the same fraction of the angle total and frequency total.
Angle = frequency ÷ total × 360. Frequency = angle ÷ 360 × total.
If one sector has both values, use it to recover the total. Check completed frequencies and angles add correctly.

Example 1

Calculate each sector angle.

Given information

Category	Frequency
A	8
B	10
C	12
D	18

Add the angles and totals

Category	Frequency	Angle
A	8
B	10
C	12
D	18
Total	48

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 60°, B 75°, C 90°, D 135°.

Example 2

Calculate each sector angle.

Given information

Category	Frequency
A	15
B	18
C	24
D	15

Add the angles and totals

Category	Frequency	Angle
A	15
B	18
C	24
D	15
Total	72

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 75°, B 90°, C 120°, D 75°.

Your turn

Question 1

Calculate each sector angle.

Given information

Category	Frequency
A	16
B	20
C	24
D	36

Check answer

Add the angles and totals

Category	Frequency	Angle
A	16
B	20
C	24
D	36
Total	96

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 60°, B 75°, C 90°, D 135°.

Question 2

Calculate each sector angle.

Given information

Category	Frequency
A	25
B	30
C	40
D	25

Check answer

Add the angles and totals

Category	Frequency	Angle
A	25
B	30
C	40
D	25
Total	120

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 75°, B 90°, C 120°, D 75°.

Question 3

Calculate each sector angle.

Given information

Category	Frequency
A	24
B	30
C	36
D	54

Check answer

Add the angles and totals

Category	Frequency	Angle
A	24
B	30
C	36
D	54
Total	144

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 60°, B 75°, C 90°, D 135°.

Question 4

Calculate each sector angle.

Given information

Category	Frequency
A	35
B	42
C	56
D	35

Check answer

Add the angles and totals

Category	Frequency	Angle
A	35
B	42
C	56
D	35
Total	168

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 75°, B 90°, C 120°, D 75°.

Question 5

Calculate each sector angle.

Given information

Category	Frequency
A	32
B	40
C	48
D	72

Check answer

Add the angles and totals

Category	Frequency	Angle
A	32
B	40
C	48
D	72
Total	192

Black: given data. Blue: working we add.

Add the frequencies to find the whole group.

Angle for A

Frequency ÷ total × 360. Repeat for each row.

Angles: A 60°, B 75°, C 90°, D 135°.