Formula

A pie chart sector's angle is proportional to its share

Statistics • Data Interpretation • Pie Chart

Formula

θ = \frac{part}{whole} \times 36 0^{\circ}

In a pie chart the whole circle of

36 0^{\circ}

represents the whole total, and a component is drawn as a sector of central angle

θ = \frac{part}{whole} \times 36 0^{\circ}

; equivalently that component's percentage share is

\frac{θ}{36 0 ^{\circ}} \times 100

How to use it

1To turn an angle into a percentage, divide by $360$ and multiply by $100$ ; the useful shortcut is that $3. 6^{\circ}$ is exactly $1%$ .
2No absolute figure is needed in either direction: the angle fixes the share whatever the size of the total.
3If one absolute value IS given, it calibrates the whole chart - the total equals that value divided by its own share.

Worked example

A sector of a pie chart has central angle

5 4^{\circ}

. What percentage of the total does it represent?

Step-by-step

1
$\frac{54}{360} = 0.15$
Why: The sector's share of the circle is its share of the total.
2
$0.15 \times 100 = 15%$

Answer

15%

Watch out

The angles of all the sectors must add to

36 0^{\circ}

; a chart whose angles do not has been misread or is incomplete. Sector AREA is proportional to the angle, but sector RADIUS is not, so comparing radii compares nothing.

Builds on

x %

of a quantity

Also known as

pie chart, sector angle, central angle of a sector, circle graph, share of the total from an angle

Appears in past papers

Formula

Worked example

Appears in past papers

2020 (I)

2018 (I)

2017 (II)

2017 (I)

2016 (II)