Pie chart percentage calculator

What is a pie chart percentage calculator?

A pie chart percentage calculator turns a single part of a whole into the two numbers you need to draw it on a pie chart: the percentage it represents and the angle of its slice in degrees. A pie chart shows how a total splits into categories, with each category drawn as a wedge whose size is proportional to its share. To draw such a wedge accurately you first work out what fraction of the total it is, then convert that fraction into an angle of the full 360° circle.

Enter the value of one slice and the total of all slices combined; the calculator returns both the share as a percentage and the central angle you would use to sketch the slice by hand or to check a chart your software produced.

How does the calculator work?

Give the calculator the value of the slice you care about and the total of the whole dataset. It first divides the value by the total to get the share, multiplies by 100 to express it as a percentage, and then scales that share across the full circle to get the slice angle:

Where:

• value is the size of the single slice.
• total is the sum of every slice in the chart, which must be greater than zero.
• percentage is the slice’s share of the whole, between 0% and 100%.
• angle is the central angle of the slice in degrees, between 0° and 360°.

Because a full circle is 360°, every percentage point of the pie is worth exactly 3.6° of angle. A slice that is 25% of the data fills a quarter of the circle, or 90°.

Worked examples

1. A quarter of the pie. A slice has value 25 out of a total of 100. $\text{percentage} = \frac{25}{100} \times 100 = 25\%, \qquad \text{angle} = \frac{25}{100} \times 360 = 90°$ The slice is one quarter of the chart, so it spans a right angle.

2. A fractional slice. A slice has value 3 out of a total of 8. $\text{percentage} = \frac{3}{8} \times 100 = 37.5\%, \qquad \text{angle} = \frac{3}{8} \times 360 = 135°$ This slice covers a little more than a third of the circle.

3. Two parts of five. A slice has value 2 out of a total of 5. $\text{percentage} = \frac{2}{5} \times 100 = 40\%, \qquad \text{angle} = \frac{2}{5} \times 360 = 144°$ The slice fills two fifths of the pie.

Practical notes

• The total must be greater than zero. With no data there is no circle to divide, so the percentage and angle are undefined.
• The angles of every slice in a chart should add up to 360°, and their percentages should add up to 100%. If they do not, a value or the total has been mistyped.
• Rounding each slice independently can make the angles miss 360° by a fraction of a degree; for a polished chart, adjust the largest slice to absorb the rounding gap.
• The same value can describe a count, a currency amount, or any other measure — only the ratio of value to total matters for the slice size.

FAQ

How do I convert a percentage to a pie chart angle?

Multiply the percentage by 3.6 to get the angle in degrees, because the full 360° circle is split across 100 percentage points. For example, 25% becomes 25 × 3.6 = 90°.

Why does the total have to be positive?

The percentage is the value divided by the total. Dividing by zero is undefined, and a chart with no data has no slices to draw, so a total of zero cannot produce a meaningful result.

Can a slice be more than 100%?

No. As long as the slice value does not exceed the total, each slice stays between 0% and 100% and its angle stays between 0° and 360°. If you enter a value larger than the total you are describing more than the whole, which a single pie chart cannot represent.

How is this different from a plain percentage?

The percentage part is the ordinary percentage calculation of a part over a whole. The pie chart calculator adds the second step of turning that percentage into a slice angle so you can actually draw the wedge.