Pie Chart Angle Calculator

Created by Anna Szczepanek, PhD
Reviewed by Davide Borchia
Last updated: Jul 04, 2023

Our pie chart angle calculator is here to help if you need help with calculating pie chart angles. We will give you the pie chart angle formula and explain how to calculate pie chart angles given raw data or given percentages. Also, we'll discuss how to recover percentages from angles.

Let's go!

Pie chart angle formula

As you most probably already know, a pie chart is a way to visualize proportions in categorical data using a circular graph. The whole graph (pie) is divided into several slices corresponding to different categories in our data. Each slice represents one category, so we can easily assess how big this slice (category) is compared to the whole pie (sample).

Since the whole circle is 360°, the formula for the central angle corresponding to a given category is:

Angle of category = (Category frequency / Total frequency) x 360°.

If you think about this for a little while, you can come to the conclusion that Category frequency / Total frequency × 100% is the percentage of the category in question. This allows us to rewrite the formula more succinctly:

Angle of category = (Percentage of category/100%) x 360°.

How do I calculate pie chart angles?

To determine the angles in a pie chart, you need to:

  1. Find the total frequency, i.e., the total number of observations in your dataset.
  2. Divide the number of observations in a category by the total frequency.
  3. Multiply the result of Step 2 by 360° (the full angle).
  4. You've just found the angle in the pie chart representing this category!
  5. Repeat Steps 2 and 3 for every category in your dataset.
  6. Draw a circle with the calculated angles (use a protractor) to get a pie chart of your data.

If you want to discover other aspects of pie charts or deepen your knowledge about math topics related to pie charts, here are several Omni tools that will be useful:


How do I convert percentages to angles in a pie chart?

To convert the percentages to angles, you need to remember that the full angle (the whole pie) corresponds to 360°. Hence, the angle of a category is given by the formula Angle of category = (Percentage of category/100%) × 360° .

How do I find percentages given data in a pie chart?

To turn raw data into percentages, follow these steps:

  1. Find out how many observations there are in your data set.
  2. Divide the number of observations in a category by the total number of observations found in Step 1.
  3. Convert the fraction found in Step 2 to percentage by multiplying it by 100%.
  4. Repeat Steps 2 and 3 for each category.

How do I find percentages given angles in a pie chart?

To recover percentages from angles in a pie chart, apply the formula Percentage = (Angle/360°) × 100%. For instance, 54° translates to 54°/360° × 100% = 15%.

Additionally, if you know the total number of observations in your data set, you can recover the number of observations in each category by multiplying the percentage of this category by the total number of observations.

Anna Szczepanek, PhD
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