Pie Chart Calculator: Percentages and Sector Angles for Each Category
Turn category values into pie chart percentages and sector angles (degrees), or convert percentages and angles back, then see the pie chart drawn.
How it works
Percentage = value ÷ total × 100 · Angle (°) = value ÷ total × 360 = percentage × 3.6 · Percentage = angle ÷ 360 × 100 · Count = percentage ÷ 100 × total count
A pie chart splits a circle into sectors whose size matches each category’s share of the total. Add up all the values, divide each value by that total to get its share, then multiply the share by 100 for the percentage and by 360 for the sector angle in degrees. Every 1% of the total takes up 3.6° of the circle, so the percentages always add up to 100% and the angles to 360°. The table also gives the start and end angle of each slice, which is what you need to draw the chart by hand with a protractor, and the exact fraction when the values are whole numbers. You can work backwards too. Choose Percentages to turn percentages into angles, or Angles to read percentages off a chart you were given. If they add up to less than 100% (or 360°), a Remainder slice fills the gap; if they add up to more, the slices are scaled down in proportion. Enter the total count to turn each slice back into the number of observations. This differs from a frequency table calculator, which counts raw data: here you already have one number per category and want the chart.
Worked example
A monthly budget of Rent 1,200, Food 450, Transport 300, Savings 250 and Other 200 adds up to 2,400. Rent is 1,200 ÷ 2,400 = 0.5, so it is 50.00% of the pie and 0.5 × 360° = 180.00° (from 0° to 180°). Food is 450 ÷ 2,400 = 18.75%, or 67.50°; Transport 12.50% (45.00°); Savings 10.42% (37.50°); Other 8.33% (30.00°). The angles add up to 180 + 67.5 + 45 + 37.5 + 30 = 360°, and Rent is the largest slice.
Sources: Omni Calculator: Pie chart calculator (worked example 20, 80, 20, 50, 30) · Omni Calculator: Pie chart angle (54° = 15%) · Loughborough University: Pie chart central angle calculator
Frequently asked questions
How do you calculate the angle for a pie chart?
Divide the category’s value by the total of all values and multiply by 360°. For example, 50 out of 200 is 0.25 of the total, so its sector is 0.25 × 360° = 90°.
How do I convert a percentage to degrees in a pie chart?
Multiply the percentage by 3.6, because 100% of the circle is 360°. So 15% is 54°, 25% is 90° and 45% is 162°.
How do I find the percentage from a pie chart angle?
Divide the angle by 360° and multiply by 100. A 54° slice is 54 ÷ 360 × 100 = 15% of the whole. Choose Angles above to convert a whole chart at once.
How do I find how many people a slice represents?
Multiply the slice’s percentage by the total count. If 5% of 420 survey replies chose an option, that slice stands for 0.05 × 420 = 21 people. Enter the total count to get this for every slice.
When should I not use a pie chart?
Use one only when the parts make up a whole and there are a handful of categories. With many small slices, values that do not add to a meaningful total, or when you need to compare close values, a bar chart is easier to read.
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This calculator is for educational purposes. Double-check important results before acting on them.