Pie Chart Degrees: How to Convert Degrees to Percentages (and Back)

The one fact behind every pie chart angle

A pie chart is a full circle, and a full circle is 360 degrees. The whole circle also represents 100% of the data. So 1% of a pie chart is 3.6 degrees (360 ÷ 100), and every conversion between degrees and percentages is just multiplying or dividing by 3.6.

Percentage to degrees

Degrees = percentage × 3.6

• 10% → 36°
• 25% → 90° (a quarter of the circle)
• 33.3% → 120° (a third)
• 50% → 180° (half)
• 75% → 270°

Example: a survey shows that 25% of students chose swimming. The swimming slice is 25 × 3.6 = 90°. If you prefer fractions, the same answer comes from 25 ⁄ 100 × 360.

Degrees to percentage

Percentage = degrees ÷ 3.6 (equivalently, degrees ÷ 360 × 100)

• 36° → 10%
• 50° → 13.9%
• 120° → 33.3%
• 247° → 68.6%
• 300° → 83.3%

Example: a slice measures 50° on a printed chart. Its share of the whole is 50 ÷ 3.6 = 13.9%. Use the degrees to percentage converter if you would rather not do the division by hand.

Raw data to degrees (drawing a pie chart by hand)

When you have counts rather than percentages, skip the percentage step entirely: angle = value ÷ total × 360.

Say you asked 10 people a question on an agree–disagree scale and got 6 strongly agree, 3 agree and 1 neutral. The total is 10, so:

• Strongly agree: 6 ÷ 10 × 360 = 216° (60%)
• Agree: 3 ÷ 10 × 360 = 108° (30%)
• Neutral: 1 ÷ 10 × 360 = 36° (10%)

Check: 216 + 108 + 36 = 360. The angles of a pie chart must always add up to 360°, just as the percentages must add up to 100%. Draw the slices with a protractor starting at the 12 o'clock line and working clockwise, or type the three counts into the free pie chart maker and let it compute the angles.

Degrees to a number of people (or dollars, or hours)

Exam questions often reverse the problem: "A pie chart of 48 people has a 120° slice for Bus. How many people take the bus?" The slice's fraction of the whole is 120 ÷ 360 = 1⁄3, so the answer is 48 × 1⁄3 = 16 people. In general: value = angle ÷ 360 × total.

A related variant gives you one slice's value and angle and asks about another: "75° represents 150 units — what does 50° represent?" Because angle and value are proportional, each degree is worth 150 ÷ 75 = 2 units, so 50° represents 100 units. You can also work out the total: 360 × 2 = 720 units.

Degrees on a clock-style pie chart

Time pies use the same arithmetic because a 24-hour day is one whole. Each hour is 360 ÷ 24 = 15° (4.17%); on a 12-hour clock face each hour is 30°. Eight hours of sleep on a 24-hour pie is 8 × 15 = 120°, i.e. a third of the circle. See the hours in a day pie chart for a ready-made example.

Quick reference table

• 1% = 3.6°
• 5% = 18°
• 10% = 36°
• 12.5% = 45° (one eighth)
• 20% = 72°
• 25% = 90°
• 33.3% = 120°
• 40% = 144°
• 50% = 180°
• 60% = 216°
• 66.7% = 240°
• 75% = 270°
• 100% = 360°

Common mistakes

• Dividing by 100 instead of 360 when going from a value to an angle. The circle has 360 parts, not 100.
• Rounding each angle to a whole degree and ending up with 359° or 361°. Keep one decimal place, or put the rounding difference into the largest slice.
• Measuring a 3D chart with a protractor. The tilt distorts every angle; only flat pie charts can be measured. See why 3D pie charts mislead.
• Forgetting the total. An angle alone tells you the share, never the amount. You need the total to turn 120° into "16 people".

Frequently Asked Questions

How do I convert a percentage to degrees in a pie chart?

Multiply the percentage by 3.6, because the full circle (100%) is 360 degrees. A 25% slice is 25 × 3.6 = 90 degrees; a 15% slice is 54 degrees.

How do I convert degrees to a percentage in a pie chart?

Divide the angle by 3.6 (or by 360 and multiply by 100). A 90-degree slice is 25%; a 120-degree slice is 33.3%; a 247-degree slice is 68.6%.

How do I find the angle of a slice from raw data?

Divide the slice's value by the total, then multiply by 360. If 30 of 120 people chose swimming, the angle is 30 ÷ 120 × 360 = 90 degrees.

Why should the angles in a pie chart add up to 360?

Because a pie chart represents one whole split into parts. If your angles sum to more or less than 360 degrees after rounding, round to one decimal place or adjust the largest slice by the difference.

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