The exact angles in a complete pie chart add to 360°. If you round each angle separately to the nearest degree, the rounded labels can add to 359° or 361° because the individual rounding differences do not always cancel.
Keep the original counts or fractions while you work. For an exact missing sector, subtract the exact angles from 360° or calculate from the missing count.
- Divide each category count by the total count.
- Multiply by 360° to find each angle.
- Round only at the step requested in the question.
Worked example | Seven votes across four categories
Four categories receive 1, 1, 1 and 4 votes. Each one-vote category takes 360° ÷ 7, or about 51.429°. The four-vote category takes 4 × 360° ÷ 7, or about 205.714°.
Rounded to the nearest degree, the labels are 51°, 51°, 51° and 206°. They add to 359°. The exact angles add to (1 + 1 + 1 + 4) × 360° ÷ 7 = 360°.
Find a missing sector from exact information
If the fourth angle is hidden and you know the counts, use 4/7 of 360°. Subtracting the three rounded 51° labels from 360° gives 207°. That is the amount needed to make those three rounded numbers sum to 360°, while the fourth exact angle rounds to 206°.
Before subtracting displayed values, check whether the question gives exact angles or labels rounded independently. If you have only rounded values, an exact missing angle may be impossible to recover.
Try a chart whose labels add to 361°
Four categories receive 1, 1, 1 and 8 votes. Find their angles to the nearest degree, then add the rounded answers.
Answer. Each one-vote angle is 360° ÷ 11, or about 32.727°. The eight-vote angle is about 261.818°. The labels are 33°, 33°, 33° and 262°, and their sum is 361°.
Frequently asked questions
Does a 359° total prove a category is missing?
Independent rounding can explain a small mismatch. Use the category counts or unrounded angles to check whether anything is missing.
Should I add one degree to the last label?
Follow the question’s instructions. If it asks for each angle to the nearest degree, leave each independently rounded result as calculated.
Official information
SEAB, 2027 SEC G3 Mathematics syllabus (K310), Data Analysis and Approximation and Estimation. Syllabus checked 11 November 2026. The examples are original.