How to Calculate Percentage
A percentage expresses a number as a fraction of 100. Whether you're calculating a discount, a test score, or a growth rate, the same three formulas cover every situation. This guide explains each one with worked examples you can follow by hand — then use the calculator to check your work.
Last updated: March 31, 2026
The Formula
Percentage = (Part ÷ Whole) × 100 Part = (Percentage ÷ 100) × Whole Percent Change = ((New − Old) ÷ |Old|) × 100
Variable Definitions
| Symbol | Name | Description |
|---|---|---|
| Part | Part | The portion you are comparing — the smaller piece of the total |
| Whole | Whole | The total or reference amount you are comparing against |
| New | New Value | The value after a change has occurred |
| Old | Old Value | The original value before the change |
Step-by-Step Example
A student scored 54 out of 80 on a test. What percentage did they score? The previous week they scored 45. What was the percentage improvement?
Given
Solution
- 1Divide part by whole:
54 ÷ 80 = 0.675 - 2Multiply by 100 to get percentage:
0.675 × 100 = 67.5% - 3Calculate the change from previous week:
54 − 45 = 9 - 4Divide change by old value:
9 ÷ 45 = 0.2 - 5Convert to percentage improvement:
0.2 × 100 = 20% improvement
The student scored 67.5%, a 20% improvement over the previous week.
Ready to calculate?
Use the free Percentage Calculator — instant results, no sign-up.
Common Mistakes to Avoid
Dividing in the wrong order — 54/80 is correct, 80/54 gives a number greater than 1.
Forgetting to multiply by 100 — the formula gives a decimal (0.675), not a percentage (67.5%).
Using the new value instead of the old value as the denominator in percent change — the base is always the original.
Confusing percentage points with percent change — going from 10% to 15% is a 5 percentage-point increase but a 50% relative increase.