The Percentage Formula Explained
One relationship, three arrangements. The percentage formula connects three values: the part, the whole, and the percentage. Know any two and you can find the third. This article lays out all three versions, explains where they come from, and shows you examples of each.
What "Percent" Actually Means
The word "percent" comes from the Latin per centum, meaning per hundred. So 40% means 40 out of every 100. It is a standardised way to express a ratio so you can compare things on the same scale. 40 out of 160 students passed: that is 25%. 12 out of 48 parts are defective: that is also 25%. Different raw numbers, same percentage, easy to compare.
The Core Relationship
Every percentage problem involves three quantities:
- Part: the portion you are looking at
- Whole: the total it comes from
- Percentage: the rate expressed per 100
They are connected by:
Rearranging gives the other two versions:
Which version to use depends on what you are trying to find.
Formula 1: Finding the Part
Use this when you know the total and the rate and need the actual amount.
Question: What is 35% of 260?
Part = 260 x 35 / 100 = 91.
So 35% of 260 is 91. Practical use: a shop gives you a 35% discount off a $260 item. Savings: $91. You pay $169.
More detail on this version in our guide on how to calculate percentage of a number.
Formula 2: Finding the Percentage
Use this when you know both the part and the whole and need to express the relationship as a rate.
Question: 42 out of 168 products are returned. What is the return rate?
Percentage = 42 / 168 x 100 = 25%.
Practical use: exam scores, sales conversion rates, defect rates, voter turnout. Any time you want to express a count as a share of a total.
Full worked examples in how to calculate what percent one number is of another.
Formula 3: Finding the Whole
Use this when you have the part and the percentage and need to reconstruct the total.
Question: 63 people represent 45% of a survey group. How big was the full group?
Whole = 63 / (45 / 100) = 63 / 0.45 = 140.
Check: 140 x 0.45 = 63. Correct.
This is also called "reversing" a percentage and appears frequently in retail (recovering pre-discount prices) and tax calculations.
Converting Between Percentages, Decimals, and Fractions
| Percentage | Decimal | Fraction |
|---|---|---|
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 10% | 0.10 | 1/10 |
| 33.3% | 0.333 | 1/3 |
| 66.7% | 0.667 | 2/3 |
| 12.5% | 0.125 | 1/8 |
To go from percentage to decimal: divide by 100 (move the decimal two places left).
To go from decimal to percentage: multiply by 100 (move the decimal two places right).
To go from fraction to percentage: divide top by bottom, then multiply by 100. 3/8 = 0.375 = 37.5%.
A Note on Percentage Points
Percentage points and percentages are not the same thing. If interest rates rise from 2% to 5%, they rose by 3 percentage points. But the percentage change in the rate itself is (5 minus 2) / 2 x 100 = 150%. "Percentage points" measure absolute difference between two percentage values. "Percentage" (or percentage change) measures relative change. Mixing them up is one of the most common statistical errors in media coverage. See our deeper look at percentage difference vs percentage change.
Using the Free Calculator
The percentage calculator on this site covers all three formula versions: finding the part, the percentage, and the percent change. No algebra required.
Frequently Asked Questions
What is the basic percentage formula?
Part = Whole x Percentage / 100. It has three versions depending on which variable you are solving for.
How do I rearrange the percentage formula?
The three forms are: Part = Whole x Percentage / 100. Percentage = Part / Whole x 100. Whole = Part / (Percentage / 100).
What does percent mean?
Percent comes from the Latin per centum, meaning per hundred. A percentage expresses a number as a fraction of 100. So 40% means 40 out of every 100.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. The fraction 3/8 = 0.375 x 100 = 37.5%.
How do I convert a decimal to a percentage?
Multiply by 100 (or move the decimal two places right). 0.65 = 65%. 1.2 = 120%.