Percentages Made Simple: Every Formula You'll Ever Need
Percent of a number, percentage change, increase and decrease, reverse percentages and percentage points, all the formulas with clear examples.
Percentages show up everywhere, discounts, tips, taxes, interest, test scores, statistics. Yet most of us half-remember the formulas and reach for a calculator without really knowing what it is doing. Here is every percentage calculation you will realistically need, each with a plain example you can follow.
1. Finding a percentage of a number
The most common one. To find X% of a number, multiply the number by X and divide by 100.
Result = (number × percent) ÷ 100
Example: 20% of 250 = (250 × 20) ÷ 100 = 50.
2. What percent one number is of another
To find what percent A is of B, divide A by B and multiply by 100.
Percent = (A ÷ B) × 100
Example: 30 out of 120 = (30 ÷ 120) × 100 = 25%.
3. Percentage change (increase or decrease)
To find how much something changed in percentage terms:
Change % = (new − old) ÷ old × 100
A positive answer is an increase; a negative answer is a decrease.
Example: a price rising from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase. Falling from 100 to 80 is a 20% decrease, note it is not the same percentage, because the starting point differs.
Going from 100 to 80 is a 20% drop, but going back from 80 to 100 is a 25% rise. The base you divide by changes, so the percentages differ even though the amount is the same.
4. Applying an increase or decrease
To add a percentage: multiply by (1 + percent ÷ 100). To subtract one: multiply by (1 − percent ÷ 100).
Example: a $50 item with 15% added = 50 × 1.15 = $57.50. The same item with 15% off = 50 × 0.85 = $42.50.
5. Reverse percentages
Sometimes you know the final amount and need the original, for example, removing tax from a total. Divide by (1 + percent ÷ 100).
Original = total ÷ (1 + percent ÷ 100)
Example: a price of $120 that includes 20% tax = 120 ÷ 1.20 = $100 before tax.
Quick reference table
| Goal | Formula | Example |
|---|---|---|
| X% of a number | (n × X) ÷ 100 | 20% of 250 = 50 |
| A as % of B | (A ÷ B) × 100 | 30 of 120 = 25% |
| Percentage change | (new − old) ÷ old × 100 | 80 → 100 = +25% |
| Add X% | n × (1 + X/100) | 50 + 15% = 57.50 |
| Remove X% (reverse) | total ÷ (1 + X/100) | 120 ÷ 1.20 = 100 |
If an interest rate goes from 5% to 7%, that is a 2 percentage-point rise, but a 40% relative increase. News headlines mix these up constantly, keep them straight and you will read statistics more accurately than most people.
Skip the mental math. Our percentage calculator handles percent-of, what-percent and percentage-change in one place.
Open the Percentage Calculator →The bottom line
Five formulas cover almost every percentage you will ever meet: percent of a number, A as a percent of B, percentage change, applying a change, and reversing one. Learn the pattern once, watch out for percentage points, and percentages stop being guesswork.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20% of 250 is (250 × 20) ÷ 100 = 50.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original, then multiply by 100. For example, from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
What is the difference between percent and percentage points?
If a rate rises from 5% to 7%, that is a 2 percentage-point increase, but a 40% increase in relative terms. Percentage points measure the gap between two percentages; percentages measure relative change.