Percentages show up everywhere: sale tags, tips, tax, pay raises, and test scores. The good news is that almost every percentage problem uses one of three simple formulas.
This guide walks through each formula with worked examples you can follow on paper, on your phone, or with our free percentage calculator.
Key takeaways
- “Percent” means “per hundred” — 25% is simply 25 out of 100.
- To find X% of Y: divide X by 100, then multiply by Y.
- To find what percent X is of Y: divide X by Y, then multiply by 100.
- Percent change uses the starting value as the base, not the ending value.
What a percentage really means
The word “percent” comes from the Latin per centum, meaning “per hundred.” So 25% literally means 25 out of every 100. If a test has 100 questions and you answer 25 correctly, your score is 25%.
Thinking in hundredths makes percentages intuitive. 50% is half, 25% is a quarter, 10% is a tenth, and 1% is one hundredth. Every percentage problem is just a question about parts of 100.
Quick intuition check
Formula 1: What is X% of Y?
This is the most common percentage question — tips, discounts, tax, and commissions all use it. The formula is: divide the percentage by 100 to get a decimal, then multiply by the number.
For example, to find 20% of $48.50: first convert 20% to 0.20, then multiply 0.20 × 48.50 = $9.70. That is your tip.
| Problem | Step 1: convert | Step 2: multiply | Answer |
|---|---|---|---|
| 15% of 80 | 15 ÷ 100 = 0.15 | 0.15 × 80 | 12 |
| 7.5% of $1,200 | 7.5 ÷ 100 = 0.075 | 0.075 × 1,200 | $90.00 |
| 33% of 90 | 33 ÷ 100 = 0.33 | 0.33 × 90 | 29.7 |
Formula 2: X is what percentage of Y?
Use this when you know the part and the whole and want the percentage — for example, “I saved $180 of my $900 paycheck; what percent did I save?” Divide the part by the whole, then multiply by 100.
180 ÷ 900 = 0.20, and 0.20 × 100 = 20%. You saved 20% of your paycheck. The most common mistake here is dividing in the wrong order: always put the part on top.
Worked example
Formula 3: Percentage increase and decrease
Percent change compares a new value to an old value. Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive answer is an increase; a negative answer is a decrease.
Suppose your rent rises from $1,200 to $1,290. The change is $90. Divide $90 by the starting rent of $1,200 to get 0.075, or 7.5%. Always divide by the starting value — that is the base of the comparison.
| Situation | Calculation | Result |
|---|---|---|
| Price $50 → $65 | (65 − 50) ÷ 50 × 100 | 30% increase |
| Weight 180 → 162 lbs | (162 − 180) ÷ 180 × 100 | 10% decrease |
| Pay $22/hr → $24/hr | (24 − 22) ÷ 22 × 100 | 9.09% increase |
Percentage points vs. percent: a common trap
If an interest rate moves from 4% to 6%, it rose by 2 percentage points — but the relative increase is 50% (2 ÷ 4 × 100). News headlines sometimes blur this distinction, so it pays to read carefully.
When someone says “support grew by 5%,” they usually mean a relative change. When they say “5 percentage points,” they mean simple subtraction of the two rates. Ask which one is meant if it matters to your decision.
Mental-math shortcuts worth knowing
You rarely need a calculator for round percentages. To find 10% of anything, move the decimal one place left: 10% of $64 is $6.40. From there, build other percentages: 20% is double 10%, and 5% is half of 10%.
For 15% (a common tip), find 10%, halve it for 5%, and add them: 10% of $40 is $4, 5% is $2, so 15% is $6. With a little practice these take seconds.
- 1% of anything: move the decimal two places left ($200 → $2).
- 10% of anything: move the decimal one place left ($200 → $20).
- 25%: divide by 4. 50%: divide by 2. 75%: divide by 4, then multiply by 3.
- To add X%: multiply by (1 + X ÷ 100). To subtract X%: multiply by (1 − X ÷ 100).
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Every formula in this guide is built into the calculator.
Try the Percentage CalculatorFrequently asked questions
How do I calculate 20% of a number?
Divide 20 by 100 to get 0.20, then multiply by the number. For example, 20% of 150 is 0.20 × 150 = 30. A shortcut: divide the number by 5.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 as a percent of 120 is (30 ÷ 120) × 100 = 25%.
What is the formula for percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100: ((New − Old) ÷ Old) × 100.
What is the difference between percent and percentage points?
Percentage points are the simple difference between two percentages (6% − 4% = 2 points). Percent change is relative: that same move is a 50% increase (2 ÷ 4 × 100).
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