Percentage Calculator
The three percentage questions you actually ask — "what is X% of Y," "X is what percent of Y," and "percentage change" — each solved with the steps shown.
What is X% of Y?
X is what percent of Y?
Percentage increase / decrease
The percentage formulas
A is what % of B = (A ÷ B) × 100
% change = ((New − Old) ÷ Old) × 100
20% of 150 = 150 × 0.20 = 30 · 30 of 150 = 30 ÷ 150 × 100 = 20% · 150 → 180 = 30 ÷ 150 × 100 = 20% increase
A jacket is on sale for $120 after a 20% discount. What was the original price? Original = 120 ÷ (1 − 0.20) = 120 ÷ 0.80 = $150.
Compare a raise instead: your new salary is $57,500 after a 15% increase. Original = 57,500 ÷ (1 + 0.15) = 57,500 ÷ 1.15 = $50,000. The key mistake to avoid: don't multiply the new value by 0.80 or 1.15 — divide by it, since the percentage was applied to the original, unknown value, not the result you already have.
Percentages in everyday life
The same three operations cover most real questions: a tip is "X% of Y," a test score is "A is what percent of B," and a price change or raise is percentage change. One common trap: a percentage increase and the reverse decrease aren't symmetric — going up 20% then down 20% doesn't return you to the start (150 → 180 → 144). For money-specific versions see the discount, tip, and sales tax calculators, and for the standalone change tool, percentage change.
The percentage-point trap
One mistake worth watching for: a change from 20% to 25% is a rise of 5 percentage points, but a 25% relative increase (5 ÷ 20 = 25%). News headlines and marketing often blur this distinction, so when a number sounds surprising, check whether it's expressed in percentage points or as a relative percentage change — the two can tell very different stories from the same underlying data.
Common percentage-to-fraction equivalents
| Percentage | Fraction |
|---|---|
| 10% | 1/10 |
| 12.5% | 1/8 |
| 20% | 1/5 |
| 25% | 1/4 |
| 33.3% | 1/3 |
| 50% | 1/2 |
| 66.7% | 2/3 |
| 75% | 3/4 |
Recognizing these fraction equivalents makes mental math faster than reaching for a calculator for common cases — 25% of a number is just that number divided by 4, and 75% is three-quarters of it. For exact fraction arithmetic beyond these common cases, the fraction calculator handles the conversion directly.
Common percentage mistakes
- Multiplying instead of dividing when reversing a percentage. If you know the result after a percentage change, divide by (1 ± the rate) to recover the original — don't multiply by it. See the reverse-percentage example above.
- Assuming an increase and an equal decrease cancel out. They don't, because the second percentage applies to a different (already-changed) base value.
- Treating percentage points and percent change as interchangeable. A "5-point" change and a "5%" change are very different sizes unless the starting value happens to be 100.
Frequently asked questions
How do I calculate a percentage of a number?
Number × (percent ÷ 100). 20% of 150 = 30.
How do I find what percent one number is of another?
Part ÷ whole × 100. 30 of 150 = 20%.
How do I calculate percentage change?
(New − Old) ÷ Old × 100. 150 → 180 = 20% increase.
What is the difference between percentage points and percent change?
A move from 20% to 25% is 5 percentage points, but it's a 25% relative increase (5 ÷ 20). Confusing the two is a common source of misleading statistics.
How do I find the original number before a percentage change?
Divide by (1 ± the rate) — minus for a decrease, plus for an increase. $120 after a 20% discount: 120 ÷ 0.80 = $150 original.
Does increasing then decreasing by the same percentage return the original value?
No — the second percentage applies to the new, changed value. 150 up 20% is 180; 180 down 20% is 144, not 150.
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Last reviewed: September 2026.