Percentage Calculator
Free online percentage calculator with 6 different calculation types. Find percentages, percentage change, difference, increase, and decrease. See also Percentage Change Calculator and Decimal to Percent.
What is X% of Y?
Example: What is 25% of 200? Answer: 50
Percentage of a Number
Example: 20% of 12 = 2.4
X is what % of Y?
Example: 50 is what % of 200? Answer: 25%
X is Y% of what?
Example: 50 is 25% of what? Answer: 200
Percentage Change
Example: From 80 to 100 = 25% increase
Percentage Difference
Example: Difference between 100 and 150 = 40%
Increase / Decrease by %
Example: 500 changed by 10% = 550 (increase) or 450 (decrease)
What is a Percentage?
A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere in daily life — from shopping discounts and tax rates to exam scores and statistics. The symbol "%" represents percent. For example, 25% means 25 out of 100, which equals the fraction 1/4 or the decimal 0.25.
Percentage Formulas
Basic Percentage
What is X% of Y? → Answer = (X / 100) × Y
X is what % of Y? → Percentage = (X / Y) × 100
X is Y% of what? → Total = X / (Y / 100)
Percentage Change
Change = ((New − Old) / |Old|) × 100
Percentage Difference
Difference = (|A − B| / ((|A| + |B|) / 2)) × 100
Increase / Decrease
Increased value = Value × (1 + Percent / 100)
Decreased value = Value × (1 − Percent / 100)
Worked Examples
What is 15% of 200?
(15 / 100) × 200 = 0.15 × 200 = 30
45 is what % of 180?
(45 / 180) × 100 = 0.25 × 100 = 25%
Percentage change from 80 to 100?
((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25% increase
500 increased by 10%?
500 × (1 + 0.10) = 500 × 1.10 = 550
Common Percentage Reference Table
| Percentage | Fraction | Decimal | Example (of 100) |
|---|---|---|---|
| 1% | 1/100 | 0.01 | 1 |
| 5% | 1/20 | 0.05 | 5 |
| 10% | 1/10 | 0.10 | 10 |
| 20% | 1/5 | 0.20 | 20 |
| 25% | 1/4 | 0.25 | 25 |
| 33.33% | 1/3 | 0.3333 | 33.33 |
| 50% | 1/2 | 0.50 | 50 |
| 66.67% | 2/3 | 0.6667 | 66.67 |
| 75% | 3/4 | 0.75 | 75 |
| 100% | 1/1 | 1.00 | 100 |
| 150% | 3/2 | 1.50 | 150 |
| 200% | 2/1 | 2.00 | 200 |
Technical Details
Percentage calculations are fundamental to mathematics, finance, science, and everyday life. In finance, percentages express interest rates, returns on investment, tax rates, and discounts. In statistics, they represent proportions, probabilities, and margins of error. In science, they express concentrations, efficiency, and error rates. This calculator handles all six common percentage operations with full decimal precision. Note that percentage change and percentage difference are different calculations — change measures relative to the starting value, while difference measures relative to the average of both values.
Frequently Asked Questions
How do I calculate a percentage?
To find X% of Y, divide X by 100 and multiply by Y. For example, 20% of 150 = (20/100) × 150 = 30.
What is the difference between percentage change and percentage difference?
Percentage change measures how much a value has changed relative to its original value (directional — increase or decrease). Percentage difference measures how far apart two values are relative to their average (non-directional — always positive).
Can a percentage be more than 100%?
Yes. A percentage over 100% means the value exceeds the reference amount. For example, if sales grew from 100 to 250, that is a 150% increase. The new value is 250% of the original.
How do I convert a percentage to a decimal?
Divide by 100. For example, 75% = 75/100 = 0.75. To convert back, multiply by 100: 0.75 × 100 = 75%.
How do I calculate a discount?
Multiply the original price by (1 − discount/100). For example, a 20% discount on $80: $80 × (1 − 0.20) = $80 × 0.80 = $64. The discount amount is $80 × 0.20 = $16.
Practice Questions
Try these on your own:
- A jacket originally costs $120 and is on sale for 35% off. What is the sale price? (Answer: $78)
- You scored 42 out of 56 on a test. What percentage did you score? (Answer: 75%)
- A town's population grew from 24,000 to 27,600. What is the percentage increase? (Answer: 15%)
- If 18% of a number is 63, what is the number? (Answer: 350)
- A laptop was $850 last year and now costs $680. What is the percentage decrease? (Answer: 20%)
- Sales tax is 8.25%. How much tax do you pay on a $64 purchase? (Answer: $5.28)
Common Mistakes to Avoid
One of the most frequent errors is confusing percentage change with percentage difference. Percentage change has a clear direction (old → new) and uses the old value as the base, while percentage difference is symmetric and uses the average of both values. Another common mistake is applying successive percentages incorrectly — a 20% increase followed by a 20% decrease does NOT return you to the original value (you end up 4% lower). Students also often forget that "percent" literally means "per hundred," so 25% = 25/100 = 0.25. When calculating discounts, remember to subtract from the original price — finding 30% of $80 gives you the discount amount ($24), not the final price ($56). Finally, watch out for percentage points vs. percentages: going from 10% to 15% is a 5 percentage point increase but a 50% relative increase.
Key Takeaways
- "Percent" means "per hundred" — always divide the percentage by 100 before using it in calculations.
- To find X% of Y: multiply Y by (X ÷ 100). Example: 25% of 80 = 80 × 0.25 = 20.
- Percentage change = ((New − Old) / |Old|) × 100. A positive result means increase; negative means decrease.
- Successive percentage changes don't simply add up — they compound multiplicatively.
- Converting between fractions, decimals, and percentages: 3/4 = 0.75 = 75%.
- Percentage difference uses the average of both values as the denominator, making it direction-independent.