Percentage Calculations
The all-in-one percentage tool: find X% of Y, what percent is A of B, percentage change, reverse percentage (original from final), and markup. Percent means per hundred—25% = 25/100 = 0.25.
Why This Mathematical Concept Matters
Why: Sales tax (8.5% of $45), tips (18% of bill), grades (42/50 = ?%), salary raises, retail markup. Percentages are everywhere. This calculator handles the five most common operations.
How: Part: multiply whole by percentage/100. Ratio: divide part by whole, ×100. Change: (new−old)/old×100. Reverse: divide final by (1+tax/100) or (1−discount/100). Markup: cost × (1+markup/100).
- ●Reverse percentage: if price after 20% tax is $120, original = $120/1.20 = $100.
- ●Markup vs margin: 40% markup on $50 cost = $70 price; margin = 20/70 = 28.6%.
- ●What percent: 42 of 50 = 42/50 × 100 = 84%.
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Step-by-Step Breakdown
⚠️For educational and informational purposes only. Verify with a qualified professional.
🧮 Fascinating Math Facts
— Etymology
— Reverse
Key Takeaways
- • A percentage is simply a number expressed as a fraction of 100
- • "Percent" comes from Latin per centum, meaning "by the hundred"
- • Percentage change and percentage difference are not the same calculation
- • A 50% increase followed by a 50% decrease does not return you to the original value
- • Markup percentage and profit margin are different: 100% markup = 50% margin
Did You Know?
How Percentages Work
A percentage represents a proportion out of 100. When you say "25%", you mean 25 out of every 100, which is the fraction 25/100 or the decimal 0.25.
Three Core Operations
1. Finding a percentage of a value: Multiply the value by the percentage expressed as a decimal. For example, 15% of 80 = 0.15 x 80 = 12.
2. Finding what percent one number is of another: Divide the part by the whole and multiply by 100. For example, 12 is what % of 80? (12/80) x 100 = 15%.
3. Finding percentage change: Subtract old from new, divide by old, multiply by 100. For example, from 80 to 100: ((100-80)/80) x 100 = 25% increase.
Reverse Percentage (finding the original)
If a price after a 20% increase is $120, the original price = $120 / 1.20 = $100. If a price after a 20% discount is $80, the original price = $80 / 0.80 = $100.
Expert Tips
The Commutative Trick
8% of 50 equals 50% of 8 (both = 4). Swap the numbers to make mental math easier when one percentage is simpler to compute.
Successive Percentages
Two successive changes of a% and b% give a total change of a + b + (ab/100)%. So 20% then 30% = 56%, not 50%.
Markup vs Margin
Markup is based on cost (profit/cost x 100), while margin is based on selling price (profit/price x 100). A 100% markup = 50% margin.
Quick Mental Math
To find 15%: calculate 10% (move decimal) + 5% (half of 10%). For 25%: divide by 4. For 33%: divide by 3. For 75%: subtract 25% from the whole.
Common Percentage Table
| Percentage | Fraction | Decimal | Of 100 | Of 250 |
|---|---|---|---|---|
| 10% | 1/10 | 0.10 | 10 | 25 |
| 20% | 1/5 | 0.20 | 20 | 50 |
| 25% | 1/4 | 0.25 | 25 | 62.5 |
| 33.3% | 1/3 | 0.333 | 33.3 | 83.3 |
| 50% | 1/2 | 0.50 | 50 | 125 |
| 75% | 3/4 | 0.75 | 75 | 187.5 |
| 100% | 1/1 | 1.00 | 100 | 250 |
Frequently Asked Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage divided by 100. For example, 20% of 150 = 150 x (20/100) = 150 x 0.20 = 30.
What is the difference between percentage change and percentage difference?
Percentage change has a clear "before" and "after" (direction matters). Percentage difference is symmetric — it measures how far apart two values are relative to their average, regardless of order.
How do I find the original price before a discount?
Divide the discounted price by (1 - discount/100). For example, if the sale price is $80 after a 20% discount: $80 / (1 - 0.20) = $80 / 0.80 = $100.
Why doesn't a 50% increase then 50% decrease give the original?
Because each percentage is applied to a different base. A 50% increase on 100 gives 150. Then a 50% decrease on 150 gives 75 — not 100. The decrease is applied to the larger number.
What is the difference between markup and margin?
Markup = (Profit / Cost) x 100. Margin = (Profit / Selling Price) x 100. If cost is $50 and selling price is $100: markup is 100%, margin is 50%.
How do I calculate compound percentage changes?
Multiply the individual factors: (1 + r1/100) x (1 + r2/100) x ... - 1. For example, +10% then +20%: 1.10 x 1.20 = 1.32, which is a 32% total increase.
Quick Reference Numbers
Note: This calculator provides mathematical results for educational and practical purposes. For financial decisions, always verify calculations with a qualified professional. Rounding may cause small differences in displayed values.