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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.

Concept Fundamentals
Y × (X/100)
X% of Y
(A/B)×100
A is ?% of B
(New−Old)/Old×100
Change
Final/(1±p/100)
Reverse

Did our AI summary help? Let us know.

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%.

Key quantities
Y × (X/100)
X% of Y
Key relation
(A/B)×100
A is ?% of B
Key relation
(New−Old)/Old×100
Change
Key relation
Final/(1±p/100)
Reverse
Key relation

Ready to run the numbers?

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%.
Sources:PercentageMarkup

Run the calculator when you are ready.

Five Percentage OperationsPart of whole, ratio, change, reverse, markup—all from one calculator.

Quick Examples — Click to Load

Calculation Mode

Input Values

%
percentage_calc
CALCULATED
$ calc --mode="percentOf"
Result
50.00
Part Value
50.00
Ratio
0.2500
Summary
25% of 200 = 50.00
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Value Comparison

Part vs Whole

Step-by-Step Breakdown

CALCULATION
Formula
Result = (Percentage / 100) × Value
Convert to decimal
25% = 0.2500
25 ÷ 100
Multiply
0.2500 × 200
0.2500 × 200
ANSWER
RESULT
50.00

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?

📜The % symbol evolved from an Italian abbreviation "per cento" — over centuries, the "cento" was shortened to "00" with a slash through itSource: Mathematics History
🧮Ancient Romans used fractions based on 12 (duodecimal). Percentages based on 100 only became standard in the 15th centurySource: Number Theory
💡If an item is discounted 20% then another 30%, the total discount is 44%, not 50% — percentages don't simply addSource: Consumer Math
📊In statistics, a change from 1% to 2% is both a 1 percentage point increase AND a 100% relative increase — context mattersSource: Statistics
🏦Compound interest at 7.2% doubles your money in ~10 years (Rule of 72), while simple interest would take ~14 yearsSource: Finance
🌍Sales tax rates vary wildly worldwide: 0% in Oregon, 27% in Hungary (VAT) — percentages directly affect consumer behaviorSource: Economics

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

PercentageFractionDecimalOf 100Of 250
10%1/100.101025
20%1/50.202050
25%1/40.252562.5
33.3%1/30.33333.383.3
50%1/20.5050125
75%3/40.7575187.5
100%1/11.00100250

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

1/100
What 1% means
72/r
Doubling Time Rule
x1.5
50% Increase Factor
x0.8
20% Discount Factor

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.

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