Master every type of percentage calculation with clear formulas, step-by-step instructions, and real-world examples.
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." When you see the symbol %, it simply means "out of 100." So 45% is the same as 45 out of 100, or 45/100, or 0.45 as a decimal.
Percentages are one of the most practical math concepts you will ever use. They appear on restaurant bills (tips), in stores (discounts), on bank statements (interest rates), in school (grades), and in the news (statistics). Understanding how to calculate percentages gives you the ability to quickly evaluate deals, compare data, and make informed decisions in everyday life.
The reason percentages are so useful is that they create a common scale. Comparing 17 out of 23 with 42 out of 58 is not intuitive, but when you convert them to 73.9% and 72.4%, the comparison is immediate. Percentages normalize different totals into a single, easy-to-understand scale.
Every percentage calculation relies on the relationship between three values: the part, the whole, and the percentage. The fundamental formula is:
Percentage = (Part / Whole) x 100
From this single formula, you can derive two other forms depending on which value you are solving for:
Part = Whole x (Percentage / 100)Whole = Part / (Percentage / 100)
These three equations cover every basic percentage problem. Whichever value is unknown, rearrange the formula to solve for it. The rest of this guide walks through each scenario with examples.
This is the most common percentage question: "What is X% of Y?" You are given the percentage and the whole, and you need to find the part.
Part = Whole x (Percentage / 100)
Step 1: Write the percentage as a decimal by dividing it by 100. For example, 25% becomes 25 / 100 = 0.25.
Step 2: Multiply the whole number by this decimal. For example, 0.25 x 200 = 50.
Step 3: The result is your answer. 25% of 200 is 50.
Question: What is 15% of 340?
Step 1: 15 / 100 = 0.15
Step 2: 340 x 0.15 = 51
Answer: 51
Question: A shirt costs $80 and is on sale for 30% off. How much is the discount?
Step 1: 30 / 100 = 0.30
Step 2: 80 x 0.30 = 24
Answer: The discount is $24, so the sale price is $56.
You can use our Percentage Calculator to solve these instantly, or try the Discount Calculator for shopping scenarios.
This answers the question: "X is what percent of Y?" You know the part and the whole, and you need the percentage.
Percentage = (Part / Whole) x 100
Step 1: Divide the part by the whole. For example, 35 / 200 = 0.175.
Step 2: Multiply the result by 100. For example, 0.175 x 100 = 17.5%.
Step 3: The result is your percentage. 35 is 17.5% of 200.
Question: You scored 42 out of 50 on a test. What is your percentage score?
Step 1: 42 / 50 = 0.84
Step 2: 0.84 x 100 = 84%
Answer: You scored 84%.
This answers the question: "X is Y% of what number?" You know the part and the percentage, and you need the whole.
Whole = Part / (Percentage / 100)
Step 1: Convert the percentage to a decimal. For example, 20% becomes 0.20.
Step 2: Divide the part by this decimal. For example, 45 / 0.20 = 225.
Step 3: The result is your whole. 45 is 20% of 225.
Question: A tip of $9 represents 18% of the bill. What was the total bill?
Step 1: 18 / 100 = 0.18
Step 2: 9 / 0.18 = 50
Answer: The total bill was $50.
Use our Tip Calculator to quickly split bills and calculate tips.
Percentage change measures how much a value has increased or decreased relative to its original value. This is widely used in finance, economics, and everyday comparisons.
Percentage Change = ((New Value - Old Value) / Old Value) x 100
If the result is positive, the value increased. If negative, it decreased.
Question: A stock price went from $40 to $52. What is the percentage increase?
Step 1: New - Old = 52 - 40 = 12
Step 2: 12 / 40 = 0.30
Step 3: 0.30 x 100 = 30%
Answer: The stock increased by 30%.
Question: A laptop was $1,200 last year and now costs $960. What is the percentage decrease?
Step 1: New - Old = 960 - 1200 = -240
Step 2: -240 / 1200 = -0.20
Step 3: -0.20 x 100 = -20%
Answer: The price decreased by 20%.
Try our Percentage Change Calculator for instant results.
Percentage difference compares two values when neither is clearly the "original." It uses the average of the two values as the reference point.
Percentage Difference = (|Value1 - Value2| / ((Value1 + Value2) / 2)) x 100
Question: City A has a population of 85,000 and City B has 72,000. What is the percentage difference?
Step 1: |85,000 - 72,000| = 13,000
Step 2: (85,000 + 72,000) / 2 = 78,500
Step 3: (13,000 / 78,500) x 100 = 16.56%
Answer: The percentage difference is approximately 16.56%.
Use the Percentage Difference Calculator for quick comparisons.
To convert any fraction to a percentage, divide the numerator by the denominator and multiply by 100.
Percentage = (Numerator / Denominator) x 100
Question: Convert 7/8 to a percentage.
Step 1: 7 / 8 = 0.875
Step 2: 0.875 x 100 = 87.5%
Answer: 7/8 = 87.5%
See our Percentage to Fraction Converter for a full conversion tool with simplification.
Converting a decimal to a percentage is the simplest conversion: multiply by 100 (or move the decimal point two places to the right).
Percentage = Decimal x 100
0.45 = 45% | 0.07 = 7% | 1.25 = 125% | 0.003 = 0.3%
Use the Percentage to Decimal Converter for the reverse conversion and more examples.
To convert a percentage to a fraction, write the percentage over 100 and simplify.
Question: Convert 75% to a fraction.
Step 1: Write as 75/100
Step 2: Find GCD of 75 and 100, which is 25
Step 3: Divide both by 25: 75/25 = 3, 100/25 = 4
Answer: 75% = 3/4
This table shows the most commonly used percentages alongside their fraction and decimal equivalents. Memorizing these will speed up mental math considerably.
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.10 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.20 |
| 25% | 1/4 | 0.25 |
| 33.33% | 1/3 | 0.3333 |
| 40% | 2/5 | 0.40 |
| 50% | 1/2 | 0.50 |
| 60% | 3/5 | 0.60 |
| 66.67% | 2/3 | 0.6667 |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.80 |
| 87.5% | 7/8 | 0.875 |
| 90% | 9/10 | 0.90 |
| 100% | 1/1 | 1.00 |
When a store advertises "40% off," you are calculating a percentage of a number. If a jacket costs $120 with 40% off, the discount is $120 x 0.40 = $48, so you pay $72. Stacking discounts requires multiplying the remaining percentages rather than adding them. A 20% off coupon after a 30% sale is not 50% off total -- it is $120 x 0.70 x 0.80 = $67.20, which is a 44% total discount. Use our Discount Calculator to double-check sale prices.
Sales tax is a percentage added to the purchase price. If the tax rate is 8.25%, you multiply the subtotal by 0.0825. A $45 meal with 8.25% tax costs $45 + $3.71 = $48.71. Tips work the same way: a 20% tip on a $45 meal is $45 x 0.20 = $9.00.
Interest rates, returns on investment, inflation, and profit margins are all expressed as percentages. If your savings account earns 4.5% annually on $10,000, you earn $450 in a year (simple interest). For compound interest, the calculation involves repeatedly applying the percentage to growing totals. See our Compound Interest Calculator for detailed projections.
Your GPA and class grades rely on percentage calculations. If you scored 87 out of 100 on one test and 45 out of 60 on another, your percentages are 87% and 75% respectively. Weighted averages use percentages to account for different assignment values. Our GPA Calculator can help with academic planning.
Nutritional labels show "% Daily Value" for nutrients, body fat percentage measures fitness, and BMI categories are defined by ranges. When a label says a food provides 15% of your daily iron, it means 15% of the recommended 18 mg, or 2.7 mg. Check your BMI or daily calorie needs with our health calculators.
Finding 10% of any number is easy: just move the decimal point one place to the left. 10% of 350 is 35. From there, you can derive many other percentages:
5% = half of 10%. So 5% of 350 = 17.50.
20% = double 10%. So 20% of 350 = 70.
15% = 10% + 5%. So 15% of 350 = 35 + 17.50 = 52.50.
1% = move the decimal two places left. 1% of 350 = 3.50.
X% of Y is always equal to Y% of X. This means 8% of 50 is the same as 50% of 8, which is 4. This trick is incredibly useful when one calculation is easier than the other. 4% of 75 is the same as 75% of 4 = 3.
25% means "one quarter," so divide by 4. 25% of 240 = 60. Similarly, 75% is "three quarters," so divide by 4 and multiply by 3. 75% of 240 = 180.
A common mistake is adding successive percentage changes. If a price increases by 10% then decreases by 10%, the result is not the original price. $100 + 10% = $110, then $110 - 10% = $99. The final price is $99, not $100. Always apply each percentage change to the current value, not the original.
Multiply the number by the percentage divided by 100. For example, to find 25% of 200, calculate 200 x (25/100) = 200 x 0.25 = 50. You can also move the decimal point two places to the left in the percentage and then multiply.
Percentage change = ((New Value - Old Value) / Old Value) x 100. A positive result means an increase, and a negative result means a decrease. For example, going from 80 to 100 is a ((100-80)/80) x 100 = 25% increase.
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375, and 0.375 x 100 = 37.5%. This works for any fraction, including improper fractions where the result will exceed 100%.
Percentage change compares a new value to an original value and has a clear direction (increase or decrease). Percentage difference compares two values when neither is the "original" by dividing the absolute difference by their average. Percentage change uses one value as the base; percentage difference uses the mean of both.
Yes. A percentage over 100% indicates that the part exceeds the whole used as a reference. For instance, if revenue grew from $1 million to $3 million, the new revenue is 300% of the original, representing a 200% increase.
Because each percentage change applies to a different base. If $100 increases by 50%, it becomes $150. A 50% decrease from $150 subtracts $75, leaving $75 -- not $100. The decrease is calculated on the larger number, removing more than was originally added.
Find 10% by moving the decimal point left one place. For 20%, double that amount. For 15%, add half of 10% to 10%. For example, on a $65 bill: 10% = $6.50, so 20% = $13.00 and 15% = $6.50 + $3.25 = $9.75.
Percentage points measure the arithmetic difference between two percentages. If interest rates go from 3% to 5%, that is a 2 percentage point increase but a 66.7% increase in the rate itself. The distinction matters in finance, economics, and statistics where precise language is important.
Divide the resulting number by (1 + percentage/100) for increases, or (1 - percentage/100) for decreases. If a price after a 20% increase is $60, the original was $60 / 1.20 = $50. If a price after a 25% discount is $75, the original was $75 / 0.75 = $100.
X% of Y is always equal to Y% of X. This is because multiplication is commutative: (X/100) x Y = (Y/100) x X. So 8% of 50 equals 50% of 8, which is 4. This shortcut makes many mental calculations much easier.
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This calculator uses standard mathematical formulas and is accurate to multiple decimal places. Results are rounded for readability but the underlying calculations use full precision.
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