Percentage Calculator
Calculate percentages in multiple ways
What is X% of Y?
X is what % of Y?
Percentage change
Increase or decrease by %
How to Use This Calculator
This percentage calculator provides four distinct calculation modes, each designed to solve a specific type of percentage problem. Simply enter your numbers and the results appear instantly without needing to click any buttons.
Mode 1: What is X% of Y? Use this when you know a percentage and want to find that portion of a number. Enter the percentage value in the first field and your base number in the second field. For example, to find 15% of 200, enter 15 and 200 to get 30. This mode is perfect for calculating discounts, tips, taxes, or any situation where you need a specific percentage of a value.
Mode 2: X is what % of Y? Use this when you have two numbers and want to know their percentage relationship. Enter the partial amount first and the total amount second. For instance, if you scored 42 points out of 50 on a test, enter 42 and 50 to discover you achieved 84%. This mode helps with grade calculations, completion percentages, and proportion analysis.
Mode 3: Percentage Change Use this to calculate how much a value has increased or decreased in percentage terms. Enter the original value in the "from" field and the new value in the "to" field. The calculator shows whether the change is positive (increase) or negative (decrease). This is essential for tracking price changes, investment returns, population shifts, or any before-and-after comparison.
Mode 4: Increase or Decrease by % Use this when you need to apply a percentage change to a number. Enter your starting value, select whether you want to increase or decrease, and enter the percentage amount. For example, to add a 20% markup to $100, enter 100, select increase, and enter 20 to get $120. This mode is ideal for pricing, salary adjustments, and growth projections.
Understanding Percentages
A percentage is a mathematical concept that expresses a number as a fraction of 100. The term derives from the Latin phrase "per centum," which translates to "by the hundred." When we write 75%, we are expressing the ratio 75 to 100, or equivalently, three-quarters of a whole. This standardized approach to expressing proportions has made percentages the universal language for comparing relative quantities across virtually every field of human endeavor.
Converting Between Fractions, Decimals, and Percentages: These three representations are interchangeable. To convert a percentage to a decimal, divide by 100 (move the decimal point two places left). So 45% becomes 0.45. To convert a decimal to a percentage, multiply by 100 (move the decimal point two places right). The decimal 0.125 becomes 12.5%. For fractions, divide the numerator by the denominator to get a decimal, then multiply by 100 for the percentage. The fraction 5/8 equals 0.625 as a decimal and 62.5% as a percentage.
Common Percentage Calculations: The most frequent percentage operations include finding a percentage of a number (used in discounts, tips, and taxes), determining what percentage one number is of another (grades, statistics, ratios), and calculating percentage change between two values (growth rates, price changes, performance metrics). Each calculation follows a simple formula, but understanding the underlying concept ensures you apply the right approach to each situation.
Percentage Points vs. Percent: This distinction often causes confusion but is critically important. When interest rates rise from 5% to 7%, they have increased by 2 percentage points, but the percentage increase is 40% (because 2 is 40% of 5). Percentage points measure the absolute difference between two percentages, while percent change measures the relative change. News reports, financial analyses, and statistical studies require careful attention to this distinction to avoid misinterpretation.
Why Percentages Matter: Percentages enable meaningful comparisons across different scales. A company earning $1 million profit and another earning $100 million might both have 10% profit margins, indicating equal efficiency regardless of size. In scientific research, percentages help compare results across studies with different sample sizes. In personal finance, percentages reveal the true cost of loans, the actual returns on investments, and the impact of inflation on purchasing power. Mastering percentage calculations empowers you to make informed decisions in countless real-world situations.
Frequently Asked Questions
How do I calculate the percentage of a number?
To find a percentage of any number, multiply the number by the percentage and divide by 100. Alternatively, convert the percentage to a decimal first by dividing by 100, then multiply. For example, to calculate 35% of 80, you can compute (35 x 80) / 100 = 28, or convert 35% to 0.35 and multiply: 0.35 x 80 = 28. Both methods yield the same result. This calculation applies to countless everyday scenarios including calculating sales tax, determining tip amounts, figuring out discounts, and computing portions of any whole quantity.
How do I find the percent increase or decrease between two numbers?
The percentage change formula is: ((New Value - Original Value) / Original Value) x 100. First subtract the original value from the new value to find the absolute change. Then divide that change by the original value to find the relative change. Finally, multiply by 100 to express it as a percentage. If your investment grew from $500 to $650, the calculation is ((650 - 500) / 500) x 100 = 30% increase. For decreases, the formula works the same way but produces a negative result. If a price dropped from $200 to $160, the change is ((160 - 200) / 200) x 100 = -20%, indicating a 20% decrease.
What is the difference between percentage points and percent?
Percentage points measure the arithmetic difference between two percentages, while percent measures relative change. If unemployment rises from 4% to 6%, it increased by 2 percentage points (the simple subtraction: 6 - 4 = 2). However, in percentage terms, unemployment increased by 50% because 2 is 50% of 4. This distinction matters greatly in finance, economics, and statistics. A credit card raising its APR from 15% to 18% increased by 3 percentage points but 20% in relative terms. Always clarify which measure is being used when discussing percentage changes in percentages.
How do I convert a decimal to a percentage?
Converting a decimal to a percentage requires multiplying by 100. Simply move the decimal point two places to the right. The decimal 0.75 becomes 75%, the decimal 0.08 becomes 8%, and the decimal 1.25 becomes 125%. This works because percentages are fractions with 100 as the denominator, so multiplying by 100 converts from the decimal (hundredths) representation to the percentage representation. Conversely, to convert a percentage to a decimal, divide by 100 or move the decimal point two places to the left. Thus 65% becomes 0.65 and 7.5% becomes 0.075.
How do I calculate a discount price?
To calculate a discount price, multiply the original price by the discount percentage (as a decimal) to find the discount amount, then subtract from the original price. For a $150 item at 30% off: $150 x 0.30 = $45 discount, so the sale price is $150 - $45 = $105. A faster method multiplies the original price by (1 - discount percentage). For the same example: $150 x 0.70 = $105. For multiple discounts applied successively (like an additional 10% off the sale price), calculate each discount in order. Starting with $150 at 30% off ($105), then 10% off that result: $105 x 0.90 = $94.50. Note that successive discounts of 30% and 10% do not equal a single 40% discount.
What is the formula for percentage change?
The percentage change formula is: Percentage Change = ((New Value - Old Value) / Old Value) x 100. This formula measures how much a quantity has changed relative to its starting point. The numerator (New - Old) gives the absolute change, which can be positive (increase) or negative (decrease). Dividing by the old value normalizes this change relative to where you started. Multiplying by 100 converts the decimal result to a percentage. For example, if your portfolio value changed from $10,000 to $12,500, the percentage change is ((12,500 - 10,000) / 10,000) x 100 = 25% increase. This formula is fundamental to finance, economics, science, and any field requiring measurement of relative change.
How do I calculate a reverse percentage (find the original number)?
To find an original number before a percentage was applied, divide by the appropriate factor. If a number increased by X%, divide the new value by (1 + X/100). If it decreased by X%, divide by (1 - X/100). For example, if a price after a 20% increase is $180, the original price was $180 / 1.20 = $150. If a sale price after a 25% discount is $75, the original price was $75 / 0.75 = $100. For finding the original value when you know the percentage portion, divide the portion by the percentage (as a decimal). If $45 represents 15% of the total, the total is $45 / 0.15 = $300. These reverse calculations are essential for determining original prices, pre-tax amounts, and base values.
What are common percentage equivalents I should memorize?
Knowing common percentage-fraction-decimal equivalents speeds up mental math significantly. The essential ones are: 50% = 1/2 = 0.5; 25% = 1/4 = 0.25; 75% = 3/4 = 0.75; 10% = 1/10 = 0.1; 20% = 1/5 = 0.2; 33.33% = 1/3 = 0.333...; 66.67% = 2/3 = 0.667...; 12.5% = 1/8 = 0.125; 5% = 1/20 = 0.05. Using these, you can quickly derive others: 15% is 10% + 5%, 30% is 3 x 10%, 40% is 2 x 20%, and so on. For tipping, knowing that 15% is 10% + half of 10%, and 20% is double 10%, makes mental calculations effortless. These equivalents also help verify calculator results and catch errors.
Percentage Examples
Sales Discount Calculation: A $250 television is advertised at 35% off during a holiday sale. To find your savings, calculate 35% of $250: 0.35 x 250 = $87.50 discount. The sale price is $250 - $87.50 = $162.50. If there is an additional 8% sales tax on the discounted price, the tax amount is 0.08 x $162.50 = $13.00, making your final cost $175.50.
Grade Calculation: On a midterm exam worth 150 points, you earned 127 points. To find your percentage score, divide your points by the total and multiply by 100: (127 / 150) x 100 = 84.67%. If the exam counts as 30% of your final grade, multiply your score by the weight: 84.67 x 0.30 = 25.4 points contributed to your final grade out of the 30 possible points from this exam.
Tip Calculation: Your restaurant bill totals $78.50 before tax. For a 20% tip based on the pre-tax amount, calculate 0.20 x $78.50 = $15.70. A quick mental math approach: 10% is $7.85, so 20% is double that, approximately $15.70. If you prefer 18%, calculate 10% ($7.85) plus 8% ($6.28) for a total tip of about $14.13.
Investment Return: You invested $5,000 in a mutual fund that is now worth $6,750. To find your return, calculate the percentage change: (($6,750 - $5,000) / $5,000) x 100 = 35% gain. If this growth occurred over 3 years, the compound annual growth rate (CAGR) is approximately 10.5% per year, calculated using the formula that accounts for compounding rather than simple division by 3.
Percentage Tips
Mental Math Shortcuts: Calculate 10% by moving the decimal point one place left. From 10%, derive other percentages easily: 5% is half of 10%, 20% is double 10%, 15% is 10% plus half of itself, and 1% is 10% divided by 10. For 25%, find half of half (divide by 4). For 33%, divide by 3. Combining these building blocks handles most everyday calculations without a calculator.
Common Fraction Equivalents: Memorizing these relationships accelerates calculations: 50% equals one-half, 25% equals one-quarter, 20% equals one-fifth, 12.5% equals one-eighth, and 10% equals one-tenth. When you see 25% off, you know the sale price is three-quarters of the original. A 20% tip means one-fifth of the bill. These equivalents make percentage problems intuitive rather than requiring computation.
Avoiding Common Mistakes: Remember that percentage change always uses the original value as the denominator, not the new value. Be careful with successive percentages, as a 20% increase followed by a 20% decrease leaves you at 96% of the original, not 100%. When comparing percentages of different bases, convert to absolute numbers for accurate comparison. A 10% discount on $1,000 ($100) saves more than a 20% discount on $300 ($60). Always verify whether quoted percentages refer to percentage points or relative percent change.
The Percentage Formulas
X is what % of Y = (X / Y) x 100
% Change = ((New - Old) / Old) x 100
Increase by X% = Value x (1 + X/100)
Decrease by X% = Value x (1 - X/100)
These formulas cover all common percentage calculations. The first formula finds a percentage of any number. The second determines what percentage one number is of another. The third calculates how much something has changed in percentage terms. The final two formulas apply percentage increases or decreases to a value.
Did you know?
- The % symbol evolved from the Italian "per cento" (per hundred) abbreviation over centuries of handwriting simplification.
- A 50% discount followed by a 50% markup does not return to the original price. It leaves you at 75% of the original value.
- If something increases by 100%, it has doubled. If it increases by 200%, it has tripled. A 300% increase means the value is now four times the original.
- The rule of 72 lets you estimate how long it takes money to double: divide 72 by the interest rate. At 8% interest, money doubles in about 9 years.
- Percentages over 100% are perfectly valid. A 150% increase means the new value is 2.5 times the original.