🔢Percentage Calculator

Percentages appear in almost every area of daily life — shopping discounts, salary raises, tax bills, test scores, investment returns, and nutrition labels. A percentage is simply a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning "out of one hundred." Our percentage calculator handles all four common percentage problems in one place: finding a percentage of a number, finding what percent one number is of another, calculating percent change, and expressing a part as a percentage of a total.

What Is a Percentage?

A percentage represents a proportion out of 100. When you say 35%, you mean 35 out of every 100, or equivalently 0.35 as a decimal or 7/20 as a fraction. Converting between these three forms is the foundation of all percentage math.

• Percent to decimal: Divide by 100. 42% = 0.42
• Decimal to percent: Multiply by 100. 0.78 = 78%
• Fraction to percent: Divide the numerator by the denominator, then multiply by 100. 3/8 = 0.375 = 37.5%

This conversion is important because most percentage formulas work more cleanly with decimals than with the percent symbol directly.

How to Find a Percentage of a Number

The most common percentage question is: "What is X% of Y?" The formula is:
Result = (X / 100) × Y

For example, what is 18% of $240? Calculate (18 / 100) × 240 = 0.18 × 240 = $43.20. This is the calculation behind restaurant tips, sales tax, commission rates, and discounts.

Real-world examples:

• A 15% tip on a $56 restaurant bill: (15 / 100) × 56 = $8.40
• 8.5% sales tax on a $320 purchase: (8.5 / 100) × 320 = $27.20
• A 6% commission on a $185,000 home sale: (6 / 100) × 185,000 = $11,100

How to Find What Percent One Number Is of Another

The second type of problem asks: "X is what percent of Y?" The formula is:
Percentage = (X / Y) × 100

If you scored 47 out of 60 on a quiz, your percentage is (47 / 60) × 100 = 78.3%. If your company's expenses were $42,000 out of a $180,000 budget, expenses consumed (42,000 / 180,000) × 100 = 23.3% of the budget.

This formula answers the question any time you have a part and a whole and want to understand their ratio as a familiar percentage rather than a fraction.

How to Calculate Percentage Change (Increase or Decrease)

Percentage change measures how much a value has grown or shrunk relative to where it started. The formula is:
Percentage Change = ((New Value − Old Value) / Old Value) × 100

A positive result means an increase; a negative result means a decrease.

Examples:

• A stock price goes from $84 to $105: ((105 − 84) / 84) × 100 = +25% increase
• Monthly electricity bill drops from $210 to $178: ((178 − 210) / 210) × 100 = −15.2% decrease
• Salary increases from $55,000 to $61,600: ((61,600 − 55,000) / 55,000) × 100 = +12% raise

The most common mistake when calculating percentage change is dividing by the new value instead of the original. Always use the starting value in the denominator. If you are measuring how much something changed, you measure it against what it was, not what it became.

Percentage of a Total: Budget and Composition Analysis

When you have a part and want to know what fraction of the whole it represents, the formula is:
Percentage = (Part / Total) × 100

This is mathematically identical to the "X is what percent of Y" formula, but it is typically applied to budget breakdowns, survey results, and composition analysis.

• Rent of $1,400 on a $4,200 monthly income: (1,400 / 4,200) × 100 = 33.3% of income
• 68 survey respondents said yes out of 250 total: (68 / 250) × 100 = 27.2% yes rate
• A food item has 380 calories from fat out of 2,000 daily calories: (380 / 2,000) × 100 = 19% of daily intake

Percentage Points vs. Percent Change: A Critical Distinction

These two terms are frequently confused, even in news reporting, and the difference matters enormously in finance and statistics.

Percentage points measure the arithmetic difference between two percentages. If the unemployment rate falls from 6% to 4%, it dropped by 2 percentage points.

Percent change measures the relative shift. That same drop from 6% to 4% is a ((4 − 6) / 6) × 100 = 33.3% relative decrease in unemployment — a very different and more dramatic number.

The distinction shows up in mortgage rates, inflation figures, poll numbers, and exam scores. A rise from 3% to 4.5% mortgage interest is a 1.5 percentage-point increase, but it represents a 50% increase in your interest rate. Always clarify which measure is being used when reading financial news.

How to Calculate Discounts and Sale Prices

Retail discount calculations are among the most common percentage problems. To find the discount amount and the sale price:

Discount Amount = Original Price × (Discount % / 100)
Sale Price = Original Price × (1 − Discount % / 100)

A jacket priced at $180 is 30% off:
Discount amount = $180 × 0.30 = $54
Sale price = $180 × 0.70 = $126

Warning on stacked discounts: Two sequential discounts do not simply add together. A 20% discount followed by an additional 15% discount on a $100 item works like this: 20% off leaves $80, then 15% off $80 = $68. The combined effective discount is 32%, not 35%. Always apply each discount to the running balance, not the original price.

Quick Mental Math Shortcuts

A few mental math tricks make common percentages fast to calculate without a calculator:

• 10%: Move the decimal one place left. 10% of $74 = $7.40
• 5%: Halve the 10% value. 5% of $74 = $3.70
• 15%: Add 10% and 5%. 15% of $74 = $7.40 + $3.70 = $11.10
• 20%: Double the 10% value. 20% of $74 = $14.80
• 25%: Divide by 4. 25% of $80 = $20
• 1%: Move the decimal two places left. 1% of $4,500 = $45
• Any %: Break it into 10% chunks and combine. 37% of $200 = (30% = $60) + (7% = $14) = $74

Common Percentage Mistakes to Avoid

Even people who work with numbers regularly make these errors:

• Dividing by the new value in percent change: Always divide by the original. ((New − Old) / Old) × 100, not ((New − Old) / New) × 100.
• Adding stacked discounts: Apply each discount sequentially, not additively.
• Confusing percentage points with percent change: A rate rising from 2% to 3% is a 1 percentage-point increase and a 50% relative increase — both statements are correct but describe different things.
• Treating percentages over 100% as impossible: A 150% increase simply means the value grew to 2.5 times its original size, which is perfectly valid.

The percentage calculator above handles all these cases accurately, so you can skip the arithmetic and focus on interpreting the result.