Percentage Calculator

Percentage Calculator (Percent, Increase/Decrease, Change)

Calculate percentages instantly with this free online percentage calculator. Find what percent one number is of another, calculate percentage increase or decrease, determine percent of a value, and solve all common percentage problems.

Get immediate results for percent calculations, percentage change, percent difference, and more without complex formulas or spreadsheets.

What This Percentage Calculator Can Do

This versatile calculator handles the most common percentage calculation types you'll encounter in everyday situations.

What is p% of x calculates the value of a percentage of a number. For example, "What is 20% of 150?" gives you 30. This calculation type is useful for finding discounts, tips, tax amounts, portions of totals, and any situation where you need to find a percentage of a value.

x is what percent of y determines what percentage one number represents of another. For example, "30 is what percent of 150?" gives you 20%. This helps you express parts as percentages of wholes, compare values as percentages, calculate completion rates, and analyze proportions.

Percent change (increase or decrease) calculates the percentage change between an original value and a new value. For example, "percentage change from 80 to 100" gives you 25% increase. This is essential for tracking growth rates, measuring performance changes, analyzing price increases or decreases, and comparing before-and-after values.

Percent difference calculates the relative difference between two independent values using their average as the base. This differs from percent change by treating both values equally rather than designating one as the "original." Use this when comparing two measurements without a clear starting point.

How to Use the Percentage Calculator

Getting percentage results takes just seconds with this straightforward calculator.

Select your calculation type based on what you need to find. Choose "What is % of" for finding a percentage of a number, "What % is of" for finding what percentage one number is of another, "Percent change" for increase/decrease calculations, or "Percent difference" for comparing two independent values.

Enter your numbers in the appropriate fields. Input the percentage value (like 20 for 20%), the base number or total, and any additional values required for your calculation type. Make sure to enter numbers without the percent sign in value fields.

Click Calculate to get your result instantly. The calculator displays the answer clearly, showing the calculated percentage, the formula used, and the result formatted appropriately.

Copy or use your result in whatever context you need it. The calculator provides answers you can immediately apply to discounts, budgets, reports, analysis, or any percentage-related task.

Percentage Basics (Quick Explanation)

Understanding what percentages represent helps you choose the right calculation and interpret results correctly.

Percent means "per hundred" and comes from the Latin "per centum." A percentage expresses a ratio or fraction with 100 as the denominator. When you write 25%, you're saying "25 per 100" or "25 out of every 100."

Converting between forms:

• 25% = 25/100 = 0.25 (decimal)
• 50% = 50/100 = 0.5 (decimal)
• 100% = 100/100 = 1 (decimal)

The percent sign (%) is shorthand for "divide by 100." When you see 20%, you can think of it as 20 / 100, which equals 0.20 in decimal form. This conversion is the foundation of percentage calculations.

Percentages can exceed 100% when the part is larger than the whole you're comparing it to. If you earn $150 when you expected $100, your earnings are 150% of your expectation, representing a ratio greater than 1. This is mathematically valid and common in growth, returns, and comparison contexts.

Common Percentage Formulas (With Examples)

Worked examples demonstrate how each formula applies to real situations.

What is p% of x? (Percent of a number)

Formula: Value = (p / 100) x x

Example: What is 20% of 150?

(20 / 100) x 150
= 0.20 x 150
= 30

Answer: 30

This calculation finds the portion of a whole. Use it for discounts (20% off $150 = $30 discount), tips (15% of $80 bill), tax amounts (6% sales tax on $200), or any situation where you're finding a fraction of a total.

x is what percent of y? (Finding the percentage)

Formula: Percent = (x / y) x 100

Example: 30 is what percent of 150?

(30 / 150) x 100
= 0.20 x 100
= 20%

Answer: 20%

This calculation expresses one value as a percentage of another. Use it for completion rates (30 of 150 tasks = 20% complete), test scores (45 correct of 50 questions = 90%), market share (30 sales of 150 total = 20% market share), or any comparison of part to whole.

Percent increase from original to new

Formula: Percent change = ((new - original) / original) x 100

Example: Percent increase from 80 to 100

((100 - 80) / 80) x 100
= (20 / 80) x 100
= 0.25 x 100
= 25%

Answer: 25% increase

This calculates growth or increase relative to the starting value. Use it for salary increases (from $50,000 to $55,000), price increases (from $80 to $100), revenue growth (from 1,000 to 1,200 units), or any situation measuring change from a baseline.

Percent decrease from original to new

Formula: Percent change = ((new - original) / original) x 100

Example: Percent decrease from 100 to 80

((80 - 100) / 100) x 100
= (-20 / 100) x 100
= -0.20 x 100
= -20%

Answer: 20% decrease (or -20% change)

The same formula works for decreases, producing a negative result. Use it for price drops (from $100 to $80), budget cuts (from 1,000 to 800 units), weight loss (from 200 to 180 pounds), or any reduction from an initial value.

Percent difference between two values

Formula: Percent difference = (|a - b| / ((a + b) / 2)) x 100

Example: Percent difference between 80 and 100

(|80 - 100| / ((80 + 100) / 2)) x 100
= (20 / 90) x 100
= 0.222... x 100
~ 22.2%

Answer: 22.2% difference

This calculates relative difference using the average as the base. Use it when comparing two independent measurements without a clear "original" value, like comparing prices between two stores, comparing test scores of two students, or analyzing measurements from two instruments.

Percent Change vs Percent Difference (Avoid Confusion)

Understanding when to use each calculation prevents common mistakes and ensures accurate results.

Percent change measures change relative to the original value. It answers "how much did this increase or decrease from the starting point?" The original value serves as the denominator (base) for the calculation. Percent change is directional and asymmetric, meaning the percent change from A to B differs from the percent change from B to A.

Example: Percent change from 50 to 100 = ((100 - 50) / 50) x 100 = 100% increase

But: Percent change from 100 to 50 = ((50 - 100) / 100) x 100 = 50% decrease (negative)

Percent difference measures relative difference using the average as the base. It answers "how different are these two values?" Both values are treated equally without designating one as the original. Percent difference is non-directional and symmetric, producing the same result regardless of which value you list first.

Example: Percent difference between 50 and 100 = (|50 - 100| / ((50 + 100) / 2)) x 100 ~ 66.7%

Same: Percent difference between 100 and 50 = (|100 - 50| / ((100 + 50) / 2)) x 100 ~ 66.7%

When to use which:

Key insight: If you have a clear starting point or reference value, use percent change. If you're comparing two equally-weighted values, use percent difference. Choosing the wrong method can significantly affect your result and interpretation.

Troubleshooting and Edge Cases

Common percentage calculation challenges have clear explanations and solutions.

"Why is my result greater than 100%?"

Explanation: Percentages can and do exceed 100% when the part is larger than the whole or when values more than double. This is mathematically correct and common in real scenarios.

Examples: If your investment grows from $100 to $250, that's a 150% increase. If you score 120 points on a 100-point test with extra credit, you scored 120% of the base total. If sales triple from 100 to 300 units, that's a 200% increase.

Solution: This isn't an error. Percentages over 100% indicate ratios greater than 1:1, which is perfectly valid for growth, returns, and comparisons exceeding the base value.

"Why is percent change different when I reverse the numbers?"

Explanation: Percent change is asymmetric because the denominator (base value) changes when you reverse the calculation. The percentage change from A to B uses A as the base, while the change from B to A uses B as the base.

Example: From 50 to 100 = 100% increase (change of 50 / base of 50). From 100 to 50 = 50% decrease (change of -50 / base of 100). The absolute change is the same (50 units), but the relative change differs due to different bases.

Solution: This is correct mathematical behavior. Always clearly identify which value is your original or starting point. If you need a symmetric comparison, use percent difference instead of percent change.

"The calculator says 'undefined' or gives an error when the base is 0"

Explanation: Division by zero is mathematically undefined. When calculating percentage change or "what percent," if the denominator (original value or whole) is 0, the calculation can't produce a meaningful percentage.

Example: "What is the percent change from 0 to 100?" requires dividing by 0, which is undefined. "50 is what percent of 0?" also requires dividing by 0.

Solution: Reframe the question using absolute values rather than percentages. Instead of "percent change from 0 to 100," say "increased by 100 units from 0" or "growth from zero baseline." Percentages require a non-zero reference point to be meaningful.

"My percentage decrease seems larger than it should be"

Explanation: When values decrease by more than 50%, the percentage naturally becomes large because the base (original value) is larger than the remaining value.

Example: A decrease from 100 to 10 is a 90% decrease. This seems dramatic but is mathematically correct: you lost 90 out of 100 units, which is 90% of the original.

Solution: This is accurate. Large percentage decreases are normal for substantial reductions. If this seems counterintuitive, remember that percent change measures relative change, not absolute change. An absolute decrease of 90 units represents 90% when starting from 100.

"Negative percentages are confusing"

Explanation: Negative percentages indicate decreases or reductions. The negative sign simply shows direction, not an error.

Example: Percent change from 100 to 80 = -20%, meaning a 20% decrease. The negative sign indicates the direction of change.

Solution: Interpret negative results as decreases. When reporting, you can say either "-20% change" or "20% decrease," both conveying the same information. The negative sign is mathematically correct and informative about direction.

Frequently Asked Questions

What is a percentage or percent?

A percentage is a ratio or fraction expressed as a number out of 100. The word "percent" comes from the Latin "per centum," meaning "per hundred." The percent sign (%) is shorthand for "divide by 100." When you see 25%, it means 25 per 100, or 25/100, which equals 0.25 as a decimal. Percentages provide a standardized way to express proportions and compare values.

How do you calculate a percentage of a number?

To find what percent p is of number x, use the formula: (p / 100) x x. First convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, to find 20% of 150: (20 / 100) x 150 = 0.20 x 150 = 30. This calculation is used for discounts, tips, tax amounts, and finding portions of totals.

How do I find what percent x is of y?

Use the formula: (x / y) x 100. Divide the part by the whole, then multiply by 100 to get the percentage. For example, "30 is what percent of 150?" = (30 / 150) x 100 = 0.20 x 100 = 20%. This expresses x as a percentage of y, useful for completion rates, test scores, and proportional comparisons.

How do you calculate percent increase?

Use the formula: ((new value - original value) / original value) x 100. Subtract the original from the new value, divide by the original, then multiply by 100. For example, increase from 80 to 100: ((100 - 80) / 80) x 100 = (20 / 80) x 100 = 25% increase. This measures growth relative to the starting value.

How do you calculate percent decrease?

Use the same formula as percent increase: ((new value - original value) / original value) x 100. The result will be negative, indicating a decrease. For example, decrease from 100 to 80: ((80 - 100) / 100) x 100 = (-20 / 100) x 100 = -20%, or 20% decrease. The formula works for both increases and decreases, with the sign indicating direction.

What is percent change and what's the formula?

Percent change measures the relative change between an original value and a new value, expressed as a percentage of the original. Formula: ((new - original) / original) x 100. Positive results indicate increases, negative results indicate decreases. This calculation shows growth or decline relative to the starting point and is widely used for tracking financial performance, population changes, and time-series comparisons.

What is percent difference and how is it different from percent change?

Percent difference measures the relative difference between two values using their average as the base, while percent change uses the original value as the base. Percent difference formula: (|value1 - value2| / ((value1 + value2) / 2)) x 100. Percent difference is symmetric (same result regardless of order) and used when comparing two independent measurements without a clear starting point. Percent change is asymmetric and used when one value is clearly the baseline.

Can a percentage be over 100%?

Yes, percentages can exceed 100% when the part is larger than the whole or when growth more than doubles the original value. If your investment grows from $100 to $300, that's a 200% increase. If you complete 150 tasks when 100 were assigned, you completed 150% of the expected amount. Percentages over 100% represent ratios greater than 1:1 and are mathematically valid.

What are percentage points and how do they differ from percent?

Percentage points measure the arithmetic difference between two percentages, while percent measures the relative change. If interest rates rise from 5% to 8%, that's a 3 percentage point increase but a 60% relative increase ((8-5)/5 x 100). Percentage points are the absolute difference between percentages. Percent change is the relative change. This distinction matters in finance, polling, and statistics where confusing the two leads to misinterpretation.

Why is my percent change "wrong" when I reverse the numbers?

Percent change is asymmetric because the base value changes when you reverse the calculation. Change from 50 to 100 uses 50 as the base (100% increase), while change from 100 to 50 uses 100 as the base (50% decrease). The absolute change is the same (50 units), but relative change differs due to different denominators. This is mathematically correct, not an error. Always identify which value is your starting point.

What happens if the total or original value is 0?

Percentage calculations involving division by zero are undefined. If the original value or whole is 0, you cannot calculate a meaningful percentage because division by zero has no mathematical meaning. Instead of asking "what's the percent change from 0 to 100," express this as "increased by 100 units from zero" or use absolute values. Percentages require a non-zero reference point.

When should I use percent versus percentage points?

Use percent (or percentage) when discussing the value itself or relative changes: "The discount is 20%," "Profits increased by 30%." Use percentage points when discussing the arithmetic difference between two percentage values: "Unemployment rose from 5% to 8%, an increase of 3 percentage points (not 3%)." In finance and statistics, this distinction is critical for accurate interpretation of data.