How to Calculate Percentages (4 Methods)

Percentages show up everywhere: sale tags, tax bills, exam scores, investment returns, recipe adjustments, and budget reports. The math behind them is straightforward once you know which formula to reach for.

This guide covers four core percentage calculations, each with a clear formula and a worked example you can follow along with. For instant answers, try our Free Percentage Calculator.

Method 1: Find X% of Y

This is the most common percentage question. “What is 15% of 200?” You need this when calculating tips, discounts, taxes, or commissions.

Formula:

$Result = Y \times \frac{X}{100}$

Steps:

1. Convert the percentage to a decimal by dividing by 100.
2. Multiply by the base number.

Example: What is 18% of $450?

• Convert: 18 / 100 = 0.18
• Multiply: $450 x 0.18 = $81.00

Mental Math Shortcut: To find 18% quickly, find 10% ($45), then 8% (which is 10% minus 2%). 2% of $450 is $9, so 8% is $36. Add them: $45 + $36 = $81.

You can also use the “flip trick.” Finding 8% of 25 is the same as 25% of 8, which is just 8 / 4 = 2. The commutative property of multiplication makes this work every time.

Method 2: X Is What Percent of Y?

This formula answers questions like “I scored 42 out of 55 on a test. What grade is that?” or “My expenses are $3,200 out of a $5,000 budget. What percentage am I using?”

Formula:

$Percentage = \frac{X}{Y} \times 100$

Steps:

1. Divide the part by the whole.
2. Multiply by 100 to convert to a percentage.

Example: You scored 42 out of 55 on an exam. What is your percentage score?

• Divide: 42 / 55 = 0.7636
• Multiply: 0.7636 x 100 = 76.4%

Example 2: Your company earned $820,000 in revenue. Your department contributed $148,000. What share is that?

• $148,000 / $820,000 = 0.1805
• 0.1805 x 100 = 18.05%

Method 3: Percentage Increase or Decrease

Use this when comparing an old value to a new value. Did your rent go up? Did your electric bill drop? This formula tells you by how much, as a percentage.

Formula:

$\% \ Change = \frac{New - Old}{Old} \times 100$

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

Steps:

1. Subtract the old value from the new value.
2. Divide by the old value (always the original number).
3. Multiply by 100.

Example (Increase): Your rent went from $1,400 to $1,575. What is the percentage increase?

• Difference: $1,575 - $1,400 = $175
• Divide by old: $175 / $1,400 = 0.125
• Multiply: 0.125 x 100 = 12.5% increase

Example (Decrease): Gas dropped from $3.80 per gallon to $3.23. What is the percentage decrease?

• Difference: $3.23 - $3.80 = -$0.57
• Divide by old: -$0.57 / $3.80 = -0.15
• Multiply: -0.15 x 100 = 15% decrease

Common mistake: Always divide by the old value. Dividing by the new value gives you a different (and wrong) answer. If your stock goes from $50 to $75, the increase is ($25 / $50) x 100 = 50%, not ($25 / $75) x 100 = 33%.

The Asymmetry Problem

Percentage drops and gains aren’t symmetrical. If your portfolio drops 50% from $10,000 to $5,000, you need a 100% gain (not 50%) to get back to $10,000.

Drop	Gain Needed to Recover
10%	11.1%
20%	25.0%
30%	42.9%
50%	100.0%
75%	300.0%
90%	900.0%

This is why protecting against losses matters more than chasing gains in investing.

Method 4: Percentage Difference Between Two Values

Unlike percentage change, percentage difference doesn’t assume one value came first. It measures how far apart two numbers are relative to their average. Use this when comparing prices at two stores, the weight of two packages, or the performance of two products.

Formula:

$\% \ Difference = \frac{|A - B|}{\frac{A + B}{2}} \times 100$

Steps:

1. Find the absolute difference between the two values.
2. Find the average of the two values.
3. Divide the difference by the average.
4. Multiply by 100.

Example: Store A sells a blender for $89. Store B sells it for $109. What is the percentage difference?

• Difference: |$89 - $109| = $20
• Average: ($89 + $109) / 2 = $99
• Divide: $20 / $99 = 0.2020
• Multiply: 0.2020 x 100 = 20.2% difference

When to use percentage difference vs. percentage change:

• Percentage change: When there is a clear “before” and “after” (salary increase, price hike, population growth).
• Percentage difference: When comparing two independent values with no directional relationship (two products, two cities, two test scores).

Quick Reference Table

Question	Formula	Example
What is X% of Y?	Y x (X/100)	15% of 200 = 30
X is what % of Y?	(X/Y) x 100	42 of 55 = 76.4%
% increase/decrease	((New-Old)/Old) x 100	$50 to $75 = 50%
% difference	(|A-B|/Avg) x 100	89 vs 109 = 20.2%

Real-World Applications

Shopping: A jacket is marked down from $120 to $84. Use Method 3: ($84 - $120) / $120 x 100 = -30%. That is a 30% discount.

Investing: You bought a stock at $42 and it is now at $58. Use Method 3: ($58 - $42) / $42 x 100 = 38.1% return.

Grades: You answered 87 out of 100 questions correctly. Use Method 2: 87 / 100 x 100 = 87%.

Budgeting: Your food spending went from $600/month to $720/month. Use Method 3: ($720 - $600) / $600 x 100 = 20% increase.

Skip the Math

Our Percentage Calculator handles all four methods instantly. Enter your numbers, pick the calculation type, and get your answer with the formula shown. Pair it with the Sales Tax Calculator for tax-related percentage problems or the ROI Calculator for investment returns.

Frequently Asked Questions

How do I convert a fraction to a percentage?

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. If you have a mixed number like 2 3/4, convert it to an improper fraction first (11/4), then divide: 11 / 4 = 2.75 = 275%.

Why does my percentage change formula give a negative number?

A negative result means a decrease. If your weight went from 180 lbs to 165 lbs, the change is (165 - 180) / 180 x 100 = -8.3%. The negative sign tells you it dropped 8.3%. Drop the negative sign and call it an 8.3% decrease.

Is “percentage points” the same as “percent”?

No, and confusing them is a common error in news reports. If an interest rate moves from 5% to 7%, that is a 2 percentage point increase but a 40% percent increase (because 2/5 x 100 = 40%). Percentage points measure the raw difference between two percentages. Percent measures the relative change.

Can a percentage be greater than 100%?

Absolutely. If your investment doubles, that is a 100% increase. If it triples, that is a 200% increase. Percentages above 100% simply mean the result is larger than the base value. A company growing revenue from $1 million to $3.5 million achieved 250% growth.