How to Calculate Percentage: 3 Methods With Worked Examples

Quick Answer: To find X% of a number: multiply by X ÷ 100. Example: 20% of 150 = 150 × 0.20 = 30. For percentage change: [(New − Old) ÷ Old] × 100. Use our Free Percentage Calculator for instant results.

Percentages are everywhere — sale discounts, test scores, tax rates, pay raises, interest rates, nutrition labels. The ability to calculate them quickly and confidently is one of the most practical math skills an adult can have. The good news is that there are really only three core operations you need to master, and each one follows a simple formula.

This guide walks through all three methods with clear worked examples, then explains percentage change, reverse percentages, and how to handle the most common real-world situations. If you want instant answers without the arithmetic, the Percentage Calculator does all the heavy lifting for you.

What Is a Percentage?

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 say something is 35%, you mean 35 out of every 100 — or equivalently, the decimal 0.35, or the fraction 35/100.

That equivalence is the key to all percentage arithmetic:

35% = 35/100 = 0.35
8% = 8/100 = 0.08
150% = 150/100 = 1.50

Converting between these three forms is the first thing to internalize, because every percentage formula is just arithmetic on fractions or decimals with an extra x100 to bring things back to the familiar percent scale.

Method 1: The Core Percentage Formula

The most fundamental percentage calculation answers the question: what percentage is the part of the whole?

Formula:

Percentage = (Part / Whole) x 100

Worked Example 1: A student answers 42 questions correctly out of 60. What is their score as a percentage?

Identify the part: 42
Identify the whole: 60
Divide: 42 / 60 = 0.70
Multiply by 100: 0.70 x 100 = 70%

Worked Example 2: A car originally costs $24,000. After a rebate, the buyer pays $21,600. What percentage of the original price did they pay?

Part = 21,600; Whole = 24,000
21,600 / 24,000 = 0.90
0.90 x 100 = 90%

The rebate saved them 10% of the original price.

Rearranging the formula: That same relationship lets you find either the part or the whole if the other two values are known.

To find the part: Part = (Percentage / 100) x Whole
To find the whole: Whole = Part / (Percentage / 100)

So if you know that 30% of a class is 18 students, the whole class size is 18 / 0.30 = 60 students.

Method 2: The Proportion Method

Some people find it easier to think in proportions rather than formulas. The proportion method sets up a ratio and solves for the unknown value.

Setup: Part / Whole = Percentage / 100

Cross-multiply to solve for whichever value is missing.

Worked Example: What is 35% of 280?

Set up the proportion:

x / 280 = 35 / 100

Cross-multiply:

x x 100 = 280 x 35 x x 100 = 9,800 x = 9,800 / 100 = 98

So 35% of 280 is 98.

Why this method is useful: The proportion method is especially helpful when you are working with word problems that do not already point you toward a specific formula. Writing out the ratio explicitly reduces errors because you can see exactly which values go where before you start calculating.

Another example: A store sells 84 items in a week. If this represents 60% of their monthly inventory movement, how many items do they move per month?

84 / x = 60 / 100 84 x 100 = 60 x x 8,400 = 60x x = 8,400 / 60 = **140 items per month**

Method 3: The Decimal Shortcut

The fastest mental-math technique is to convert the percentage to a decimal and multiply or divide directly. This method skips the extra x100 step because the decimal already encodes the percentage.

To find X% of a number: Convert X% to a decimal by dividing by 100, then multiply.

Percentage	Decimal	Mental Trick
50%	0.50	Divide by 2
25%	0.25	Divide by 4
10%	0.10	Divide by 10
1%	0.01	Divide by 100
20%	0.20	Divide by 5
15%	0.15	Find 10%, halve it, add together

Worked Example 1: A restaurant bill comes to $86.00 and you want to leave an 18% tip.

10% of $86 = $8.60
8% of $86 = $6.88
18% = $8.60 + $6.88 = $15.48

Or directly: 86 x 0.18 = $15.48.

Worked Example 2: You earn $3,200 per month and your rent is $960. What percentage of your income goes to rent?

960 / 3,200 = 0.30 = 30%

This is at the upper boundary of the commonly recommended 30% rule for housing costs.

Calculating Percentage Change

Percentage change measures how much a value has increased or decreased relative to its starting point. This is the formula behind stock returns, inflation figures, and year-over-year revenue comparisons.

Formula:

Percentage Change = ((New Value - Old Value) / Old Value) x 100

A positive result is a percentage increase. A negative result is a percentage decrease.

Worked Example (increase): A house was worth $320,000 three years ago and is now worth $388,000.

((388,000 - 320,000) / 320,000) x 100 = (68,000 / 320,000) x 100 = 0.2125 x 100 = **21.25% increase**

Worked Example (decrease): A company’s revenue fell from $5.4 million to $4.2 million.

((4,200,000 - 5,400,000) / 5,400,000) x 100 = (-1,200,000 / 5,400,000) x 100 = -0.2222 x 100 = **-22.2% (a 22.2% decrease)**

For quick percentage change calculations, the Percentage Calculator handles both increases and decreases automatically without any manual steps.

Adding and Subtracting a Percentage

A common real-world task is adding or removing a percentage from a number — applying a discount, adding tax, or calculating a pay raise.

To add X% to a number: Result = Original x (1 + X/100)

Example: Adding a 7% sales tax to a $45 item: 45 x 1.07 = **$48.15**

To subtract X% from a number: Result = Original x (1 - X/100)

Example: Taking 25% off a $120 jacket: 120 x 0.75 = **$90.00**

Reverse Percentage: Finding the Original Value

Sometimes you know the final number after a percentage was applied, and you need to work backwards to find the original.

If a percentage was added: Original = Final / (1 + X/100)

If a percentage was subtracted: Original = Final / (1 - X/100)

Worked Example: A laptop costs $663 after a 10% discount. What was the original price?

Original = 663 / (1 - 0.10) = 663 / 0.90 = **$736.67**

Note the common mistake: do not simply add 10% back on top of $663. That gives $729.30, which is wrong. You must divide by the decimal, not add the percentage back, because the 10% that was removed was 10% of the original price — not 10% of the discounted price.

Percentage in Personal Finance

Percentages drive almost every financial decision you make. A few applications worth knowing:

Salary negotiation: If you earn $65,000 and receive a 5% raise, that is 65,000 x 0.05 = $3,250 more per year, or about $271 extra per month before taxes. The Salary Calculator can break down exactly how much that raise is worth after tax deductions.

Credit card interest: A card charging 24.99% APR on a $3,000 balance costs approximately 3,000 x (0.2499 / 12) = $62.48 per month in interest. If your minimum payment is $75, only $12.52 chips away at the principal.

Investment growth: The Rule of 72 lets you estimate how long it takes for an investment to double. Divide 72 by the annual return percentage. At 8% annual growth: 72 / 8 = 9 years to double. At 6%: 72 / 6 = 12 years.

Inflation: At 3% annual inflation, purchasing power halves in about 72 / 3 = 24 years. The $150 grocery run today costs roughly $300 in 2050.

Common Percentage Mistakes to Avoid

Confusing percentage and percentage point. If an interest rate rises from 3% to 5%, it increased by 2 percentage points — but the interest rate itself increased by 2/3 x 100 = 66.7%. These are two different statements. Percentage points describe absolute differences between two percentage figures; percentage change describes the relative shift.

Adding percentages together incorrectly. A 50% increase followed by a 50% decrease does not return you to the original. Starting at 100: 100 x 1.50 = 150, then 150 x 0.50 = 75. You end up 25% below where you started. Each percentage applies to a different base.

Using the wrong base for percentage change. Always divide by the original value, not the new value. A stock that drops from $100 to $80 fell 20% — not 25% (which would be 20/80, using the wrong base).

Rounding too early. When chaining percentage calculations, carry extra decimal places until the final step. Early rounding compounds into a noticeable error on larger numbers.

Forgetting to convert to decimal. 15% is 0.15, not 15. Multiplying by 15 instead of 0.15 gives an answer 100 times too large.

Quick Reference: All Percentage Formulas

Calculation	Formula	Example
X% of Y	(X / 100) x Y	15% of 80 = 12
What % is X of Y?	(X / Y) x 100	12/80 x 100 = 15%
% increase	((new - old) / old) x 100	80 to 92 = 15% increase
% decrease	((old - new) / old) x 100	80 to 68 = 15% decrease
Add X% to number	Original x (1 + X/100)	80 + 15% = 92
Subtract X% from number	Original x (1 - X/100)	80 - 15% = 68
Original before % added	Final / (1 + X/100)	92 / 1.15 = 80
Original before % removed	Final / (1 - X/100)	68 / 0.85 = 80

Bookmark this table or use the Percentage Calculator for instant results on any of these.

Percentage Calculator — instant results for all five percentage types
Salary Calculator — see how a percentage pay raise translates to take-home pay
Compound Interest Calculator — compound interest as a percentage of principal over time
Discount Calculator — final price after single or stacked discounts

Compound Interest Explained shows how percentage growth compounds over time and why it matters for savings and debt.
How GCF and LCM Work covers another core math concept that pairs naturally with fractions and ratios.

Sources

Khan Academy. “Intro to Percentages.” https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates
Math is Fun. “Percentage.” https://www.mathsisfun.com/percentage.html
National Council of Teachers of Mathematics (NCTM). “Illuminations: Percent Activities.” https://illuminations.nctm.org/

Frequently Asked Questions

What is the basic percentage formula? +

Percentage = (Part / Whole) × 100. Divide the part by the whole, then multiply by 100 to convert the decimal to a percentage.

How do I find what percentage one number is of another? +

Divide the first number by the second, then multiply by 100. For example, 45 out of 60 is (45 / 60) × 100 = 75%.

How do I calculate a percentage of a number? +

Multiply the number by the percentage divided by 100. For example, 20% of 150 is (20 / 100) × 150 = 30.

What is the formula for percentage change? +

Percentage change = ((New Value − Old Value) / Old Value) × 100. A positive result means an increase; a negative result means a decrease.

How do I add a percentage to a number? +

Multiply the number by (1 + percentage/100). To add 15% to 200: 200 × 1.15 = 230. To subtract 15%: 200 × 0.85 = 170.