Percentage Calculator

This percentage calculator finds the percentage of a number, works out what percent one value is of another, and calculates percentage increase or decrease between two numbers. Enter any two known values and the tool returns the third instantly, whether you need X percent of Y, the percentage one number represents of another, or the result of a value changing by a given percent.

The calculator helps students converting marks into grade percentages, shoppers checking discounts and percent-off deals, and professionals working out raises, taxes, tips, profit margins, and data comparisons. It handles whole numbers and decimals, and each mode works in reverse, so you can solve for any missing value in the part, whole, and percentage relationship.

Below the tool, you will find the percentage formula in its three forms, worked examples for every calculation type, quick methods for finding percentages without a calculator, and answers to the most common percentage questions.

How to Use the Percentage Calculator

The calculator has four modes, and each one answers a different percentage question. Pick the mode that matches the value you are missing, enter the two numbers you know, and the calculator fills in the third automatically.

Mode 1: What is X% of Y?

Use this mode to find a percentage of a number. Enter the percentage in the first field and the number in the second. For example, to check a 20% discount on a $150 jacket, enter 20 and 150. The calculator returns 30, so you save $30 and pay $120.

Mode 2: X is what percent of Y?

Use this mode to find what percentage one number represents of another. Enter the part in the first field and the whole in the second. For example, if you scored 45 out of 60 on a test, enter 45 and 60. The calculator returns 75%, which is your test score as a percentage.

Mode 3: X is Y% of what?

Use this mode to find the whole when you only know a part and its percentage. Enter the known value and the percentage it represents. For example, if a $30 deposit covers 15% of a total bill, enter 30 and 15. The calculator returns 200, so the full bill is $200.

Mode 4: Percentage increase or decrease

Use this mode to raise or lower a number by a percent. Enter the starting value, choose increase or decrease, and enter the percentage. For example, if a $40,000 salary rises by 6%, enter 40,000 and 6 with increase selected. The calculator returns $42,400.

Input tips

• The calculator accepts whole numbers and decimals, so you can enter values like 7.5 or 0.25 in any field.
• Enter percentages as plain numbers without the % symbol. Type 20, not 20%.
• Each mode also works in reverse. If you know the result but not one of the inputs, enter the values you have and the calculator solves for the missing one.
• In the increase and decrease mode, a negative result simply means the value fell rather than rose, which is useful when comparing prices or tracking changes over time.

Percentage Formula and How It Works

A percentage expresses a number as a fraction of 100. The word comes from "per hundred," so 25% means 25 out of every 100, which is the same as the decimal 0.25 or the fraction 1/4. Every percentage problem involves three values: the part, the whole, and the percentage itself. If you know any two, you can always find the third.

The core percentage formula is:

Percentage = (Part / Whole) × 100

Rearranging that same equation gives you the other two forms, depending on which value is missing:

Which formula do you need?

• You know the part and the whole, and want the percentage: use the first formula. Scoring 45 out of 60 gives (45 / 60) × 100 = 75%.
• You know the percentage and the whole, and want the part: use the second formula. Finding 20% of 150 gives (20 × 150) / 100 = 30.
• You know the part and the percentage, and want the whole: use the third formula. If 30 is 15% of a number, then (30 × 100) / 15 = 200.

These three forms are the same equation solved for a different unknown, which is exactly what the calculator does behind each mode.

Converting between percentages, decimals, and fractions

• Percentage to decimal: divide by 100, or move the decimal point two places left. 75% becomes 0.75.
• Decimal to percentage: multiply by 100, or move the decimal point two places right. 0.4 becomes 40%.
• Fraction to percentage: divide the numerator by the denominator, then multiply by 100. 3/8 becomes 0.375, which is 37.5%.
• Percentage to fraction: write the percentage over 100 and simplify. 40% becomes 40/100, which simplifies to 2/5.

Working in decimals is often faster for mental math. Finding 15% of 80 is the same as 0.15 × 80, which equals 12.

How to Calculate Percentage Increase and Decrease

Percentage change measures how much a value has grown or shrunk relative to where it started. The formula is:

Percentage Change = ((New Value − Original Value) / Original Value) × 100

The original value always sits in the denominator, because the change is measured against the starting point. A positive result is a percentage increase, and a negative result is a percentage decrease. For example, if rent rises from $1,200 to $1,320, the change is ((1,320 − 1,200) / 1,200) × 100 = 10%, a 10% increase. If a laptop drops from $800 to $680, the change is ((680 − 800) / 800) × 100 = −15%, a 15% decrease.

Applying a percentage change to a number

When you already know the percentage and want the new value, skip the subtraction and use a multiplier:

• To increase a number by p%, multiply it by (1 + p/100). A $40,000 salary with a 6% raise becomes 40,000 × 1.06 = $42,400.
• To decrease a number by p%, multiply it by (1 − p/100). A $150 jacket with 20% off becomes 150 × 0.80 = $120.

The multiplier method also works in reverse. If a discounted price of $120 reflects 20% off, divide by 0.80 to recover the original $150. This is the reliable way to find an original price before a discount or a value before tax.

Percentage change vs percentage difference

These two terms are often mixed up, but they answer different questions:

• Percentage change compares a new value against an original value, so direction and starting point matter. Use it for prices over time, salary raises, and growth rates.
• Percentage difference compares two values with no before and after, so it uses their average as the base: (|A − B| / ((A + B) / 2)) × 100. Use it to compare two prices from different stores or two measurements taken at the same time.

Comparing 10 and 6 shows why the results differ. As a change from 10 down to 6, that is a 40% decrease. As a percentage difference, it is (4 / 8) × 100 = 50%.

Why a 50% drop and a 50% rise do not cancel out

Percentage changes are not symmetric, because each change is measured from a different base. Take $100:

• A 50% decrease brings it to $50.
• A 50% increase from $50 brings it to $75, not back to $100.

The decrease was measured from 100, but the increase was measured from the smaller base of 50. To get back to $100 from $50, you need a 100% increase. This matters in real decisions: a stock that falls 50% must double to recover, and a price that rises 25% only needs a 20% cut to return to where it started.

Percentage Examples

The worked examples below cover all four calculator modes. Each one follows the same pattern: the scenario, the inputs, the formula applied, and the result, so you can match any real problem to the mode that solves it.

Example 1: Finding a percentage of a number

Scenario: A $150 jacket is on sale at 20% off. How much is the discount?

Inputs: percentage = 20, whole = 150

Formula: Part = (Percentage × Whole) / 100

Calculation: (20 × 150) / 100 = 30

Result: The discount is $30, so the sale price is $120.

Example 2: Finding what percent one number is of another

Scenario: You scored 45 out of 60 marks on an exam. What is your score as a percentage?

Inputs: part = 45, whole = 60

Formula: Percentage = (Part / Whole) × 100

Calculation: (45 / 60) × 100 = 75

Result: Your exam score is 75%.

Example 3: Finding the whole from a part (reverse percentage)

Scenario: A $30 booking deposit covers 15% of the total cost. What is the full amount?

Inputs: part = 30, percentage = 15

Formula: Whole = (Part × 100) / Percentage

Calculation: (30 × 100) / 15 = 200

Result: The total cost is $200.

Example 4: Percentage increase

Scenario: A salary rises from $40,000 to $46,000. What is the percentage increase?

Inputs: original value = 40,000, new value = 46,000

Formula: Percentage Change = ((New − Original) / Original) × 100

Calculation: ((46,000 − 40,000) / 40,000) × 100 = 15

Result: The salary increased by 15%.

Quick reference

How to Calculate Percentages Without a Calculator

Most everyday percentages break down into a few easy building blocks. Master 10% and 1%, and you can work out almost anything in your head.

Start with 10% and 1%

• To find 10% of any number, move the decimal point one place to the left. 10% of 340 is 34. 10% of 68 is 6.8.
• To find 1%, move the decimal point two places to the left. 1% of 340 is 3.4.

Build other percentages from those blocks. For 30%, find 10% and multiply by three: 10% of 340 is 34, so 30% is 102. For 12%, add 10% and two lots of 1%: 34 + 3.4 + 3.4 = 40.8.

Memorize the common values

• 50% is half. 50% of 86 is 43.
• 25% is a quarter, or half of a half. 25% of 120 is 30.
• 5% is half of 10%. 5% of 340 is 17.
• 20% is 10% doubled. 20% of 45 is 9.
• 75% is three quarters, or 50% plus 25%.

The reversal trick

X% of Y always equals Y% of X, so flip the numbers whenever the reversed version is easier. 4% of 75 looks awkward, but 75% of 4 is clearly 3. Likewise, 8% of 50 becomes 50% of 8, which is 4.

Tips and discounts on the spot

For a 15% tip, take 10% of the bill and add half of that again. On a $60 bill, 10% is $6, half is $3, so the tip is $9.

For a 20% tip, take 10% and double it.

For discounts, work out what you pay rather than what you save. 30% off means you pay 70%, so a $50 item at 30% off costs 0.7 × 50 = $35 in one step.

Percentage vs Percentage Points

A percentage point is the simple difference between two percentages. If a value moves from 10% to 12%, it has risen by 2 percentage points, because 12 − 10 = 2.

The percentage change between those same two values is a different number. Measured relative to the starting point, a move from 10% to 12% is ((12 − 10) / 10) × 100 = 20%, a 20% increase. Both statements describe the same shift, but they answer different questions: percentage points measure the absolute gap, while percentage change measures the relative growth.

The distinction matters most where percentages themselves are the values being compared:

• Interest rates. A mortgage rate rising from 4% to 5% is a 1 percentage point increase, but a 25% increase in the rate. On a large loan, describing that shift as "1%" understates what it does to a monthly payment.
• Polling and elections. A candidate moving from 40% to 44% support has gained 4 percentage points. Reporting it as a 10% gain is also true but reads as a much bigger swing.
• News and statistics. Unemployment falling from 8% to 6% is a drop of 2 percentage points, yet a 25% relative decline. Headlines often pick whichever framing sounds more dramatic.

When you read a percentage comparison, check which base is being used. If the figure describes a change between two percentages, the honest unit is usually percentage points.

Frequently Asked Questions

How do you calculate a percentage of a number?

Divide the percentage by 100, then multiply by the number. To find 20% of 150, calculate 20 / 100 = 0.2, then 0.2 × 150 = 30. A faster route is the single formula (Percentage × Number) / 100, which gives the same result in one step.

How do you find what percent one number is of another?

Divide the first number by the second, then multiply by 100. To find what percent 45 is of 60, calculate 45 / 60 = 0.75, then 0.75 × 100 = 75%. The first number is the part, the second is the whole, and the result is the percentage.

What is the formula for percentage?

The percentage formula is Percentage = (Part / Whole) × 100. Rearranged, it also gives Part = (Percentage × Whole) / 100 and Whole = (Part × 100) / Percentage. All three are the same equation solved for a different unknown, so knowing any two values lets you find the third.

How do you calculate percentage increase?

Subtract the original value from the new value, divide by the original value, then multiply by 100. A salary rising from 40,000 to 46,000 gives ((46,000 − 40,000) / 40,000) × 100 = 15%, a 15% increase. A negative result means the value decreased instead.

How do you calculate a percentage backwards (reverse percentage)?

Multiply the known part by 100, then divide by the percentage it represents. If 30 is 15% of a number, calculate (30 × 100) / 15 = 200. For prices after a discount, divide by the multiplier instead: a $120 price after 20% off is 120 / 0.80 = $150 originally.

How do you convert a fraction or decimal to a percentage?

To convert a decimal, multiply by 100: 0.75 becomes 75%. To convert a fraction, divide the numerator by the denominator first, then multiply by 100: 3/8 = 0.375, which is 37.5%. To go the other way, divide the percentage by 100.

How do you calculate average percentage?

If each percentage comes from the same-sized group, add the percentages and divide by how many there are. If the groups differ in size, convert each percentage to its actual value, add those values, divide by the combined total, then multiply by 100. This weighted method gives the accurate average.

How do you calculate percentage of marks?

Divide the marks you scored by the total marks available, then multiply by 100. Scoring 45 out of 60 gives (45 / 60) × 100 = 75%. For multiple subjects, add all marks obtained, divide by the combined maximum marks, then multiply by 100.

What is the difference between percentage and percentile?

A percentage measures a part of a whole, such as scoring 75% on a test. A percentile ranks a value against a group: scoring in the 75th percentile means you performed better than 75% of test takers. A percentage describes your result, a percentile describes your position.

Can a percentage be more than 100?

Yes. A percentage over 100 means the part is larger than the reference value. If sales grow from 200 to 500, the new figure is 250% of the original, and the increase is 150%. Percentages only stay at or below 100 when describing a portion of a fixed whole.