What is the percentage formula?

The core percentage formula is: P × V1 = V2, where P is the percentage (as a decimal), V1 is the base value, and V2 is the result. Rearranged: Percentage = (V2 / V1) × 100. Example: 15% of 80 = 0.15 × 80 = 12. Reverse: 12 is what percent of 80? (12/80) × 100 = 15%.

How do you calculate percentage change?

Percentage change = ((New Value - Old Value) / |Old Value|) × 100. A positive result is an increase; negative is a decrease. Example: price goes from $50 to $65. Change = ((65-50)/50) × 100 = 30% increase. From $65 back to $50: ((50-65)/65) × 100 = -23.08% decrease. Note the asymmetry: a 30% increase followed by a 23.08% decrease returns to the original value.

How do you find the original value before a percentage increase?

Divide the final value by (1 + percentage/100). Example: a price after a 20% increase is $120. Original = 120 / 1.20 = $100. For a decrease: divide by (1 - percentage/100). A price after a 25% decrease is $75. Original = 75 / 0.75 = $100. This is the reverse percentage calculation.

How do you calculate percentage of a total?

Percentage of total = (Part / Total) × 100. Example: a student scores 42 out of 60. Percentage = (42/60) × 100 = 70%. If the total is made of several parts, each part's percentage is its value divided by the sum of all parts, multiplied by 100. All parts percentages must sum to 100%.

Percentage Calculator 2026 - Percent of a Number, Change, Difference & More

What is P% of X?

Find a percentage of any number. Example: what is 15% of 200?

What is % of ?

Result

X is What % of Y?

Find what percentage one number is of another. Example: 30 is what % of 120?

is what % of ?

Result

X is P% of What?

Find the base number when you know a value and the percentage it represents. Example: 45 is 30% of what?

is % of what?

Result

Percentage Change

Find the percentage increase or decrease from one value to another. Example: from 80 to 100 is a 25% increase.

From to

Percentage Change

Percentage Difference

Compare two values without a defined starting point, using their average as the reference. Example: difference between 10 and 14.

Value 1 Value 2

Percentage Difference

Increase / Decrease by %

Find the result of increasing or decreasing a number by a percentage. Example: 250 increased by 20% = 300.

by %

Result

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." The symbol % indicates that the number is scaled out of 100.

Percentages, decimals, and fractions are three equivalent ways to represent the same ratio:

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/8	0.125	12.5%
1/3	0.333…	33.33…%

Converting a percentage to a decimal: divide by 100 (or move the decimal point two places left). Converting a decimal to a percentage: multiply by 100. The core percentage formula is P × V1 = V2, where P is the decimal form of the percentage, V1 is the base, and V2 is the result.

The Three Core Percentage Questions

Any percentage problem reduces to one of three questions, which correspond to the first three calculators above:

1. What is P% of X?

Result = (P / 100) × X Example: what is 18% of 250? Result = 0.18 × 250 = 45

2. X is what % of Y?

Percentage = (X / Y) × 100 Example: 45 is what % of 250? Percentage = (45 / 250) × 100 = 18%

3. X is P% of what?

Base = X / (P / 100) = (X × 100) / P Example: 45 is 18% of what? Base = 45 / 0.18 = 250

These three formulas are rearrangements of the same equation. If you know any two of the three values (percentage, base, result), you can always solve for the third.

Percentage Change vs Percentage Difference

These two terms are frequently confused. They measure different things and use different formulas.

Percentage Change

Percentage change measures how much a value has changed relative to a specific starting value. It requires a clear "before" and "after." The sign tells you the direction: positive means an increase, negative means a decrease.

% Change = ((New - Old) / |Old|) × 100 Example: price rises from $50 to $65 % Change = ((65 - 50) / 50) × 100 = +30% (increase) Price falls from $65 back to $50: % Change = ((50 - 65) / 65) × 100 = -23.08% (decrease)

Notice the asymmetry: a 30% increase followed by a 23.08% decrease returns to the original. A 30% increase is not reversed by a 30% decrease. This surprises many people and is the source of common errors in financial reporting.

Percentage Difference

Percentage difference compares two values that have no defined order or direction. It uses the average of the two values as the reference instead of one specific starting value.

% Difference = |V1 - V2| / ((V1 + V2) / 2) × 100 Example: comparing $50 and $65 % Difference = |50 - 65| / ((50+65)/2) × 100 = 15/57.5 × 100 = 26.09%

Use percentage change when there is a clear baseline (last year's revenue, yesterday's price, a target value). Use percentage difference when comparing two values of equal standing, such as two lab measurements, two competing products' prices, or two survey results.

⚠️

Never average percentages by adding them and dividing by the number of percentages. If one item is 50% of the total and another is 30% of the total, the average percentage contribution is not simply (50+30)/2 = 40%. You must weight by the actual values. This mistake appears frequently in sports statistics, economic reporting, and business presentations.

Percentage Increase and Decrease

To increase or decrease a value by a percentage, convert the percentage to a decimal multiplier and apply it to the original value:

Increased value = Original × (1 + P/100) Example: 500 increased by 15%: 500 × 1.15 = 575 Decreased value = Original × (1 - P/100) Example: 500 decreased by 15%: 500 × 0.85 = 425

Reverse Percentage: Finding the Original

If a value has already been increased or decreased and you want to recover the original, divide by the multiplier:

Original = Final / (1 + P/100) - after an increase Example: final price $138 after 15% increase: 138 / 1.15 = $120 Original = Final / (1 - P/100) - after a decrease Example: sale price $85 after 15% off: 85 / 0.85 = $100

💡

A common error: if a shirt costs $85 after a 15% discount, people often calculate the original as $85 + 15% of $85 = $97.75. That is wrong. The correct method is $85 / 0.85 = $100. The 15% was taken off the original price, not off the sale price.

Real-World Percentage Applications

Sales Tax

A $120 item with 8.5% sales tax: tax amount = 0.085 × 120 = $10.20. Total = $130.20. To find the pre-tax price from the total: 130.20 / 1.085 = $120.00.

Discounts

A $200 item at 30% off: discount = 0.30 × 200 = $60. Sale price = $140. Sequential discounts of 20% and 10% are not equal to a single 30% discount. $200 × 0.80 × 0.90 = $144, which is a 28% total discount - not 30%.

Tip Calculation

A quick 20% tip on a $85 bill: 10% is $8.50, so 20% is $17.00. For 15%: take 10% ($8.50) and add half ($4.25) = $12.75.

Grade Weighting

A student's grade is 60% exams, 25% homework, 15% participation. Scores: exam 80, homework 90, participation 95. Weighted grade = 0.60×80 + 0.25×90 + 0.15×95 = 48 + 22.5 + 14.25 = 84.75.

Interest and APR

Monthly interest rate from annual: 6% APR / 12 = 0.5% per month. On a $5,000 balance: 0.005 × 5,000 = $25 monthly interest. Compound interest over 12 months at 0.5%/month: 5,000 × (1.005)^12 = $5,308.39, implying an effective annual rate of 6.168% (slightly above the stated 6% APR due to compounding).

Percentage Points vs Percentages

If the unemployment rate rises from 4% to 6%, it has risen by 2 percentage points, but by 50% relative to the original rate. These are different things. A change in percentage points is the arithmetic difference; a percentage change uses the original as the base. Both statements are technically correct, which is why headlines often use whichever sounds more dramatic.

Frequently Asked Questions

How do I calculate a percentage of a number?

Multiply the number by the percentage divided by 100. Formula: Result = (Percentage / 100) × Number. Example: 35% of 400 = (35/100) × 400 = 0.35 × 400 = 140. Mental math shortcut: for 10%, move the decimal point one place left. For 5%, halve that. For 15%, add 10% and 5%. For 20%, double the 10% value.

What is the difference between percentage and percentage points?

A percentage point is the arithmetic difference between two percentages. If an interest rate goes from 3% to 5%, it increased by 2 percentage points. But the percentage change in the rate is ((5-3)/3) × 100 = 66.7%. The distinction matters in finance, economics, and polling. When someone says rates rose "1%," they almost always mean 1 percentage point (e.g., from 4% to 5%), not a 1% relative increase (which would bring 4% to only 4.04%).

How do you reverse a percentage increase to find the original price?

Divide the final price by (1 + percentage/100). If a price after a 25% increase is $250, the original = 250 / 1.25 = $200. For a decrease: divide by (1 - percentage/100). If a sale price after a 25% discount is $150, the original = 150 / 0.75 = $200. Do not add the percentage back to the discounted price - that gives the wrong answer because the percentage was applied to the original, not the sale price.

Can a percentage be over 100%?

Yes. A percentage greater than 100% means the result exceeds the original base. If revenue triples, that is a 200% increase (from 100% to 300%). If you save 110% of your income, you are saving more than you earn (by drawing from savings or other sources). Percentages over 100% are common in growth rates, returns, and markup calculations. A 200% markup on a $10 cost means the selling price is $10 + 2×$10 = $30.

Why is a 50% increase followed by a 50% decrease not back to the original?

Because the 50% decrease applies to the new (higher) value, not the original. Starting at $100: after a 50% increase → $150. A 50% decrease on $150 → $75. The result is 25% below the starting value, not back to $100. To reverse a 50% increase, you need a 33.33% decrease (from $150 to $100: (150-100)/150 = 33.33%). This asymmetry in percentage changes is why compound returns are calculated geometrically, not arithmetically.