Skip to content

Percentage Calculator

Calculate percentages instantly. Find X% of Y, percentage change, percentage difference, reverse percentages, and more with step-by-step breakdowns.

Percentage Worksheet
%

Something wrong or missing? Tell us — we read every report and fix issues fast.

How to Calculate Percentages

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." Percentages are used everywhere — discounts, tax rates, test scores, statistics, and financial calculations.

Finding X% of a Number

To find X% of Y, convert the percentage to a decimal by dividing by 100, then multiply by the number:

Formula: Result = (X / 100) × Y

Example: 15% of 300 = (15/100) × 300 = 0.15 × 300 = 45

Finding What Percent X is of Y

To determine what percentage one number represents of another, divide the part by the whole and multiply by 100:

Formula: Percentage = (Part / Total) × 100

Example: What percent is 75 of 250? (75/250) × 100 = 30%

Calculating Percentage Change

Percentage change measures how much a value has increased or decreased relative to its original value:

Formula: % Change = ((New - Old) / |Old|) × 100

Example: A price went from $80 to $100. Change = ((100-80)/80) × 100 = 25% increase

Finding the Whole from a Part

When you know a part and what percentage it represents, you can find the whole:

Formula: Whole = Part / (Percentage / 100)

Example: 36 is 15% of what? 36 / 0.15 = 240

Percentage Difference

Percentage difference compares two values symmetrically — neither is treated as the "original." It uses the average of both values as the base:

Formula: % Difference = |A - B| / ((|A| + |B|) / 2) × 100

Example: Values 75 and 90. Difference = |75-90| / ((75+90)/2) × 100 = 15/82.5 × 100 = 18.18%

Adding a Percentage

To increase a value by a percentage:

Formula: Result = Value × (1 + Percentage / 100)

Example: 250 + 12% = 250 × 1.12 = 280

Reverse Percentage

When you know the final amount after a percentage was added, find the original:

Formula: Original = Result / (1 + Percentage / 100)

Example: A price is $336 after 12% markup. Original = 336 / 1.12 = $300

Percentage Examples

  • 20% of 500 = (20/100) × 500 = 100
  • 45 is what % of 180? (45/180) × 100 = 25%
  • Change from 200 to 250: ((250-200)/200) × 100 = 25% increase
  • 36 is 15% of what? 36 / 0.15 = 240
  • % Difference between 75 and 90: 18.18%
  • 250 + 12%: 280
  • $336 after 12% added, original: $300

When to Use Each Calculator Mode

  • X% of Y: Discounts, tax calculations, tips
  • X is what %: Test scores, proportions, market share
  • % Change: Price changes, growth rates, performance metrics
  • Find Whole: "I saved $36 which was 15% off — what was the original price?"
  • % Difference: Comparing two measurements where neither is the "baseline"
  • Add %: Markup pricing, tax-inclusive totals
  • Reverse %: Finding pre-tax price, removing markup, reversing compound interest

Mental Math Shortcuts

  • 10%: Move the decimal one place left. 10% of $85 = $8.50
  • 5%: Find 10%, then halve it. 5% of $85 = $4.25
  • 20%: Find 10%, then double it. 20% of $85 = $17.00
  • 1%: Move the decimal two places left. 1% of $85 = $0.85
  • Any %: Combine the above. 15% = 10% + 5%. 7% = 5% + 1% + 1%

Handy trick: X% of Y equals Y% of X. So 8% of 50 = 50% of 8 = 4. Use whichever direction is easier to compute.

Percent vs Percentage Points

These terms are often confused but mean different things:

  • Percentage points: The absolute difference between two percentages. Going from 5% to 7% is a 2 percentage point increase
  • Percent change: The relative change. Going from 5% to 7% is a 40% increase (2/5 × 100)

This distinction matters in news, finance, and statistics. "Unemployment rose 2 percentage points" (5% to 7%) is very different from "unemployment rose 2 percent" (5% to 5.1%).

Related Calculators

Fraction Calculator — Step-by-Step Solver Add, subtract, multiply, divide, compare, and solve fractions with full step-by-step work. Chain up to 9 fractions, mixed numbers, simplify, and decimal conversions. Equivalent Fractions Calculator — First 100 Results Find equivalent fractions for any proper, improper, or mixed fraction. Shows the first 100 equivalent fractions instantly. Average Calculator — Mean, Median, Mode, Range, SD Calculate mean (sum divided by count), median, mode, range, and standard deviation with step-by-step work. Includes weighted average mode and a full statistics measures reference. Ratio Calculator — Simplify, Solve, Scale, Compare Simplify ratios, solve proportions, scale, split, compare, and generate equivalent ratio tables — all in one tool. Exponent Calculator — Powers, Roots, Logs, e^x Calculate powers, roots, exponentials, and logarithms. Solve xⁿ, ⁿ√x, eˣ, and log expressions with full work shown. Square Root Calculator — Simplify Radicals + Steps Calculate square roots, cube roots, and nth roots. Simplify radicals with prime factorization steps and the Babylonian method walkthrough.

Frequently Asked Questions

What is 0.01% of 2000?

0.01% of 2000 is 0.2. To find any percentage of a number, divide the percentage by 100 and multiply by the number: 0.01 / 100 = 0.0001, and 0.0001 × 2000 = 0.2. The same rule gives 25% of 200 = 0.25 × 200 = 50. Watch the decimal point, since 0.01% is one hundredth of one percent.

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

Divide the part by the whole and multiply by 100. For example, 50 out of 200 is (50 / 200) × 100 = 25%. If the part is larger than the whole, the answer is above 100%, which is valid: 150 is 300% of 50. Always put the reference value, the whole, in the denominator.

How do you calculate percentage change?

Percentage change = (new value - old value) / old value × 100. A positive result is an increase and a negative result is a decrease. Sales growing from 50 to 150 is a 200% increase. Percentage difference is a different measure: it compares two values symmetrically, dividing the gap by their average instead of by the old value.

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

Divide the final amount by 1 plus the percentage as a decimal. If $112 is the price after a 12% markup, the original price is 112 / 1.12 = $100. Subtracting 12% of $112 instead gives $98.56, which is wrong, because the 12% was taken of the original price, not the final one.

How do you calculate a discount percentage?

Discount percentage = (original price - sale price) / original price × 100. An item marked down from $80 to $60 has a discount of (80 - 60) / 80 × 100 = 25%. Always divide by the original price, not the sale price; dividing by $60 would wrongly suggest a 33% discount on the same markdown.