Percentage Calculator

X% of Y = (X/100) × Y · % change = ((Y−X)/X) × 100

Ratio & Percent

How to Use This Tool

Percentage calculator

Enter two numbers to calculate percentages, percentage change, or percentage difference. This tool handles the three most common percentage questions: “what is X% of Y,” “X is what percent of Y,” and “what is the percentage change from X to Y.” Below is a breakdown of the formulas, worked examples, and a reference table for quick lookups.

Three types of percentage calculations

What is X% of Y?

Multiply Y by X/100. What is 15% of 200? 200 x 0.15 = 30. This is the calculation you use for tips, discounts, and tax.

X is what percent of Y?

Divide X by Y, then multiply by 100. 45 is what percent of 180? (45 / 180) x 100 = 25%. This tells you what fraction of the whole a number represents.

Percentage change from X to Y

Subtract X from Y, divide by X, then multiply by 100. The percentage change from 80 to 100 is ((100 – 80) / 80) x 100 = 25% increase. If Y is smaller than X, the result is negative, meaning a decrease.

Percentage formulas

Calculation Formula Example
X% of Y Y x (X / 100) 20% of 150 = 150 x 0.20 = 30
X is what % of Y (X / Y) x 100 30 is what % of 150 = (30/150) x 100 = 20%
% change ((New – Old) / Old) x 100 (120 – 100) / 100 x 100 = 20% increase
% difference (|A – B| / ((A + B) / 2)) x 100 |80 – 120| / 100 x 100 = 40%
Add X% to Y Y x (1 + X/100) Add 8% tax to $50 = 50 x 1.08 = $54
Subtract X% from Y Y x (1 – X/100) 25% off $80 = 80 x 0.75 = $60

Common percentages reference

This table shows frequently used percentages and their decimal and fraction equivalents.

Percentage Decimal Fraction
1% 0.01 1/100
5% 0.05 1/20
10% 0.10 1/10
12.5% 0.125 1/8
15% 0.15 3/20
20% 0.20 1/5
25% 0.25 1/4
33.3% 0.333 1/3
50% 0.50 1/2
66.7% 0.667 2/3
75% 0.75 3/4
100% 1.00 1/1

When you need percentage calculations

Shopping and discounts

A shirt costs $60 and is marked 30% off. The discount is $60 x 0.30 = $18, so the sale price is $42. If the sales tax rate is 8.25%, the tax on $42 is $42 x 0.0825 = $3.47, making the total $45.47.

Tips

To tip 20% on a $75 dinner bill: $75 x 0.20 = $15. A quick shortcut for 15%: find 10% ($7.50), then add half of that ($3.75) to get $11.25. For 20%, just double the 10% figure.

Grade calculations

You scored 42 out of 50 on a test. Your percentage is (42 / 50) x 100 = 84%. If the test counts for 30% of your final grade, it contributes 84 x 0.30 = 25.2 points toward your final score out of 100.

Finance and investing

A stock goes from $40 to $52. The percentage gain is ((52 – 40) / 40) x 100 = 30%. If it then drops from $52 to $40, the percentage loss is ((40 – 52) / 52) x 100 = -23.1%. The same dollar move produces different percentages depending on the starting value.

Percentage change compared to percentage difference

Percentage change measures how much a single value has moved from its starting point. It has a clear direction: the old value is the base. “Sales went from 200 to 250” is a 25% increase because the base is 200.

Percentage difference compares two values that do not have a before-and-after relationship. “City A has 300,000 people, City B has 250,000” gives a percentage difference of (50,000 / 275,000) x 100 = 18.2%, using the average of the two values as the base. Neither city is the “old” or “new” value, so percentage change would not apply.

Tips for working with percentages

  • Percentages are reversible. 8% of 50 equals 50% of 8. Both give 4. If one direction is easier to calculate mentally, use it.
  • To convert a percentage to a decimal, move the decimal point two places left. 45% becomes 0.45. To go back, move it two places right.
  • Successive percentage changes do not simply add up. A 50% increase followed by a 50% decrease does not bring you back to the start. 100 becomes 150, then 150 x 0.50 = 75. You end up 25% below where you started.
  • When comparing percentage changes, pay attention to the base. A 10% raise on a $50,000 salary ($5,000) is very different from a 10% raise on a $100,000 salary ($10,000), even though the percentage is the same.

Mental math shortcuts for percentages

To find 10% of any number, move the decimal point one place left. 10% of 85 is 8.5. From there you can build other percentages: 5% is half of 10%, 20% is double, 1% is one-tenth.

To find 25%, divide by 4. 25% of 160 is 40. To find 33%, divide by 3. 33% of 90 is 30. These shortcuts work because 25% = 1/4 and 33.3% = 1/3.

For tipping, the 10% shortcut is the fastest method. On a $67.40 bill: 10% is $6.74, so 15% is about $10.11 and 20% is about $13.48.

Frequently asked questions

How do I calculate a percentage of a number?

Multiply the number by the percentage expressed as a decimal. 35% of 200 = 200 x 0.35 = 70.

What is percentage change?

It measures how much a value has increased or decreased relative to its original amount. The formula is ((new – old) / old) x 100. A positive result means an increase, negative means a decrease.

How do I find the original price before a discount?

Divide the sale price by (1 – discount rate). A $60 item after 25% off was originally $60 / 0.75 = $80.

Can a percentage be more than 100?

Yes. A 200% increase means the value tripled. If sales went from 50 to 150, the increase is ((150 – 50) / 50) x 100 = 200%.

What is the difference between percent and percentage points?

If an interest rate goes from 3% to 5%, it increased by 2 percentage points. The percentage change is ((5 – 3) / 3) x 100 = 66.7%. Percentage points measure the absolute difference between two rates. Percentage change measures the relative difference.

How do I calculate compound percentage growth?

Multiply the starting value by (1 + rate) raised to the number of periods. $1,000 growing at 5% annually for 3 years: $1,000 x 1.05 x 1.05 x 1.05 = $1,157.63. You cannot just multiply 5% x 3 = 15% because each year the base grows.

Measurement guides

Formula & Explanation

Percentages are ratios expressed as a fraction of 100. The word 'percent' comes from Latin 'per centum', meaning 'by the hundred'.