Percentage Calculator

Calculate percentages, increases, and decreases with our simple calculator. Choose the calculation type to get started.

Calculation Type

Percentage (%)

Tips:

To calculate a discount, find X% of the original price, then subtract from the original price
For tax calculations, find the tax percentage of the base amount, then add to the base amount
When calculating percentage increase/decrease, remember the formula: ((New - Original) / Original) × 100
Percentages can be greater than 100% when the comparison value exceeds the base value

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. It's often denoted using the percent sign, "%". Percentages are used to express how large or small one quantity is relative to another quantity, making them invaluable for comparisons across various contexts.

Basic Percentage Concepts

The word "percentage" comes from the Latin "per centum," meaning "by the hundred." When we say "25%," we're essentially saying "25 out of 100" or "25/100," which can be simplified to "1/4" or "0.25" in decimal form.

Key conversions:

To convert a percentage to a decimal: divide by 100 (or move the decimal point two places to the left)
To convert a decimal to a percentage: multiply by 100 (or move the decimal point two places to the right)
To convert a fraction to a percentage: divide the numerator by the denominator, then multiply by 100

Basic Percentage Formulas

Finding X% of a number:

Result = (Percentage / 100) × Value

Example: 20% of 150 = (20 / 100) × 150 = 0.2 × 150 = 30

Finding what percentage one number is of another:

Percentage = (Value / Total) × 100

Example: 25 is what percentage of 200? (25 / 200) × 100 = 0.125 × 100 = 12.5%

Finding the percentage increase or decrease:

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

Example: From 100 to 125 = ((125 - 100) / 100) × 100 = (25 / 100) × 100 = 25% increase

Example: From 80 to 60 = ((60 - 80) / 80) × 100 = (-20 / 80) × 100 = -25% (a 25% decrease)

The Historical Development of Percentages

The concept of percentages dates back thousands of years. Ancient Romans used fractions based on 100, similar to our modern percentage system. However, the percent sign (%) as we know it today didn't appear until the 17th century.

Initially, percentages were primarily used in commerce for calculating interest and taxes. The Italian mathematician Fibonacci helped popularize the decimal system in Europe through his book "Liber Abaci" (1202), which made percentage calculations more accessible.

By the 18th and 19th centuries, percentages became a standard way to express proportions in finance, statistics, science, and everyday life, largely due to their intuitive nature and ease of comparison.

Practical Applications of Percentages

Finance and Business

Interest rates on loans and investments
Discount calculations for sales
Tax calculations (income tax, sales tax, VAT)
Profit margins and markups
Investment returns and growth rates
Inflation rates
Performance metrics and KPIs

Everyday Applications

Tipping at restaurants
Calculating discounts while shopping
Understanding nutrition facts on food labels
Battery life indicators on devices
Grades and test scores in education
Election results and polling data
Probability and statistics in daily life

Common Percentage Problems and Solutions

Percentage Increase and Original Value

If a value has increased by 25% to become 150, what was the original value?

Solution: Let the original value be x. Then:

x + 0.25x = 150

1.25x = 150

x = 150 ÷ 1.25 = 120

Therefore, the original value was 120.

Successive Percentage Changes

If a price increases by 10% and then decreases by 10%, is it back to the original price?

Solution: Let's start with a price of $100.

After 10% increase: $100 + 10% of $100 = $100 + $10 = $110

After 10% decrease: $110 - 10% of $110 = $110 - $11 = $99

The final price is $99, which is 1% less than the original price. This shows that successive percentage changes don't simply cancel out.

Compound Percentage Growth

If an investment grows by 8% annually, how much will $1,000 become after 3 years?

Solution: Using the compound growth formula: FV = PV × (1 + r)^n

FV = $1,000 × (1 + 0.08)^3

FV = $1,000 × (1.08)^3

FV = $1,000 × 1.2597

FV = $1,259.70

Percentage Tips and Tricks

Quick Mental Calculations

10% of a number: Move the decimal point one place to the left. Example: 10% of 250 = 25
5% of a number: Find 10% and divide by 2. Example: 5% of 250 = 25 ÷ 2 = 12.5
1% of a number: Move the decimal point two places to the left. Example: 1% of 250 = 2.5
25% of a number: Divide by 4. Example: 25% of 250 = 250 ÷ 4 = 62.5
20% of a number: Divide by 5. Example: 20% of 250 = 250 ÷ 5 = 50
331/3% of a number: Divide by 3. Example: 331/3% of 250 = 250 ÷ 3 = 83.33

Percentage Equivalents

Memorizing common percentage equivalents can speed up calculations:

Percentage	Decimal	Fraction
10%	0.1	1/10
12.5%	0.125	1/8
20%	0.2	1/5
25%	0.25	1/4
33.33%	0.3333...	1/3
50%	0.5	1/2
66.67%	0.6666...	2/3
75%	0.75	3/4

Percentage Calculator