Percentage Calculator

How to Calculate Percentages — A Complete Guide

A percentage expresses a number as a fraction of 100. The word itself comes from the Latin "per centum", meaning "by the hundred". Understanding percentages is one of the most practical mathematical skills you can learn, because they appear everywhere from shopping discounts and tax bills to loan interest and exam grades. This guide walks you through the three most common percentage calculations step by step, with clear formulas and worked examples.

Before using the calculators above, it helps to understand the underlying maths. Once you know the formula behind each calculation, you can solve percentage problems by hand, spot mistakes, and estimate answers in seconds. Below we break down each of the three calculators on this page, explain the formula, and then show how the same method applies to real situations like sales, taxes, and interest.

The three core percentage calculations

Almost every percentage question you will encounter falls into one of three categories. The first calculator on this page answers "what is X% of Y?" — for example, what is 20% of an 80-dollar bill. The second answers "X is what percent of Y?" — for example, 15 is what percent of 60. The third measures change: "by what percent did a value increase or decrease going from X to Y?" — for example, a salary rising from 2,000 to 2,400.

Step-by-step: finding a percentage of a number

To find X% of Y, convert the percentage into a decimal by dividing it by 100, then multiply by the whole. So 20% of 80 becomes 0.20 × 80 = 16. You can also think of it as multiplying the two numbers and dividing by 100: (20 × 80) / 100 = 16. Both methods give the same result, so choose whichever feels more natural. This is the calculation you use when working out a tip, a discount, or the portion of a budget spent on one category.

Step-by-step: expressing one number as a percentage of another

To find what percentage X is of Y, divide X by Y and multiply by 100. For example, to find what percent 15 is of 60, calculate 15 / 60 = 0.25, then 0.25 × 100 = 25%. This tells you that 15 is one quarter, or 25%, of 60. This method is used for test scores, market share, attendance rates, and any situation where you need to express one quantity as a share of a total.

Step-by-step: calculating percentage increase or decrease

To measure the percentage change between two values, subtract the original from the new value, divide by the original, and multiply by 100. A positive result is an increase; a negative result is a decrease. For example, if a price rises from 200 to 250, the change is (250 − 200) / 200 × 100 = 25%. If a price falls from 200 to 150, the change is (150 − 200) / 200 × 100 = −25%, meaning a 25% decrease. Always divide by the original value, not the new one — this is the most common mistake people make.

Percentage Formulas

Each percentage calculation relies on a short, memorable formula. Memorise these three and you can solve the vast majority of percentage problems without any tool at all.

1. What is X% of Y?

Formula: Result = (X / 100) × Y. Example: 20% of 80 = (20 / 100) × 80 = 0.20 × 80 = 16.

2. X is what percent of Y?

Formula: Percentage = (X / Y) × 100. Example: 15 is what percent of 60 = (15 / 60) × 100 = 25%.

3. Percentage increase or decrease from X to Y

Formula: Change = ((Y − X) / X) × 100. A positive value is an increase, a negative value is a decrease. Example: from 200 to 250 = ((250 − 200) / 200) × 100 = 25% increase.

• Convert between percentage and decimal by dividing or multiplying by 100.
• When measuring change, always divide by the original (starting) value.
• A 100% increase doubles a value; a 100% decrease removes it entirely.
• Percentages can exceed 100% — this simply means the part is larger than the original whole.

Practical Real-World Examples

Shopping discounts

A jacket originally priced at 120 dollars is marked "30% off". To find the discount, calculate 30% of 120: (30 / 100) × 120 = 36. The sale price is therefore 120 − 36 = 84 dollars. This is a direct application of the first calculator.

Taxes and VAT

If a product costs 200 dollars before tax and the sales tax rate is 8%, the tax amount is 8% of 200 = (8 / 100) × 200 = 16 dollars, making the total 216 dollars. To work the other way — finding the original price when tax is already included — divide by 1 + rate, so 216 / 1.08 = 200.

Interest rates

A savings account pays 3% annual interest. On a balance of 5,000 dollars, the interest earned in one year is 3% of 5,000 = (3 / 100) × 5,000 = 150 dollars. Over multiple years with compounding, each year the new balance becomes the base, so the growth accelerates — but the basic percentage calculation remains the same.

Exam scores

A student scores 42 out of 60 on a test. To express this as a percentage, use the second formula: (42 / 60) × 100 = 70%. This lets you compare results across tests with different maximum marks.

Salary increase

A salary rises from 2,400 to 2,700 dollars per month. Using the change formula: ((2,700 − 2,400) / 2,400) × 100 = (300 / 2,400) × 100 = 12.5%. The salary increased by 12.5%.

These examples show how the same three formulas cover almost every percentage question in daily life. Bookmark this page and use the calculators above whenever you need a quick, reliable answer.