How Percentages Work

Maintained by Prince Yadav — Founder & Lead Developer, Ganitra Calculator. This guide is written and maintained as part of Ganitra Calculator’s first-party educational content.

What a percentage means

A percentage expresses a value relative to 100. It is useful for comparing proportions, rates, changes, discounts, taxes, and many everyday calculations.

Finding a percentage of a number

To find x% of a value, convert x to a decimal and multiply by the value. For example, 15% of 200 is 0.15 × 200 = 30.

Percentage change

Percentage change compares a new value with an old value using the old value as the base.

Discounts and taxes

A discount reduces the original price, while a tax increases a pre-tax price. Reversing an inclusive tax requires care because the percentage is applied to a specific base.

Common mistakes

Do not confuse percentage change with percentage difference, and do not assume adding and subtracting the same percentage always reverses a calculation.

A worked increase example

If a price rises from 80 to 100, the increase is 20. Using the original 80 as the base gives a 25% increase. Reversing the calculation from 100 back to 80 is a 20% decrease, which shows why adding and subtracting the same percentage do not generally cancel each other.

Choosing the correct base

The most common percentage mistake is using the wrong reference value. For a discount, the original price is normally the base. For percentage change, the old value is the base. For a tax added to a pre-tax price, the taxable amount is the base.

Useful related calculations

Use the basic percentage tool for proportions and percentages of a value, the Percentage Change calculator for increases or decreases over time, and the Discount or GST tools when the base and tax or discount rules are specific to a transaction.

Related Calculators

Use the Calculator

Take the concepts from this guide and test your own assumptions in the calculator.