What is the easiest percentage formula to remember?

“Percent of” is (percent ÷ 100) × number. Everything else builds on dividing by 100 or comparing two numbers with (part ÷ whole) × 100.

How do I calculate percentages without a calculator?

Find 10% first (move the decimal one place), then combine: 5% is half of 10%, 20% is double 10%, 15% is 10% + 5%, and so on.

Is 100% the same as the whole amount?

Yes. 100% of any number is the number itself. 200% of a number is twice that number.

How to Calculate Percentages

Learn how to calculate percentages by hand and with free tools. Formulas for percent of a number, reverse percentages, increase, decrease, and real examples.

8 min read · Free educational guide

What a percentage means

A percentage is a way of expressing a number as a fraction of 100. The word itself comes from “per centum” — per hundred. So 25% means 25 out of every 100 parts, or 25/100, which simplifies to 1/4.

Percentages appear everywhere: exam scores, sales discounts, interest rates, tax rates, nutrition labels, and progress bars. Once you know a few core formulas, most “percent problems” become the same pattern with different labels.

Core formula: what is X% of Y?

This is the most common percentage calculation. Convert the percent to a decimal by dividing by 100, then multiply by the number.

Formula: result = (X ÷ 100) × Y
Example: 15% of 200 → (15 ÷ 100) × 200 = 0.15 × 200 = 30
Mental shortcut: 10% of any number is the number with the decimal point moved one place left (10% of 200 = 20). 5% is half of that (10). 15% = 10% + 5% = 20 + 10 = 30.

Reverse formula: X is what percent of Y?

When you know two amounts and want the relationship between them, divide the part by the whole and multiply by 100.

Formula: percent = (X ÷ Y) × 100
Example: 25 is what percent of 200? (25 ÷ 200) × 100 = 12.5%
Example: you scored 42 points out of 50 → (42 ÷ 50) × 100 = 84%

Increasing or decreasing a value by a percent

To apply a percentage change to a starting value, multiply by (1 + rate) for an increase or (1 − rate) for a decrease, where rate is the percent divided by 100.

Increase: new = value × (1 + percent/100) — e.g. 100 × 1.15 = 115 for +15%
Decrease: new = value × (1 − percent/100) — e.g. 100 × 0.85 = 85 for −15%
Amount of change: value × (percent/100)

Percentage change from A to B

When you have an old value and a new value, percentage change measures relative growth or decline. Always divide by the original (starting) value, not the new one.

Formula: ((new − original) ÷ |original|) × 100. From 80 to 100 is a 25% increase. From 100 to 80 is a 20% decrease — notice the percentages are not the same size when the base changes.

Common mistakes to avoid

Confusing percentage points with percent change is frequent: if a tax rate moves from 10% to 12%, that is a 2 percentage point rise, but a 20% relative increase. Also watch zero as a base — you cannot compute “percent of zero as the whole” or “change from zero” in the usual way.

When stacking discounts, do not simply add percentages. A 20% off sale then an extra 10% off is not 30% off; the second discount applies to the reduced price.

Practice with free calculators

Use PercentBox when you want instant answers and to double-check homework or shopping math. The tools show the same formulas described here so you can learn while you calculate.

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FAQ

What is the easiest percentage formula to remember?: “Percent of” is (percent ÷ 100) × number. Everything else builds on dividing by 100 or comparing two numbers with (part ÷ whole) × 100.
How do I calculate percentages without a calculator?: Find 10% first (move the decimal one place), then combine: 5% is half of 10%, 20% is double 10%, 15% is 10% + 5%, and so on.
Is 100% the same as the whole amount?: Yes. 100% of any number is the number itself. 200% of a number is twice that number.