Percentage Formulas Cheat Sheet — The Only Guide You Need

Percentages appear everywhere — on receipts, pay stubs, nutrition labels, loan statements, and exam results. Yet when the moment comes to actually calculate one, most people reach for a search engine. This cheat sheet puts every percentage formula you will ever need in a single page, complete with real-world examples you can apply immediately.

1. The Basic Percentage Formula

The foundational formula answers the question: What is X% of Y?

Result = (Percentage / 100) × Total

Example: What is 18% of 250? Divide 18 by 100 to get 0.18, then multiply by 250. The answer is 45. You can use this whenever you need to find a portion of a whole — calculating sales tax, splitting a bill, or figuring out how many questions you need to pass an exam.

2. Finding What Percentage One Number Is of Another

This formula answers: X is what percent of Y?

Percentage = (Part / Whole) × 100

Example: You scored 42 out of 60 on a test. What is your percentage? 42 ÷ 60 = 0.70, then 0.70 × 100 = 70%. This same formula works for calculating batting averages, completion rates, market share, and any other ratio you want to express as a percentage.

3. Percentage Increase

Use this when a value goes up and you want to express the growth as a percentage.

% Increase = ((New − Old) / Old) × 100

Example: Your monthly rent rises from $1,400 to $1,498. The increase is $98. Divide by the original: 98 ÷ 1,400 = 0.07. Multiply by 100 to get a 7% increase. This formula is essential for tracking salary growth, revenue changes, and price inflation.

4. Percentage Decrease

The same formula applies when a value drops — the result will simply be negative.

% Decrease = ((New − Old) / Old) × 100

Example: A stock falls from $80 to $68. Change: $68 − $80 = −$12. Divide: −12 ÷ 80 = −0.15. The stock dropped by 15%. If you prefer a positive number, take the absolute value and state the direction explicitly.

5. Converting Fractions and Decimals to Percentages

Fraction to percentage: divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.

Decimal to percentage: multiply by 100. For example, 0.625 × 100 = 62.5%.

Percentage to decimal: divide by 100. For example, 45% ÷ 100 = 0.45.

Percentage to fraction: place the percentage over 100 and simplify. For example, 60% = 60/100 = 3/5.

6. Percentage Difference vs. Percentage Change

These two measures serve different purposes and are often confused.

Percentage change compares a new value to an original value. It has a clear direction (increase or decrease) and uses the original as the base.

% Change = ((New − Old) / Old) × 100

Percentage difference compares two values when neither is clearly the “original.” It uses the average of the two as the base and is always expressed as a positive value.

% Difference = (|A − B| / ((A + B) / 2)) × 100

Example: City A has 320,000 residents and City B has 280,000. The percentage difference is |320,000 − 280,000| ÷ ((320,000 + 280,000) / 2) × 100 = 40,000 ÷ 300,000 × 100 = 13.33%. Use percentage difference when comparing two independent measurements, such as prices from two stores, test scores from two classes, or populations of two cities.

7. Tips and Tricks for Mental Math

The 10% shortcut: to find 10% of any number, simply move the decimal point one place to the left. 10% of $85 is $8.50. From there you can quickly derive other common percentages: 5% is half of 10%, 20% is double, and 15% is 10% plus 5%.

The flip trick: X% of Y always equals Y% of X. Struggling with 8% of 50? Flip it: 50% of 8 = 4. Much easier.

Break it into parts: to calculate 35% of a number, find 30% (3 × 10%) and 5% (half of 10%), then add them together. This is faster than multiplying by 0.35 in your head.

8. Real-World Applications

Tipping

A standard 20% tip on a $65 dinner bill: 10% is $6.50, so 20% is $6.50 × 2 = $13.00. For 15%, add half of 10%: $6.50 + $3.25 = $9.75.

Discounts

A jacket is marked 30% off the original $140 price. 10% of $140 is $14, so 30% is $14 × 3 = $42 off. You pay $140 − $42 = $98. Stacked discounts are applied sequentially, not added: a 20% coupon on top of a 30% sale is not 50% off. Instead, you pay 70% of the original, then 80% of that: $140 × 0.70 × 0.80 = $78.40.

Tax

If sales tax is 8.25%, find the tax on a $200 purchase: $200 × 0.0825 = $16.50. The total is $216.50. For quick estimates, round 8.25% to 8% (just under a tenth), which gives $16 — close enough for budgeting on the fly.

Try It Yourself

Bookmark this page for quick reference, and when you need instant answers without any mental math, use our free Percentage Calculator. It covers all six calculation modes — basic percentage, percentage of, percentage change, tips, discounts, and margins — with plain-English explanations for every result. No sign-up, no data collection, and it works offline once loaded.

Need a deeper walkthrough? Read our step-by-step guide on how to calculate percentage increase and decrease.