Percentage Formula Cheat Sheet: Find the Right One in 10 Seconds
Most percentage cheat sheets are just a list of formulas with no way to tell which one applies to your situation. This one starts from the question you're actually asking, not the formula itself, since figuring out which formula you need is usually the harder part.
There are five distinct percentage questions that come up in everyday life, and they use five different formulas. Mixing them up (using the wrong one for your situation) is the single biggest source of percentage errors, more common than any arithmetic mistake. Below is a quick way to identify which one you need, followed by the full formula reference.
Which Formula Do You Need? Start Here
Answer these in order until one fits
The Five Formulas, in Full
1. Basic Percentage (X% of Y)
15% of 80: (15 ÷ 100) × 80 = 12.
2. X is What Percent of Y
24 out of 40 questions correct: (24 ÷ 40) × 100 = 60%.
3. Percentage Change (Increase or Decrease)
A price moving from $50 to $65: ((65 − 50) ÷ 50) × 100 = 30% increase.
4. Reverse Percentage
A $60 item after a 25% discount was originally: 60 ÷ (1 − 0.25) = $80.
5. Percentage Points (Comparing Two Percentages)
Approval rating moving from 38% to 41% is a 3 percentage point rise, a different figure from the percentage change (about 7.9%). The full breakdown of why these two numbers diverge is in the percentage vs percentage points guide.
Quick Reference Table
| You're asking | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 15% of 80 = 12 |
| X is what % of Y? | (X ÷ Y) × 100 | 24/40 = 60% |
| Percentage change from A to B | ((B − A) ÷ A) × 100 | 50 → 65 = 30% |
| Original before a % was applied | Final ÷ (1 ± %) | $60 after 25% off → $80 |
| Gap between two percentages | New % − Old % | 41% − 38% = 3 points |
How These Show Up in Real Questions
Percentage problems rarely arrive labeled with their formula type. They show up as plain-language questions, and recognizing the pattern in the wording is most of the battle.
| How the question is phrased | What it actually is |
|---|---|
| "What's 20% off $45?" / "How much is the tip on $60?" | Basic percentage (X% of Y) |
| "I got 34 out of 50, what's my grade?" / "What share of my income is rent?" | X is what % of Y |
| "My rent went from $1200 to $1350, how much did it go up?" | Percentage change |
| "This is $42 after 30% off, what was it before?" | Reverse percentage |
| "Candidate A polled 38%, now 41%, how much did they gain?" | Percentage points, not percentage change |
A Worked Example Using Several Formulas Together
Real situations often chain more than one of these formulas in sequence, which is where a cheat sheet with only isolated examples falls short. Take a jacket originally priced at $80. It goes on sale at 25% off, then an extra 10% is taken off at checkout, and finally 8% sales tax is added.
First, the 25% discount: 80 × (1 − 0.25) = $60. Then the extra 10% off that new price, not the original: 60 × (1 − 0.10) = $54. Finally, tax on top: 54 × 1.08 = $58.32 final price. Applying the second discount to the original $80 instead of the already-discounted $60 is a common mistake here, and it would produce an incorrect final answer of about $56.16 instead of the correct $58.32. Each step uses the result of the previous one, not the original number, which is exactly the compounding logic covered in the Percentage Increase/Decrease Calculator.
The One Mistake That Breaks All Five Formulas
Every formula above depends on correctly identifying which number is the base, the number everything else is measured against. In the basic percentage formula, Y is the base. In percentage change, the original value is the base, not the new one. In reverse percentage, the unknown original is the base, which is exactly why you divide instead of multiply. Misidentifying the base is a bigger source of wrong answers than any arithmetic slip, since the arithmetic is usually simple once the right base is chosen.
A quick way to check: ask what the percentage is "of." A discount is a percentage of the original price, so the original price is the base. A test score is a percentage of the total possible points, so the total is the base. A percentage change is relative to where something started, so the starting value is the base, never the ending one. When a calculation gives a suspicious-looking answer, this is almost always the first thing worth checking before assuming a calculator or formula is wrong.
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Frequently Asked Questions
What is the basic formula for finding a percentage of a number?
Divide the percentage by 100, then multiply by the number. For 15% of 80: (15 ÷ 100) × 80 = 12.
How do I calculate percentage increase or decrease?
Subtract the original value from the new value, divide by the original value, then multiply by 100. A price rising from $50 to $65 is a 30% increase, calculated as ((65 − 50) ÷ 50) × 100.
How do I find the original number before a discount was applied?
Divide the final price by (1 minus the discount as a decimal). A $60 item after a 25% discount was originally priced at 60 ÷ 0.75 = $80.
Why is choosing the wrong base number the most common percentage mistake?
Every percentage formula measures one number relative to another, called the base. Using the wrong number as the base (for example, dividing by the new value instead of the original in a percentage change calculation) produces a wrong answer even when every other step is correct.
Is there a difference between percentage change and percentage points?
Yes. Percentage change compares a before and after value of the same quantity. Percentage points measure the plain gap between two percentages being compared to each other, such as two poll results. They usually produce different numbers for the same data.