A percentage is a fraction of 100, and three different questions get called percentage problems: what is X% of Y, what percentage is X of Y, and what is the change from X to Y. Each uses a different formula. The FindUtils Percentage Calculator handles all three, and this guide shows the arithmetic behind each so you can check the answer.

The Three Formulas

Most percentage confusion comes from reaching for the wrong one of these.

QuestionFormulaExample
What is 15% of 80?(percent ÷ 100) × value0.15 × 80 = 12
What percent is 12 of 80?(part ÷ whole) × 100(12 ÷ 80) × 100 = 15%
Change from 80 to 92?((new − old) ÷ old) × 100(12 ÷ 80) × 100 = +15%

The second and third produce the same number here only because the example was chosen that way. They answer different questions and diverge immediately: the change from 92 back to 80 is −13.04%, not −15%.

Percentage Increase and Decrease

To increase a number by a percentage, multiply by 1 + (percent ÷ 100). To decrease, multiply by 1 − (percent ÷ 100).

  • 80 increased by 15% → 80 × 1.15 = 92
  • 80 decreased by 15% → 80 × 0.85 = 68

Writing it as a single multiplier is worth the habit. It makes chained changes obvious, and it makes the next section's trap visible before you fall into it.

The Reversal Trap

A percentage increase and the same percentage decrease do not cancel out. This is the single most common percentage mistake, and it costs real money in retail and salary contexts.

Take 100, add 20%, then subtract 20%:

100 × 1.20 = 120
120 × 0.80 = 96

You end at 96, not 100. The increase was 20% of 100; the decrease was 20% of 120, which is a bigger number. To undo a 20% increase you divide by 1.2, which is a decrease of about 16.67%.

The same arithmetic explains why a price cut of 50% followed by a further 20% is not 70% off. It is 0.5 × 0.8 = 0.4, so 60% off.

Step-by-Step: Using the Calculator

Step 1: Pick the Question You Are Actually Asking

Open the Percentage Calculator and choose the mode that matches your question. Getting this right is most of the work; the arithmetic that follows is trivial either way.

Step 2: Enter the Numbers in the Right Order

For percentage change, the ORDER matters. The old value is the denominator. Swapping them gives a different answer, and the error is silent because both numbers look plausible.

Step 3: Sanity-Check the Direction

A decrease should be negative and an increase positive. If the sign surprises you, the values are the wrong way round.

Step 4: Check the Reverse If You Need It

If you need to undo the change, divide rather than subtracting the same percentage. Everything runs in your browser, so nothing you enter is uploaded.

Real Scenarios

Sale price. A coat is 85 marked down 30%. The new price is 85 × 0.70 = 59.50. The saving is 25.50.

Tip on a bill. A 67.40 bill with an 18% tip: 67.40 × 1.18 = 79.53.

Salary change. A rise from 42,000 to 45,500 is (3,500 ÷ 42,000) × 100 = 8.33%.

Exam mark. 47 out of 60 is (47 ÷ 60) × 100 = 78.3%. For a whole course with weighted assessments, the Grade Calculator handles the weighting.

VAT removal. A price of 120 including 20% VAT was 120 ÷ 1.2 = 100 before tax — not 120 × 0.8, which gives 96 and is the reversal trap again.

Percentage Points vs Percent

These are different units and mixing them makes a claim wrong rather than imprecise.

If an interest rate moves from 2% to 3%, that is a rise of 1 percentage point and also a rise of 50 percent. Both are true. "Rates rose 50%" and "rates rose 1 point" describe the same move, and either is misleading without the other.

Free Calculators vs Doing It in a Spreadsheet

AspectFindUtils (free)Spreadsheet
SetupNoneWrite the formula yourself
Formula visibleYes, explainedYes, if you wrote it
Risk of the wrong formulaLow, modes are labelledHigh, all three look similar
Repeat calculationsOne at a timeExcellent for many rows
Account requiredNoDepends on the tool

For a column of a thousand values, use a spreadsheet. For one number checked correctly, a labelled mode removes the chance of reaching for the wrong formula.

Common Mistakes

Mistake 1: Reversing an Increase by Subtracting the Same Percent

Divide by the multiplier instead. Undoing +20% means ÷ 1.2, a 16.67% decrease.

Mistake 2: Swapping Old and New in Percentage Change

The old value goes on the bottom. From 80 to 92 is +15%; from 92 to 80 is −13.04%.

Mistake 3: Adding Percentages of Different Bases

30% off then 20% off is 44% off, not 50%. Multiply the multipliers: 0.7 × 0.8 = 0.56.

Mistake 4: Confusing Percentage Points With Percent

A move from 2% to 3% is one point and fifty percent. Say which you mean.

Mistake 5: Removing Tax by Multiplying

To strip 20% VAT, divide by 1.2. Multiplying by 0.8 takes off too much.

Tools Used in This Guide

FAQ

Q1: Is the percentage calculator free? A: Yes. FindUtils tools require no signup, no usage limits and no watermarks. The calculation runs in your browser and nothing you enter is uploaded.

Q2: How do I calculate a percentage of a number? A: Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12.

Q3: What is the percentage increase formula? A: ((new − old) ÷ old) × 100. From 80 to 92 that is (12 ÷ 80) × 100 = 15%. The old value is always the denominator.

Q4: Why does a 20% increase then a 20% decrease not return the original number? A: The two percentages are taken from different bases. The increase is 20% of the original, the decrease is 20% of the larger result. 100 becomes 120, then 96. To undo a 20% increase, divide by 1.2.

Q5: How do I remove VAT or sales tax from a price? A: Divide by 1 plus the rate. To strip 20% VAT from 120, divide by 1.2 to get 100. Multiplying by 0.8 gives 96, which is wrong.

Q6: What is the difference between percent and percentage points? A: A move from 2% to 3% is a rise of one percentage point and also a rise of fifty percent. Percentage points measure the gap between two percentages; percent measures relative change.

Q7: How do I apply two discounts? A: Multiply the multipliers rather than adding the percentages. 30% off then 20% off is 0.7 × 0.8 = 0.56, so 44% off in total.

Next Steps