Percent, explained like you’ll actually remember it

A percentage is a way to express a part of something as a fraction of 100. So when you see 25%, it literally means “25 out of 100,” or 25/100. That’s why percent is so useful: it lets you compare different sizes on the same scale.

Here’s the one conversion that powers almost every percentage calculation: Percent → Decimal. To convert a percent into a decimal, divide by 100. For example, 15% becomes 0.15. Then you can multiply it by whatever number you’re working with.

• Percent of a number: X% of Y = (X ÷ 100) × Y
• What percent: X is what % of Y = (X ÷ Y) × 100
• Percent change: ((New − Old) ÷ Old) × 100
• Increase/decrease by %: New = Base × (1 ± X/100)

Notice how every formula is really just a ratio. In real life, percent is a language for ratios: “This is this much compared to that much.” Once you know the baseline, percent becomes easy.

Percent questions often hide the baseline in the sentence. Example: “Sales increased 20%.” Increased compared to what? Last month? Last year? The baseline is whatever you start from. That’s why percent change uses Old (the starting value) in the denominator.

If you only memorize one sentence: Percent change is always measured against the starting value. If your starting value is 0, percent change is undefined (you can’t divide by zero).

Real-world examples (shopping, grades, growth)

Example: What is 15% of 200?
Convert 15% to decimal: 15 ÷ 100 = 0.15
Multiply: 0.15 × 200 = 30
✅ Answer: 15% of 200 is 30

Example: 45 is what percent of 60?
Divide: 45 ÷ 60 = 0.75
Convert to percent: 0.75 × 100 = 75%
✅ Answer: 45 is 75% of 60

Example: Price goes from $50 to $65. What’s the percent change?
Difference: 65 − 50 = 15
Divide by old: 15 ÷ 50 = 0.30
Convert to percent: 0.30 × 100 = 30%
✅ Answer: 30% increase

Example: Increase $80 by 12% (like adding tax).
12% as decimal is 0.12, so multiplier is 1 + 0.12 = 1.12
New = 80 × 1.12 = 89.60
✅ Answer: $89.60

Sanity checks: 10% of 200 is 20, so 15% should be a bit more → 30 makes sense. These quick checks help you avoid the “oops, I typed 150 instead of 15” problem.

Step-by-step logic (why each formula works)

Percent of a number works because percent is a fraction of 100. If you want X% of Y, you are asking for X/100 of Y. And “of” in math usually means multiply: (X/100) × Y.

What percent X is of Y is just reversing the question. If X is part of Y, then the fraction is X/Y. To convert a fraction to a percent, multiply by 100. That’s why the formula is (X ÷ Y) × 100.

Percent change measures how big the change is compared to where you started. If you started at Old and ended at New, the raw change is (New − Old). To convert that into a “relative” change, divide by Old. Then multiply by 100 to express it as a percent.

• Mixing up the baseline: For percent change, denominator is Old.
• Forgetting to divide by 100: 20% is 0.20, not 20.
• Dividing by the wrong number: “X is what % of Y” → divide X by Y, not Y by X.
• Percent points vs percent: Going 20% → 30% is +10 percentage points, but +50% relative.

“Percentage points” are absolute differences between percents (30% − 20% = 10 points). “Percent increase” compares the difference relative to the starting percent (10 ÷ 20 = 50% increase).

Frequently Asked Questions

• What’s the difference between percent and percentage?

  “Percent” (like 20%) is the number itself. “Percentage” is often used more generally to mean a percent value or a way of expressing something in percent terms. In practice, people use them interchangeably.

• Why is percent change undefined when the old value is 0?

  Because the percent change formula divides by the old value. Dividing by 0 isn’t defined in real-number math. If you go from 0 to 10, you can describe it as “an increase of 10” or “from zero to ten,” but not a finite percent.

• How do I calculate a discount price?

  If something is discounted by X%, multiply the original price by (1 − X/100). Example: 25% off $80 → 80 × 0.75 = $60.

• How do I calculate a tip quickly?

  For 10% tip, move the decimal left once. For 15%, take 10% + half of 10%. Or use the calculator and save/share the result.

• Can percentages be greater than 100%?

  Yes. If X is bigger than Y, then “X is what % of Y” will be above 100%. Example: 150 is 150% of 100. Percent can represent “more than the whole baseline.”

• Is a -20% change the same as a 20% decrease?

  In common usage, yes: negative percent change means a decrease, positive means an increase. This calculator labels it clearly to avoid confusion.