One Idea, Three Questions, Instant Answers
Percentages show up everywhere — a sale price at the store, a tip at a restaurant, your raise at work, a grade on a test. This free percentage calculator handles the three questions people actually ask: what is X% of Y, what percent one number is of another, and how much a number changed in percent terms. Pick the tab that matches your question, type your numbers, and get an instant answer with the full calculation shown, no sign-up and nothing to install.
Percentages sound like math-class material, but they’re really just a language for talking about parts of things. If you can master three simple moves — “percent of,” “what percent is this,” and “how much did it change” — you can answer almost any percentage question without a second thought.
A positive result means the value increased; a negative result means it decreased. The change is always measured against the old value.
How to Use This Calculator
- Pick your tab. Tap “X% of Y” to find a percent of a number, “X is what % of Y?” to turn a fraction into a percent, or “% Change” to measure an increase or decrease.
- Type your numbers. Each tab has just two fields with hints and example values to guide you.
- Click “Calculate” — or just type, because the answer updates live as you change the numbers.
Every result includes the step-by-step math, so you can see exactly how the answer was found — useful for checking homework or double-checking a bill. Try these: 20% of 150 (should give 30), 30 as a percent of 120 (25%), or a change from 80 to 100 (+25%).
What Is a Percentage?
A percentage is simply a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred” — so 25% literally means 25 out of every 100. That simple idea is why percentages are everywhere: they turn messy comparisons into a single number on a familiar 0-to-100 scale.
Every percentage has three common forms. Take 25%: as a fraction it is 25/100 (which simplifies to 1/4), as a decimal it is 0.25, and in words it is “twenty-five percent.” Converting between forms is the key skill behind all percentage math — to turn a percent into a decimal, divide by 100 (move the decimal point two places left); to turn a decimal into a percent, multiply by 100 (move the point two places right).
Formulas With Worked Examples
There are three formulas, one per tab. Each is shown with a worked example you can follow by hand.
Example: what is 20% of $150? Convert 20% to the decimal 0.20, then multiply: 0.20 × 150 = $30.
Example: you answered 30 questions right out of 120 total. Divide 30 by 120 to get 0.25, then multiply by 100: 25%.
Example: a price rose from $80 to $100. Subtract first (100 − 80 = 20), divide by the old value (20 ÷ 80 = 0.25), then multiply by 100: +25%.
A handy mental shortcut for common cases: 10% of anything is just the decimal point moved one place left ($15 here), so 20% is double that ($30), and 15% is 10% plus half of 10%. For percent change, the old value is always the divisor — dividing by the new value instead is the most common mistake people make. Note that change is asymmetric: a 50% drop from $100 gives $50, but a 50% rise from $50 only reaches $75.
Tips for Flawless Percentage Math
- Match the tab to the question. If you want “what percent,” you need the second tab (X is what % of Y), not the first — mixing them up is the number-one source of wrong answers.
- For % change, always divide by the old value. “From $40 to $50” divides by 40, not 50.
- Watch the sign. A negative percent change means a decrease; the tool colors increases green and decreases red so the direction is obvious.
- Mind “percentage points” vs. “percent.” Going from 20% to 25% is a 5-percentage-point rise, but a 25% increase in relative terms — headlines mix these up constantly.
- Don’t add percentages that shouldn’t be added. A 20% discount followed by another 20% discount isn’t 40% off; it’s 36% off the original (you pay 80% of 80%, which is 64%).
- Decimals are fine. The tool accepts values like 12.5% or $48.99 — useful for real-world prices and rates.
More Math Tools
Reverse Percentages: Finding the Original Value
When you know the value after a change, recover the original by dividing instead of subtracting:
Paid $60 after a 25% discount? You paid the remaining 75%, so the original price was $60 ÷ 0.75 = $80. A bill of $240 that already includes 20% tax? The pre-tax price was $240 ÷ 1.2 = $200.
The tempting shortcut is wrong: $240 minus 20% is $192, which is $8 too low. The tax was calculated on the original price, not on the final total, so only division unwinds it.
Frequently Asked Questions
What is a percentage calculator used for?
It answers any “what percent” question: finding a percent of a number (20% of 150), converting a ratio to a percent (30 out of 120), or measuring percent change (a price rising from $80 to $100). Common uses include discounts, tips, taxes, grades, and growth rates.
How do you calculate a percentage of a number by hand?
Divide the percent by 100 to make a decimal, then multiply by the number. For 20% of 150: 20 ÷ 100 = 0.20, then 0.20 × 150 = 30. Alternatively, divide the number by 100 and multiply by the percent — same result.
What is the formula for percent increase and decrease?
Percent change = ((New value − Old value) ÷ Old value) × 100. If the result is positive, the value increased; if negative, it decreased. Example: $80 to $100 gives ((100 − 80) ÷ 80) × 100 = +25%.
Can a percentage be more than 100%?
Yes. Over 100% simply means “more than the whole.” A value growing from $50 to $150 is a 200% increase, and scoring 120 out of 100 on a test with bonus points is 120%. Percentages only cap at 100 when they describe a part of a fixed whole.
What is the difference between percent and percentage points?
“Percent” describes relative change, while “percentage points” describe the absolute gap. If interest rates rise from 4% to 6%, that is a 2-percentage-point increase — but a 50% relative increase (2 ÷ 4 × 100).
Is percent change the same as percent difference?
No. Percent change compares a difference to the starting value, while percent difference compares it to the average of the two values. Percent change answers “how much did it grow?”; percent difference answers “how far apart are these two numbers?”
How do I find the original value before a percentage change?
Divide the final value by the multiplier: Original = Final ÷ (1 ± percent ÷ 100). A $60 sale price after 25% off means the original was $60 ÷ 0.75 = $80.
How do I calculate a tip or tax as a percentage of a price?
Multiply the price by the percentage as a decimal. A 20% tip on a $45 bill is 0.20 × $45 = $9, making $54 in total. An 8% sales tax on $50 is 0.08 × $50 = $4.
What’s 15 percent of 20?
3. Fifteen percent of a number is 15 × the number ÷ 100, so 15 × 20 ÷ 100 = 3. If the 20 is money, the answer is money: 15 percent of 20 dollars is $3 — the kind of quick discount or tip math the first mode of the calculator above handles instantly.