What is a percentage?
A percentage is a way of expressing a part of a whole as a number out of 100. The word comes from the Latin per centum, meaning "by the hundred" — and that's exactly what it does. Saying "37%" is the same as saying 37 out of every 100, or 0.37 as a decimal, or 37/100 as a fraction. They are three different costumes for the same number.
Percentages matter because they let people compare things on the same scale. A test where you got 84 out of 110 and a test where you got 63 out of 80 are hard to compare at a glance — but converted to percentages (76% and 79%) the comparison is instant. The same trick works for tax rates, sale discounts, interest, growth in revenue, drug efficacy, exam scores, and survey results. Anywhere a fraction shows up, a percentage can stand in for it.
The Percentage Calculator handles the three calculations that come up most often: finding a percent of a number (what is 18% of $48?), figuring out what percent one number is of another (15 is what percent of 60?), and computing the percentage change between two numbers (the price went from $80 to $100 — what's the increase?).
How to use the Percentage Calculator
The calculator has three modes, each with two inputs. Pick the mode that matches the question you're asking:
- What is X% of Y? — enter the percentage and the base number. Example: 25% of 200 → 50.
- X is what percent of Y? — enter the part and the whole. Example: 30 is what percent of 120 → 25%.
- Percentage change from X to Y — enter the original and new value. Example: from 80 to 100 → +25%. From 100 to 80 → −20%.
Inputs accept decimals (try 12.5 or 0.075). Negative numbers are allowed and produce signed results. The output updates as you type — there's no Calculate button. It's free and runs entirely in your browser, so no numbers leave your device.
The formulas behind percentages
Three formulas cover almost every percent question you'll meet:
1. Percent of a number: Result = (Percent ÷ 100) × Base
2. One number as a percent of another: Percent = (Part ÷ Whole) × 100
3. Percent change: Change = ((New − Old) ÷ Old) × 100
Worked example for formula 1: what is 15% of $80? Plug it in: (15 ÷ 100) × 80 = 0.15 × 80 = $12. The mental shortcut is to take 10% (move the decimal one place left, so $8) plus half of that for the extra 5% ($4) — total $12.
Worked example for formula 2: 21 is what percent of 60? (21 ÷ 60) × 100 = 0.35 × 100 = 35%. This one matters for grading ("you got 21 out of 60 right"), survey results ("21 of 60 people said yes"), and conversion rates.
Worked example for formula 3: a stock that went from $40 to $52. Change = ((52 − 40) ÷ 40) × 100 = (12 ÷ 40) × 100 = +30%. Note the divisor is the old value, not the new one. Reversing it (using 52 as the divisor) would give the wrong answer of about 23%, which is a common mistake.
One more nuance worth knowing: percent change is asymmetric. A 50% drop followed by a 50% gain doesn't get you back to where you started. $100 dropping 50% becomes $50; $50 rising 50% becomes $75 — not $100. To recover from a 50% loss, you need a 100% gain.
Common percentage scenarios
The same three formulas show up in dozens of everyday situations. Here's how a few of the most common map to them:
| Scenario | What you're calculating | Formula type | Quick example |
|---|---|---|---|
| Restaurant tip | Tip amount on a bill | Percent of a number | 20% of $48 = $9.60 |
| Sales tax | Tax added to a purchase | Percent of a number | 8% of $35 = $2.80 |
| Sale discount | Money off the sticker price | Percent of a number | 30% off $120 = $36 off |
| Test score | Points earned out of total | Part as percent of whole | 42 / 50 = 84% |
| Conversion rate | Buyers as percent of visitors | Part as percent of whole | 87 / 4,200 = 2.07% |
| Salary raise | Increase from old to new pay | Percent change | $60k → $66k = +10% |
| Stock loss | Decrease from peak price | Percent change | $80 → $52 = −35% |
| Year-over-year growth | Revenue change vs. last year | Percent change | $1.2M → $1.5M = +25% |
Notice how the first three rows all use the same formula — they're all "percent of a number" — but the framing changes how it feels. Tipping is something you add. Tax is something added on top of you. A discount is something you subtract. The math is the same; only the sign differs.
The bottom three rows (percent change) are where most people slip up. The trick is always to divide by the starting value, not the ending value. If you went from 50 to 75, you grew by 50% (25 ÷ 50). If you went from 75 to 50, you shrank by 33.3% (−25 ÷ 75). Same gap, different percentages — because the base changed.
Edge cases and limitations
Percentages have a few quirks that the calculator handles cleanly but that are worth knowing about.
Percent change from zero is undefined. If something grew from $0 to $50, the formula divides by zero. Mathematically there is no answer — the growth is "infinite," which isn't a useful number. The calculator reports this as undefined rather than guessing. In real-world reporting, the convention is to write "n/a" or "new" instead of a percentage.
Negative percentages are real numbers. If you compute "what is −15% of 200?" you get −30. This makes sense in context — a 15% loss on a $200 investment is a $30 reduction. The calculator accepts negative inputs and returns signed results.
Percentages can exceed 100%. If a stock went from $20 to $60, that's a +200% change (the gain is twice the original). If 12 customers each ordered an average of 1.4 items, that's 140% of one item per customer. The 0–100% intuition only applies when one number is strictly a part of the other.
Percentage points vs. percent change. If a tax rate went from 5% to 7%, that's a 2 percentage point increase, but a 40% relative increase. News stories that say "the rate jumped 40%" when they mean 2 percentage points are a frequent source of confusion. The calculator tells you the percent-of-old change; whether you report that as "+40%" or "+2 points" depends on context.
Related calculations
Percentages show up in nearly every other calculator on Microapp. Once you've got the percentage you need, these are the tools to reach for next:
- For figuring out the dollar amount and total of a tip on a restaurant bill (and splitting it across people), use the Tip Calculator — it's a percentage calculator with the bill-splitting math added.
- To calculate the sale price after a percent-off discount and see your savings, the Discount Calculator applies the percent-of-a-number formula and subtracts in one step.
- For loan or mortgage calculations involving percentage interest rates over time, the Loan Calculator handles the amortization math that simple percent multiplication can't.
- To see how a percentage rate of return compounds over years, try the Compound Interest Calculator. A 7% annual return doubles your money in about 10 years — but only when it compounds.
Frequently asked questions
How do I calculate 20% of a number quickly in my head?
Take 10% of the number first by moving the decimal one place left, then double it. For 10% of $45, slide the decimal: $4.50. Double it: $9. That's 20%. The same shortcut handles 15% (10% plus half of 10%) and 25% (10% × 2 + half of 10%). Once you're comfortable with 10% as the base, most everyday percentages take just a couple of seconds.
Why is "20% off then 20% off again" not 40% off?
Because the second 20% is taken off the already-reduced price, not the original. Start with $100. After 20% off, you have $80. After another 20% off $80, you have $64 — a total reduction of 36%, not 40%. Stacked percentages always compound this way: each one is applied to the latest value, not the starting one.
Is 0.5% the same as 5%?
No. 0.5% is half a percent — that's 0.005 as a decimal, or 5 out of every 1,000. 5% is 0.05, or 5 out of every 100. They differ by a factor of 10. The decimal point matters: a 5% interest rate on $10,000 is $500/year, while a 0.5% rate is $50/year.
What's the difference between percentage and percentile?
A percentage measures a part of a whole — "37% of voters chose option A." A percentile measures rank within a distribution — "you scored in the 90th percentile" means you scored higher than 90% of test-takers. Both produce a number between 0 and 100, but they answer different questions. Percentages describe quantities; percentiles describe relative position.
How do I reverse a percentage to find the original price?
If an item costs $80 after a 20% discount, the original price was $80 ÷ (1 − 0.20) = $80 ÷ 0.80 = $100. The general formula: Original = Final ÷ (1 − Discount as decimal). For tax-included totals, divide by (1 + Tax rate). A $108 receipt at 8% tax: $108 ÷ 1.08 = $100 pre-tax.
Can a percentage be more than 100%?
Yes — when one quantity is larger than the reference value it's compared to. A 150% increase means the new value is 2.5 times the old one. A 200% return on investment means you tripled your money. Percentages above 100 don't break the math; they just mean you've crossed the full-original-value mark and kept going.
Why does the calculator show negative percentages for losses?
Because the percent-change formula (((New − Old) ÷ Old) × 100) returns a negative number whenever the new value is smaller than the old one. A drop from $100 to $75 is a change of −25%. Reporting it as "25%" without the sign would lose information — the sign tells you direction (gain vs. loss), the number tells you magnitude.