Percentage Calculator

How percentages work — the basics

A percentage is a fraction expressed as parts per hundred. The word literally means "per cent" — per hundred. When we say "25%", we mean "25 out of 100" or equivalently "0.25" as a decimal. That single insight unlocks all percentage math. To convert any percentage to a decimal, divide by 100 (so 25% becomes 0.25). To go the other direction, multiply by 100 (so 0.25 becomes 25%).

Once you can move freely between the percentage form and the decimal form, every percentage problem reduces to multiplication and division. The three modes in this calculator just package the three most common arrangements of those operations — but underneath, they're all variations on the same basic idea. If you ever get stuck on a percentage problem, converting everything to decimals first usually clears it up.

The three percentage formulas

Mode 1 — What is X% of Y?

The everyday percentage. Used for tips, discounts, sales tax, commission, fractions of any whole. Formula: (X ÷ 100) × Y or equivalently X × Y ÷ 100. Both give the same answer. For 25% of 200: (25 ÷ 100) × 200 = 0.25 × 200 = 50.

The mental shortcut: 10% of any number is just the number with a decimal point shifted one place left. 10% of 480 is 48. 10% of 35 is 3.5. Once you have 10%, you can build other percentages by adding or doubling. 20% is 10% × 2. 5% is 10% ÷ 2. 15% is 10% + 5%. This shortcut is why headwaiters and shoppers can do mental percentage math instantly.

Mode 2 — X is what percentage of Y?

Used for proportions, completion rates, market share, test scores. Formula: (X ÷ Y) × 100. The smaller (or compared) number is divided by the larger (or base) number, then multiplied by 100 to turn the decimal back into a percentage. For "50 is what % of 200": (50 ÷ 200) × 100 = 0.25 × 100 = 25%.

This mode catches people out when the order is reversed. "200 is what % of 50?" is a legitimate question — the answer is 400%. (50 × 4 = 200.) Percentages can exceed 100 when the first number is larger than the second. Don't assume answers must be between 0 and 100.

Mode 3 — Percentage change from X to Y

The most error-prone mode. Used for growth rates, price changes, investment returns, year-over-year comparisons. Formula: ((Y − X) ÷ X) × 100. Note: you divide by the original value (X), not the new value (Y). This is the single most common percentage mistake.

Example: a stock goes from $100 to $125. Change: ((125 − 100) ÷ 100) × 100 = 25% increase. Same stock goes from $125 back to $100. Change: ((100 − 125) ÷ 125) × 100 = −20% decrease. Notice the asymmetry: a 25% increase is undone by a 20% decrease, not by another 25% — because the base changed. This is why losing 50% then gaining 50% leaves you at 75%, not 100%.

Worked examples for each mode

Tip calculation (Mode 1)

Dinner bill of $87. Calculating an 18% tip: 18% of 87 = (18 ÷ 100) × 87 = 0.18 × 87 = $15.66. Total bill including tip: $102.66.

Test score (Mode 2)

Scored 47 out of 60 on an exam. What percentage is that? (47 ÷ 60) × 100 = 0.7833... × 100 = 78.33%. Pretty solid grade.

Year-over-year revenue growth (Mode 3)

Company revenue went from $2.4 million last year to $2.9 million this year. Growth: ((2.9 − 2.4) ÷ 2.4) × 100 = (0.5 ÷ 2.4) × 100 = 20.83%. A roughly 21% growth year.

Investment loss (Mode 3, negative)

Portfolio worth $50,000 dropped to $42,500 in a market correction. Change: ((42,500 − 50,000) ÷ 50,000) × 100 = (−7,500 ÷ 50,000) × 100 = −15%. A 15% loss.

Sales tax (Mode 1)

Item costs $79 in a state with 8.25% sales tax. Tax: 8.25% of 79 = 0.0825 × 79 = $6.52. Total cost: $85.52.

Common percentage mistakes

Mistake 1: Confusing "% increase" with "more than"

"Sales are 200% higher this year" is ambiguous. Does it mean sales are 2× what they were (a 100% increase), or 3× what they were (a 200% increase)? Mathematically the second is correct, but in everyday usage many people mean the first. When stakes matter (contracts, reports, decisions), spell it out: "sales tripled" or "sales doubled" is unambiguous in a way that percentages aren't.

Mistake 2: Adding percentages that compound

"20% off plus an extra 15% off" is not 35% off. The 15% applies to the already-discounted price, so the effective discount is 32%, not 35%. The Discount Calculator handles stacked percentage math automatically — see the related link below.

Mistake 3: Asymmetric gains and losses

Going down 50% then up 50% does not return you to where you started. Starting at $100, a 50% drop takes you to $50. A 50% rise from $50 is $25, so you end at $75 — down 25% from the original. The base changes each time, so the same percentage moves in opposite directions don't cancel. This is why recovering from a stock market crash takes a larger percentage gain than the percentage loss that caused it.

Mistake 4: Dividing by the wrong number for % change

For percentage change, always divide by the original (starting) value, not the new (ending) one. A common error is using whichever number is in the denominator out of habit. The result is mathematically valid for something else ("X is what % of Y") but doesn't answer the question "how much did this change?"

Mistake 5: Percentage of percentage

"The interest rate increased by 5%" is not the same as "increased by 5 percentage points." If a rate goes from 3% to 8%, that's a 5 percentage point increase but a 167% percentage increase (relative change). Financial articles often blur these — be alert to which is meant. Percentage points are absolute; percentages are relative.

Percentage Calculator FAQ

What's the difference between percent and percentage points?

A percent is a relative measure ("the rate rose by 5%" means it went up by 5% of its previous value). A percentage point is an absolute measure ("the rate rose by 5 percentage points" means it went up by exactly 5 on the 0–100 scale). If interest rates go from 3% to 8%, that's 5 percentage points or a 167% relative increase. Both descriptions are correct — they answer different questions.

Can a percentage be over 100?

Yes. 200% of 50 is 100. 350% of 80 is 280. Percentages over 100 just mean "more than the whole." Common contexts: stock returns ("up 240%"), comparison statements ("Q3 was 150% of Q2"), and growth metrics. They're not unusual or mathematically improper.

Can a percentage be negative?

Only in % change contexts. A negative percentage change means a decrease (the new value is less than the original). For "% of a number" or "% one is of another", you'd need a negative input number to get a negative result — and at that point the question usually doesn't make practical sense.

What does "percent" actually mean?

"Per cent" is Latin for "per hundred." A percentage is a number expressed as parts per hundred. So 37% means "37 per hundred" or equivalently 37 out of 100, or 0.37 as a decimal. This is why dividing by 100 converts a percentage to a decimal — it removes the "per hundred" framing.

How do I calculate a percentage in my head?

Start with 10% (just move the decimal one place left). Then build from there: 5% is half of 10%, 20% is double, 15% is 10% + 5%, 25% is a quarter (or 10% + 10% + 5%). For trickier values, round to a nearby clean percentage and adjust. 18% of 60? Close to 20% of 60 = 12, minus 2% of 60 = 1.20, so 10.80. Within a cent of the calculator answer (10.80).

Why does this calculator not need a currency?

Because percentages are pure ratios — they have no units. 25% of "200 apples" is "50 apples"; 25% of "$200" is "$50"; 25% of "200 miles" is "50 miles". The math is identical regardless of what the numbers represent. Add your own units mentally to the result — the calculator just handles the math.

How accurate are the results?

To 2 decimal places for most results, 4 decimal places for values smaller than 1. JavaScript handles the arithmetic with standard double-precision floating point, which is accurate to about 15 significant digits — more than enough for any everyday percentage calculation.