Percentage Calculator
Percent of a value, what percent X is of Y, and percent change
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What this calculator computes
The percentage calculator handles the three percent-related questions that account for the overwhelming majority of everyday percent searches: "what is X% of Y?", "X is what percent of Y?", and "what is the percent change from X to Y?". Each mode targets a distinct real-world need. The first mode — X% of Y — is the calculation behind tip totals, discount values, sales-tax additions, ingredient scaling, and probability weighting; given a percentage and a base value it returns the dollar (or unit) amount that percentage represents. The second mode — X as a percent of Y — answers comparison questions: a 12 g serving of fat in a 60 g portion is 20% of the portion, a 350 student subgroup of a 1750 cohort is 20% of the cohort. The third mode — percent change from X to Y — calculates the relative increase or decrease between two values, the math behind year-over-year growth rates, sale-price savings, weight-loss progress, and stock returns. Percent change uses the original (older) value as the denominator, which means a $100 → $150 move is +50% but a $150 → $100 move is −33.3% rather than −50%; the asymmetry trips up many users and is one of the calculator's most common error sources. All three modes accept negative numbers and decimals and return signed results, so a percent change from 100 to 50 returns −50% rather than 50%, and a $40 tip on a $200 bill is correctly 20% rather than 0.2%.
Calculator
The formula
Formula
Mode 1: X% of Y = Y × (X/100) Mode 2: X / Y × 100 = ?% Mode 3: ((Y − X) / X) × 100 = % change
Worked example
When to use this calculator
Use this calculator any time you need to compute a percentage of a value, express one value as a percentage of another, or measure a relative change between two values. The most common day-to-day uses are computing sales tax and tip on restaurant bills, calculating discount savings on retail prices, scaling recipe ingredients up or down by a percentage, expressing test scores or survey responses as percentages of the total, and comparing year-over-year revenue or population changes. Mode 3 (percent change) is the right choice for trend analysis, before-and-after comparisons, and growth-rate reporting; mode 2 is the right choice for "what fraction of the total is this" questions; mode 1 is the right choice for any "compute X% of this" application. The calculator does not handle compound percent changes (a 10% gain followed by a 10% loss is −1% net, not 0%); for repeated compounding use the compound-interest calculator instead.
Common input mistakes
- Reversing the percent-change direction. A move from 100 to 50 is a −50% change, but a move from 50 to 100 is +100% — the same absolute difference produces different percent changes because the denominator (original value) is different. Mode 3 always uses the from-value (X, the older or starting value) as the denominator; swapping X and Y inverts the sign and changes the magnitude.
- Confusing percentage points with percent change. Going from 5% interest to 7% interest is a 2 percentage-point increase but a 40% percent change (2/5 × 100). Both phrasings appear in financial reporting and the difference matters: the headline "rates rose 40%" sounds far more dramatic than "rates rose 2 points" but they describe the same move.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage expressed as a decimal — that is, divide the percentage by 100 and multiply. To find 25% of 80: 80 × (25 / 100) = 80 × 0.25 = 20. The "of" in the phrase "25% of 80" always corresponds to multiplication, and translating "%" into "÷ 100" is the universal first step in any percentage calculation.
How do I find what percent X is of Y?
Divide X by Y and multiply by 100. To express 18 as a percent of 75: (18 / 75) × 100 = 0.24 × 100 = 24%. The denominator (Y) is always the whole or total — the value the question is asking "what fraction of". Reversing the order of division gives the inverse fraction and produces the wrong answer.
How do I calculate percent change?
Subtract the original value from the new value, divide by the original value, and multiply by 100: ((Y − X) / X) × 100. A change from 80 to 100 is ((100 − 80) / 80) × 100 = 25%; a change from 100 to 80 is ((80 − 100) / 100) × 100 = −20%. The denominator must always be the original (older, starting) value, not the new value.
Why is a 50% loss not undone by a 50% gain?
Percent changes compound multiplicatively against the running balance, not the original value. A $100 portfolio that drops 50% is worth $50; a 50% gain on $50 is +$25, leaving $75 — still 25% below the original $100. To recover from a 50% loss requires a 100% gain (doubling the post-loss balance). This asymmetry is fundamental to investment math and explains why drawdowns matter so much for long-term returns.
What is the difference between percentage points and percent change?
Percentage points measure the absolute arithmetic difference between two percentages, while percent change measures the relative ratio between them. An interest-rate move from 5% to 7% is a 2 percentage-point increase (7 − 5) but a 40% percent change ((7 − 5) / 5 × 100). Both are correct but mean different things — financial reporting often uses one or the other deliberately to under-state or dramatise the move.