Percentage Calculator
Calculate what X% of Y is, what percent X is of Y, or the percentage change between two values. Three modes in one calculator, with clear step-by-step explanations.
How It's Calculated
Formula
\text{What is X\% of Y?} \quad R = \frac{Y \times X}{100}\\ \text{X is what percent of Y?} \quad R = \frac{X}{Y} \times 100\\ \text{Percentage change} \quad R = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100"Percent" literally means "per hundred" — a percentage is just a ratio expressed as a fraction of 100. This calculator handles the three most common percentage questions people actually need answered. "What is X% of Y?" scales a base number Y by a percentage X — for example, a 20% tip on a $50 bill. "X is what percent of Y?" turns a part-to-whole relationship into a percentage — for example, 25 correct answers out of 200 questions. "Percentage change from original to new" measures relative growth or shrinkage between two values over time — for example, a price that moved from $100 to $150. Percentage change is a RELATIVE measure: the same absolute change means a very different percentage change depending on the starting point, and a decrease is expressed as a negative percentage, not rejected as invalid. This calculator never caps a result — 300% of a number, or a 400% increase, are both mathematically valid outputs, not errors.
Worked Examples
What is 20% of 50?
- Formula: R = Y × X / 100
- Substitute: R = 50 × 20 / 100
- R = 1000 / 100 = 10
- 20% of 50 is 10.
What is 150% of 200? (above 100%, still valid)
- Formula: R = Y × X / 100
- Substitute: R = 200 × 150 / 100
- R = 30000 / 100 = 300
- 150% of 200 is 300 — a percentage above 100% simply means more than the whole base value.
25 is what percent of 200?
- Formula: R = X / Y × 100
- Substitute: R = 25 / 200 × 100
- R = 0.125 × 100 = 12.5
- 25 is 12.5% of 200.
150 is what percent of 100? (above 100%, still valid)
- Formula: R = X / Y × 100
- Substitute: R = 150 / 100 × 100
- R = 1.5 × 100 = 150
- 150 is 150% of 100 — the part is larger than the whole it's being compared to.
Percentage change from 100 to 150 (an increase)
- Formula: R = (New − Original) / Original × 100
- Substitute: R = (150 − 100) / 100 × 100
- R = 50 / 100 × 100 = 50
- Going from 100 to 150 is a 50% increase.
Percentage change from 200 to 150 (a decrease)
- Formula: R = (New − Original) / Original × 100
- Substitute: R = (150 − 200) / 200 × 100
- R = -50 / 200 × 100 = -25
- Going from 200 to 150 is a 25% decrease — the negative sign indicates a decrease, not an error.
Frequently Asked Questions
What does "percent" actually mean?
"Percent" comes from the Latin "per centum," meaning "per hundred." A percentage is a way of expressing a number as a fraction of 100 — 25% literally means 25 out of every 100, or 0.25 as a decimal fraction. Multiplying by a percentage is the same as multiplying by that fraction: 20% of 50 is the same calculation as 0.20 × 50.
What is "percentage change," exactly?
Percentage change measures how much a value has grown or shrunk RELATIVE to its starting point: (New − Original) / Original × 100. It answers "by what percent did this move?" rather than "what is the new value?" A positive result means an increase; a negative result means a decrease. The calculation is undefined (division by zero) when the original value is exactly 0, since there's no baseline to measure the change against.
What's the difference between "percentage points" and "percentage change"?
This is one of the most common sources of confusion in percentage math. "Percentage points" is a simple SUBTRACTION between two percentages. "Percentage change" is a RELATIVE change, calculated by dividing that difference by the original value. For example: going from 20% to 25% is a 5 PERCENTAGE-POINT increase (25 − 20 = 5), but it is a 25% RELATIVE increase, i.e. percentage change ((25 − 20) / 20 × 100 = 25%). Both statements describe the exact same move from 20% to 25% — they are not competing answers, they are answers to two different questions. Mixing them up (e.g. reporting a rate that "increased by 5%" when it actually moved from 20% to 25%, a 5-point/25%-relative move) is a common and misleading error in news reporting and casual conversation.
Why can a percentage be over 100%?
A percentage over 100% just means "more than the whole" it's being compared to. "What is 150% of 200?" (=300) means one-and-a-half times 200. "150 is what percent of 100?" (=150%) means the part (150) is larger than the whole (100) it's being measured against. Neither case is an error — this calculator never artificially caps a result at 100%.
Why does this calculator reject some inputs as invalid?
"X is what percent of Y?" and "Percentage change" both involve dividing by one of your input values (Y, or the original value, respectively). Dividing by zero is mathematically undefined, so this calculator explicitly rejects a zero denominator with a clear error message rather than returning a nonsensical result like Infinity or NaN. A negative percentage change (a decrease) is NOT rejected — only a zero denominator is.