The three modes
A percentage is just a fraction expressed out of 100, and most everyday percentage questions fall into one of three shapes. This tool covers each one so you do not have to rearrange the formula yourself.
"X% of Y" finds a portion of a number. "X is what % of Y" turns two raw numbers into a share. "Percent change from X to Y" measures how much a value grew or shrank relative to where it started.
- X% of Y: multiply Y by X divided by 100.
- X is what % of Y: divide X by Y, then multiply by 100.
- Percent change: divide the change by the starting value, then multiply by 100.
Reading the result
In "X% of Y" mode the answer is a plain number — the size of the portion. In the other two modes the answer is itself a percentage.
For percent change, a positive result is an increase and a negative result is a decrease. Note that a rise followed by an equal-looking fall does not cancel out, because each percentage is measured against a different starting point.
Practical tips
Percentages are everywhere in money decisions, from tips and sales tax to discounts and interest. Knowing which mode you need is half the battle.
- For a discounted price, find the percent of the original and subtract it.
- To reverse a percentage increase, divide by 1 plus the rate, not by the rate itself.
- Percentage points and percent change are different — a jump from 10% to 12% is 2 points but a 20% increase.
Common mistakes
The most common slip is choosing the wrong base. Percent change must always be measured against the original starting value, not the new one, or the result will be distorted.
- Do not mix up the order of the two values in percent change.
- Dividing by zero is undefined, so the relevant base cannot be zero.
- A 50% drop needs a 100% rise to recover, not another 50%.
Formula
percentOf = value1/100 · value2; isWhatPercent = value1/value2 · 100; percentChange = (value2 − value1)/value1 · 100