Percentages without the guessing.

The three percentage questions, and how to tell them apart

Almost every percentage problem is one of three shapes. Mixing them up is the single most common arithmetic mistake people make with money, so the tool keeps them on separate tabs.

1. Pick the shape of the question. The tabs across the top are the three questions. "X% of Y" is a discount or a tip. "X is what %" is a share or a grade. "% change" is a rise or a fall between two numbers.
2. For X% of Y enter the rate and the amount. 15% of 240 is 36. This is the shape used for sales tax, a discount, a commission, or a down payment.
3. For X is what % of Y enter the part and the whole, in that order. 36 out of 240 is 15%. Order matters here: swapping the two gives 667%, which is a real answer to a different question.
4. For % change enter the old value first and the new value second. Going from 240 to 276 is +15%. Going the other way, 276 down to 240, is −13%, because the base changed. This asymmetry surprises people and it is the reason a 20% loss needs a 25% gain to get back to even.

When this comes up

• Reading a sale tag. Thirty percent off $85 is $25.50 off, so you pay $59.50. Doing this before you reach the till is the difference between a purchase and a regret.
• Checking a raise or a pay cut. A move from $52,000 to $58,000 is +11.5%. When someone offers "a 5% increase" and you want to know what that is in actual money, this is the tab.
• Working out a test score or a completion rate. "X is what % of Y" covers grades, survey response rates, uptime, and how much of a project is actually done.
• Comparing two changes that are not the same size. A 10% rise on a small number can be less money than a 3% rise on a big one. Percent change tells you the relative move; it does not tell you which one matters more.

Questions