Math calculators

Every math calculator here follows the same rules: results update live as you type, the formula is shown with a worked example, and the math runs entirely in your browser — nothing you enter is uploaded anywhere. Each one is unit-tested against published reference values before it ships.

The three percentage questions, and why they get mixed up

Almost every percentage mistake comes from solving the wrong one of three distinct questions. "What is 15% of 240?" is finding a part from a whole. "36 is what percent of 240?" is finding a rate from two known quantities. "36 is 15% of what?" is recovering the whole from a part — and it is the one people most often attempt by adding or subtracting a percentage, which is wrong. The percentage calculator does all three explicitly, labelled, so you can see which question you are asking before you trust the answer.

The classic trap is percentage increase and decrease not cancelling. A price raised 20% and then cut 20% does not return to where it started: it ends 4% lower, because the second percentage is taken from a larger number. This is not a curiosity — it is the arithmetic behind a great many misleading discount claims, and behind investment returns where a 50% loss needs a 100% gain to recover.

Ratios, proportions and the rule of three

The rule of three is the oldest calculator on this list and still the most useful: three known quantities, one unknown, solved by cross-multiplication. Scaling a recipe from four people to seven, converting a map distance, working out how much paint a larger wall needs — all the same operation. Ratio problems are the same machinery with the parts named differently, and the common error is confusing a ratio with a fraction: mixing something 1:3 means one part in four total, not one part in three.

Rounding, precision, and false confidence

A calculator will happily hand you eight decimal places, and most of them are noise. If you measured a room to the nearest centimetre, an area given to a square millimetre is not more accurate — it is falsely precise, and false precision is how a rough estimate gets treated as a survey. A reasonable habit is to carry full precision through intermediate steps and round only the final answer, to roughly the precision of your least accurate input.

It is also worth knowing that rounding money at each step and rounding once at the end can produce different totals. Across a single invoice the difference is cents; across a year of them it is the sort of discrepancy that costs an afternoon to find.

Averages: mean, median and which one is lying to you

The mean is what people mean by "average", and it is the wrong summary whenever the data has a long tail. One outlier drags a mean a long way — the standard illustration is a room of ordinary earners and one billionaire, where the mean income describes nobody present. The median, the middle value, is unmoved by that outlier and is usually the more honest single figure for incomes, house prices and response times. Our average calculator shows both, because the gap between them is itself the useful signal: when mean and median are close the data is fairly symmetric, and when they are far apart something at one end is doing the talking.