Guides

Explanations of the calculations behind the tools — why the arithmetic works the way it does, and where it usually goes wrong.

Every tool on Utilario gives you an answer. These guides explain the reasoning behind it. They exist because a result you do not understand is a result you cannot check, and most mistakes with everyday arithmetic come from a small number of genuinely counterintuitive rules — reversing a percentage, counting days inclusively, comparing prices measured in different units.

Each guide is written to be read on its own, without needing the tool, and links to the tools that do the same work automatically.

How to Work Out VAT BackwardsAdding VAT is easy. Taking it off again is where almost everyone goes wrong, because the obvious move — subtracting the VAT rate — quietly gives the wrong number every single time.
Percentage Points vs PercentIf an interest rate moves from 4% to 5%, has it gone up by 1% or by 25%? Both answers are defensible, they mean completely different things, and the ambiguity is exploited often enough that it is worth being able to spot.
Counting Days and DeadlinesAlmost every dispute about a deadline comes down to one question that nobody asked at the start: does the first day count? Get that wrong and you are out by one, which is usually the difference between on time and late.
Fuel Economy Units ExplainedFuel economy is quoted in at least three incompatible ways, two of them run in opposite directions, and the word "gallon" means two different volumes depending on which side of the Atlantic you are on.
Unit Pricing in the SupermarketThe assumption that buying bigger saves money is wrong often enough to be worth checking every time — and the shelf labels that are supposed to let you check are frequently designed to make it difficult.
Why Time Zone Offsets Keep ChangingThe difference between two cities is not a property of those cities. It is a property of the date, and for a few weeks each year it is not the number everyone has memorised.
How Much Paint Do I Need?The number on the tin is a laboratory figure for one coat on a smooth, sealed, similarly coloured surface. Almost nothing in a real house is any of those things, which is why people run out.
The Rules of Roman NumeralsRoman numerals look like they have one rule — put a smaller letter first to subtract — but that rule is much narrower than most people think, and almost every mistake comes from applying it too freely.
Word Counts and Reading TimeTwo programs will happily give you two different word counts for the same document, and neither is broken. They are answering slightly different questions, and knowing which one you need matters when a limit is enforced.