Calculators

A calculator that hands you a number and says nothing else is asking to be trusted. These print the formula and every intermediate step instead, so you can check a result against your own understanding of the problem rather than against the reputation of the site that produced it.

Calculators rarely get the arithmetic wrong — they get the question wrong

Multiplication and division were settled a long time ago. When an online calculator disagrees with your accountant, your bank or your own spreadsheet, the cause is almost never a faulty sum. It is that the two of you were quietly answering different questions.

The usual culprit is the denominator. A percentage change divides by where you started; a percentage difference divides by the midpoint between two figures. A second discount applies to the already-reduced price, not the original one. A price that already includes tax has to be divided back out rather than multiplied. Every one of those is a decision about which number goes underneath the line, and not one of them is visible in a result that consists of a single figure in a large font.

The second culprit is rounding. Round each line of an invoice and then total it, and you get a different answer from totalling first and rounding once. Neither is wrong in the abstract, but they disagree — and when two systems differ by a few cents this is usually why, rather than a bug in either. A tool that shows its steps at least lets you see which convention it followed.

Formulas are not universal, and the differences are usually national

Body mass index is the same equation everywhere, but the thresholds that turn a number into a word like "overweight" are not: the cut-offs used across much of Asia sit lower than the World Health Organization defaults, because the relationship between the index and health risk varies by population. A calculator that prints a category without naming the standard it applied has hidden the only part that was actually a judgement.

Loan repayment is harder still. One nominal interest rate produces different monthly payments depending on whether interest compounds monthly or daily, whether the schedule holds the payment level or the principal level, and how the local regulator defines the annualised figure that must be advertised. Income tax is harder again, because brackets, allowances and the order of operations get rewritten by legislation every few years.

So the tools here name their formula and their assumptions on the page itself. Where an answer depends on a legal or medical standard rather than on arithmetic, that standard is stated, and the tool says plainly that what it produced is a calculation and not advice.

Why none of this needs a server

Arithmetic this small is the clearest case on the whole site for running on your own hardware. A percentage, a repayment schedule or a gap between two dates is a handful of operations that a browser finishes faster than a network round trip could begin.

A surprising number of calculator sites send your inputs away regardless. That is a business model rather than a technical requirement, because a request that reaches a server is a request that can be logged, attributed and sold against. And the inputs are often far more revealing than people assume: a loan amount, a salary, a due date or a body weight says a great deal about somebody even with no name attached to it.

These run in JavaScript that arrived with the page. After a first visit they keep working with the network switched off entirely — a useful side effect, and also the simplest proof available that nothing is being transmitted.

What a calculator on a website cannot do for you

It cannot know your circumstances. A tax figure derived from a headline rate ignores every allowance, deduction and special case that applies to you specifically, and those are usually where the real money sits. A repayment figure ignores arrangement fees, insurance requirements and early-settlement terms that can easily outweigh the interest gap between two offers.

It also should not be the thing a serious decision rests on. The right use of a tool like this is to learn the shape of a problem — how sensitive the answer is to each input, which direction a change pushes it, roughly what order of magnitude to expect — and then to carry that understanding into the conversation where the decision is actually made.