Articles
Practical guides to the calculations behind everyday decisions: the formulas, worked examples, the assumptions each one makes on your behalf, and the mistakes that produce a confident-looking wrong answer.
Every article here starts from a question someone actually needs answered — what a pay rise is worth after inflation, whether the larger pack is really cheaper, how much a set of small subscriptions costs over a year, what a discount stacked on a discount actually comes to. Each one gives the formula, walks through a realistic example with numbers, and then does the part that matters most: explains where the calculation stops being reliable.
Where a calculator on this site covers the same ground, the article links to it, so you can read the reasoning first and then run your own figures. Results throughout are estimates for planning and educational purposes; rates, taxes, fees and personal circumstances change the outcome.
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The tax rate on your last dollar of income and the tax rate on your income as a whole are two different numbers, and confusing them is behind a persistent myth about raises pushing people backwards.
Every choice rules out an alternative, and the value of the best alternative not taken is the real cost of the choice you made. Here is how to put a number on it.
Profit is what's left after costs are subtracted from revenue, on paper. Cash flow is whether the money to pay this month's bills is actually in the account. A business can have one without the other.
The 50/30/20 rule is a starting point, not a law of budgeting. Here is how to calculate your own version of it, and what it means when your real numbers don't match.
Profit, markup and margin can describe the same sale with different percentages. This guide explains what each figure means, shows the formulas step by step, and uses practical examples to make the differences clear.
Small monthly charges are designed to feel small. Converting each to an annual figure, and then to a cost per actual use, changes how they look and usually how many you keep.
Fuel cost is distance divided by efficiency times price. The formula is easy; using your car's real consumption rather than its advertised figure is what makes the answer accurate.
Counting days sounds trivial until a deadline, a leap year or the question of whether to count the first day gets involved. Here is a method that holds up.
The simple version is savings divided by monthly spending. The useful version accounts for interest, inflation and whatever income continues — and often produces a very different number.
Multiplying by 2,080 is the quick version and it is wrong more often than it is right. Here is how to convert pay rates in a way that survives unpaid leave, part-time hours and contract work.
Bigger packs are usually cheaper per unit, but not always. Here is how to calculate unit price quickly, handle mismatched units, and factor in what you will actually use.
Avalanche costs less. Snowball finishes accounts sooner. Before choosing on principle, calculate the gap for your own debts — sometimes it is hundreds, sometimes it is a rounding error.
Read the assumptions and limitations section before trusting any number for a real decision. Most of these calculations are short — a division, a multiplication, occasionally an exponent — and the arithmetic is rarely where things go wrong. What goes wrong is using a figure that does not match the situation: an advertised fuel-consumption number instead of your own, a total-spending figure where essential spending was needed, or a rate quoted on a different basis from the one you are comparing it against.
Several of the articles overlap on purpose. Percentage change, reverse percentages and stacked discounts are the same underlying idea applied to three different problems, and reading two of them together tends to make the third obvious.