Guides & explainers
Plain-language writing about the maths behind everyday decisions — what the formulas mean, where they mislead, and how to check the numbers yourself.
Why computers count in binary — and where hexadecimal fits in Binary is not arbitrary and hexadecimal is not a separate system. Why both exist, why 255 turns up everywhere, and why your 1 TB drive shows as 931 GB. Read the guide HEX, RGB and HSL: three ways of writing the same colour Every screen colour is a mix of red, green and blue light. HEX and RGB write it one way, HSL another — and one of them is far easier to work with. Read the guide What inflation quietly does to money sitting in the bank Cash does not lose value visibly — the balance never drops. But at 4% inflation, money left idle for a decade buys about a third less than it did. Read the guide Cups versus grams: why the same recipe fails twice A cup measures volume, and flour packs. That single fact explains most baking failures — plus three different cup sizes still in everyday use. Read the guide Heart rate zones: what the five bands actually mean Training zones are percentages of your heart rate reserve, not of your maximum. Here is what each band trains, and why the fat-burn zone is misunderstood. Read the guide What "feels like" temperature actually measures Wind chill and heat index are not adjusted thermometer readings. They estimate how fast your body loses or fails to lose heat — two different mechanisms. Read the guide Why fractions beat decimals more often than you think Decimals feel modern and fractions feel like school. But a third has no exact decimal, and that gap explains recipes, spanners and rounding errors. Read the guide When the average lies: mean, median and what spread tells you A single average can hide almost everything about a data set. Here is when the mean misleads, why the median resists it, and what standard deviation adds. Read the guide Break-even: the first number a small business should know Break-even tells you how many sales cover your costs. Here is how to work it out, and why raising price beats cutting overheads almost every time. Read the guide Three percentage questions almost everyone gets wrong Percentages seem simple until they are stacked, reversed or applied to a total that already includes them. Here are the three traps, and how to avoid each. Read the guide Unit price: the number supermarkets would rather you ignored Bigger packs are not always cheaper per unit. Here is how to compare sizes in seconds, and the packaging tactics that make comparison deliberately hard. Read the guide Why your 100 Mbps connection downloads at 12 MB/s Internet speeds are sold in bits and files are measured in bytes. Here is the factor of eight, what else slows a download, and how long files really take. Read the guide What is actually costing you on your electricity bill Appliance wattage matters far less than how long it runs. Here is what actually drives a bill, and where switching things off genuinely pays. Read the guide How a loan EMI is built — and why early payments are almost all interest Your monthly repayment never changes, but what it is made of shifts every month. Understanding amortisation shows why overpaying early saves so much. Read the guide The 3-4-5 rule: checking a right angle without a set square Builders have squared corners with a knotted rope for millennia. Here is the maths behind the 3-4-5 triangle and how to use it on a real job. Read the guide The metric-imperial conversions actually worth memorising You do not need conversion tables for everything. A handful of anchors, plus two mental tricks, cover almost every day-to-day conversion. Read the guide How a poll of 1,000 people can speak for millions Sample size depends on the precision you want, not the size of the population. Why 1,000 responses is enough, and what a margin of error really means. Read the guide Why minimum credit card payments keep you in debt for years Minimum payments cover the interest and little else. What a $5,000 balance really costs at each payment level, and why $5 a month changes everything. Read the guide Calories explained: where BMR, TDEE and your daily number come from Calorie targets are built from two numbers: what your body burns at rest, and how much you move. Here is how each is estimated and how far to trust the result. Read the guide Estimating paint, tiles and concrete without running short Material estimates fail in predictable ways. How to work out what a job needs, how much waste to allow, and why running short mid-pour is costly. Read the guide BMI: what it measures, and four things it cannot tell you BMI is a useful population screening tool and a blunt individual one. Here is what the number means, where it misleads, and what to look at alongside it. Read the guide Compound interest, explained with numbers you can check yourself Why time matters more than rate, what compounding frequency really changes, and the Rule of 72 — with worked figures you can verify. Read the guide Margin vs markup: the pricing mistake that quietly costs you money Margin and markup describe the same profit against different baselines. Confusing them leads to underpricing — here is the difference, with a conversion table. Read the guide