Everyday Calculations & Conversions Made Simple

The first is confusing a percentage change with a percentage point change. If an interest rate moves from 2% to 3%, that is a rise of one percentage point and an increase of fifty percent. Both statements are true, they sound similar, and they differ by a factor of fifty. News coverage and internal reports mix them constantly, usually in whichever direction sounds more dramatic.

The second is assuming percentage changes cancel out. They do not, because each is applied to a different base.

The other routinely-needed operation is reversing a percentage: working out the original price from a discounted one, or the pre-tax figure from a total. The instinct is to subtract the percentage, and that is wrong. To remove 20% tax from a £120 total you divide by 1.2 to get £100, rather than subtracting 20% of £120 to get £96. Whenever you are undoing a percentage, divide.

Most conversions are a single multiplication — the ratio between two units of the same quantity. A few are not, and those are the ones that break things.

Temperature has an offset as well as a scale factor, because its scales do not share a zero. Celsius to Fahrenheit is multiply by 1.8 then add 32. The consequence is that a temperature difference converts differently from a temperature: a rise of 10°C is a rise of 18°F, not 50°F. Applying the full formula to a difference is a classic error in weather and engineering copy alike.

Two more worth watching. Fluid ounces differ between the US and the UK, so a recipe converted with the wrong one is off by about 4%, which matters in baking. And digital storage is quoted two ways: drive manufacturers use decimal gigabytes of 1,000,000,000 bytes while operating systems often report binary gibibytes of 1,073,741,824 — which is the entire explanation for why a 1 TB drive shows up as roughly 931 GB, and why nothing is missing.

Scheduling across time zones is harder than the arithmetic suggests, because the offset between two places is not a constant. It changes whenever either place enters or leaves daylight saving, and they rarely do so on the same date.

Europe and North America both shift their clocks, several weeks apart. For those few weeks each spring and autumn, the gap between London and New York is four hours rather than the usual five. A recurring meeting set to a local time in one city silently moves in the other, twice a year.

• →The southern hemisphere runs the opposite way. Sydney enters daylight saving as Europe leaves it, so the London–Sydney gap swings between eight and eleven hours over the year.
• →Not every zone is a whole number of hours from UTC. India is UTC+5:30, Nepal UTC+5:45, and parts of Australia UTC+9:30 — arithmetic that assumes whole hours produces meetings half an hour out.
• →Some regions have abolished daylight saving, some have adopted it recently, and dates change by legislation. Anything scheduled far ahead should be stored with its zone, not as a fixed offset.
• →Abbreviations are ambiguous. CST is Central Standard Time in North America, China Standard Time, and Cuba Standard Time, spanning fourteen hours of difference.

The reliable habit for anything important: agree the time in UTC, and let each participant convert. For a recurring meeting, confirm what happens at the two changeover weeks rather than discovering it.

Age in years is easy until it needs to be exact, at which point the calendar's irregularities surface. Months have different lengths, February changes length every four years, and there is no universally agreed answer to some of the edge cases.

Consider someone born on 31 January, one month later. Is that 28 February, or 3 March? Different systems answer differently, and both are defensible. The same ambiguity affects anyone born on 29 February, whose birthday exists in only one year out of four — jurisdictions differ on whether they legally age on 28 February or 1 March in other years.

This matters wherever an age determines eligibility: a pension date, an insurance band, a school year cutoff, a legal threshold. When a form asks for an exact age in years, months and days, it usually wants the count that a court would recognise, and the safe approach is to compute it from the dates rather than estimate from a year difference.

BMI is weight divided by height squared. It was devised in the 1830s as a way of describing populations, not individuals, and it remains genuinely useful for the former and consistently misleading for the latter.

The reason is that it cannot distinguish what the weight is made of. Muscle is denser than fat, so a well-trained athlete routinely registers as overweight or obese while carrying very little body fat. It also takes no account of where fat is distributed, which is the part most closely linked to health risk, and it systematically misreads people who are very tall or very short because the height-squared relationship does not hold across the whole range.

Calorie estimates carry the same caveat. BMR — the energy used at complete rest — is calculated from formulas fitted to study populations, and individual metabolic rates vary meaningfully around the prediction. Multiplying by an activity factor to reach TDEE adds a second estimate on top of the first. The result is a starting figure to adjust from based on what actually happens, not a target to trust to the calorie.

A display can serve as a ruler or a protractor, and it is genuinely useful for measuring something small to hand — a component, a print sample, a screw — when the actual instrument is elsewhere. It needs one thing first, and skipping it is why on-screen rulers get a reputation for being wrong.

A screen cannot know its own physical size. The browser reports dimensions in CSS pixels, and how many of those fall within a centimetre depends on the panel's pixel density and the operating system's scaling setting. The same page is therefore a different physical size on a phone, a laptop and an external monitor.

Angles are more forgiving, because an angle is a ratio and does not depend on scale. An on-screen protractor gives a usable reading without calibration, provided the display is not stretching the image non-uniformly. What does affect accuracy is viewing position: sighting an angle from off to one side introduces parallax, so look straight on.

Be realistic about precision. Screen measurement is good to roughly a millimetre in practice, which is fine for checking a size, identifying a fitting or confirming a print scale, and not fine for anything that has to fit precisely. When tolerance matters, this is a way to get close before reaching for the real instrument.

An aspect ratio is the relationship between width and height, and it is what determines whether an image fits a space or gets cropped. The common ones cluster in a few families: 16:9 for video and most screens, 4:3 for older displays and many camera sensors, 1:1 for social avatars, 9:16 for phone-native vertical video, and 3:2 for most stills from an interchangeable-lens camera.

The practical question is usually the missing dimension: given a required width, what height preserves the ratio? That is a single proportion, and getting it wrong produces either a stretched image or an unplanned crop through the middle of the subject.

Worth remembering when preparing anything for multiple destinations: shoot or design with margin around the subject, so the same asset can be cropped to several ratios without cutting into what matters. A composition framed tightly for 16:9 has nothing to give when the same image is needed as a square.