Practical guides on the math behind our tools: how the formulas work, when to use which number, and common mistakes to avoid. Each guide is written to be usable on its own — the formula is shown in plain terms, worked through with realistic numbers, and checked against the named sources listed on the page.
The site is built around a simple rule: every calculation shows its method, and every result carries its formula, its assumptions, and its limitations. These guides extend that rule to the decisions the tools support — pricing a product, estimating a material, sizing an image, or scheduling across time zones. If a guide contains an error or an assumption that does not hold for your case, the correction prompt on each post goes straight to the contact page, and corrections get a direct answer.
Strings like SGVsbG8= look like a secret code, but they are plain text wearing a costume. Base64 just makes bytes text-safe — anyone can decode it in seconds, with no key. Here is what the alphabet and padding mean, where the format is genuinely useful, and how to spot when something is actually encrypted.
Break-even is fixed costs divided by contribution margin. Here is the two-step formula every small business can run — in units and in revenue — with worked examples for products and services, and the assumptions to check before you trust the number.
The compound interest formula has four moving parts, and n — how often interest is credited — is the one people overestimate. Here is what each term does, with worked numbers for annual, monthly, and daily compounding.
Every renovation estimate is the same three steps — measure the area, add waste, round up to whole units. Here is the method behind concrete bags, tile boxes, and flooring packs, with the waste percentages that separate a smooth install from a trip back to the store.
JSON is how modern programs hand data to each other — and it is just text with three rules: braces for objects, brackets for lists, quotes for names. Here is how to read one, why it is so strict, and what the formatting tools actually change.
Every fixed-rate loan payment splits into interest and principal, and the split changes every month. Here is the formula behind the schedule, with a full worked example for a car loan and the one comparison that matters before you sign.
JPEG, PNG, and WebP are not three knobs on the same machine — they are two different contracts about what a compressed file owes you. Here is what lossy and lossless actually discard, why a PNG resists 'quality' sliders, and how to pick a format by what the image must survive.
The enemy is not your memory — it is predictability. Here is why human-made passwords fail, what entropy actually measures, the passphrase strategy that fixes both problems, and what a password generator is doing when it shows you a bit count instead of a strength meter.
A 50% increase followed by a 50% decrease does not return you to the start — it leaves you 25% down. Here is why percentage changes do not reverse, how to undo a change correctly, and the percentage-points-vs-percent distinction that trips up every discount comparison.
Backups at 3 AM, reports on Mondays, health checks every quarter hour — all of them are five fields of text: minute, hour, day of month, month, day of week. Here is how to read and write cron expressions, the two traps that make them fire at the wrong time, and why the next-run check is the one that catches both.
BMI is a screening measure, not a diagnosis — a height-and-weight ratio that flags where further attention may be warranted. Here is the formula, the WHO classification, what the number genuinely captures, and the limits it cannot capture, so the result can be read without overreacting in either direction.
The instant is global; the wall time is local — and 'meet at 9' only works if everyone means the same 9. Here is how UTC fixes the ambiguity, how offset math works, and why daylight-saving transitions make even agreed times quietly shift for weeks each year.
One US gallon covers about 350 square feet per coat. Here is the two-step formula — wall area × coats ÷ coverage — that tells you exactly how much paint to buy, with room-by-room examples.
Margin is profit as a share of revenue; markup is profit as a share of cost. Here is why the two numbers differ, when each is the right one to use, and how to convert between them.