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📚 Guides · 12 definitive, math-honest explainers

Read this before you search again

The 12 guides below cover the topics the site's tools calculate. Each one is the "definitive source" on a single question — long enough to be useful, short enough to read in 10 minutes, with the math written out and the assumptions named.

Why these guides exist. The internet used to have a million small useful tools, and most of them were on a personal homepage. The modern search results for "calculate mortgage" or "what's my BMI" are dominated by sites that exist to harvest an email address, sign you up for a newsletter, or sell your output as a lead to a lender. There is no business model here. There is no newsletter, no lead form, no upsell, no pop-up. The whole point of the site is that the calculation is the product. These guides are the same: the answer is the answer; the math is the math; if the math has a known limitation, the page says so.
Money & finance · Definitive guide

How mortgages really work — and what your bank's calculator doesn't show you

The standard mortgage formula, the three things the bank's calculator never shows, and the honest way to use the numbers.

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Health metrics · Definitive guide

What BMI actually measures — and what to use instead

A population screening tool, not a personal one. The formula, the limits, and the four better metrics in rough order of cost.

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Personal finance · Definitive guide

Why compound growth is magic — and why the line goes up, not straight

Exponential growth, the rule of 72, and why the early saver always wins. The math, written out, with the assumptions named.

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Security & privacy · Definitive guide

How to choose a strong password — and why your browser already does the hard part

What makes a password weak, what makes it strong, and why your browser's built-in password manager beats the old advice.

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Code & data · Definitive guide

JSON for people who hate JSON — a practical guide for non-engineers

What JSON is, how to read it, how to spot the errors, and the tools that will format and validate it for you.

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Code & data · Definitive guide

Regular expressions without the pain — a 5-minute practical guide

The four characters that matter most, the syntax, and a worked example of a real regex from this site.

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Design · Definitive guide

How to pick a colour palette that doesn't look like a 2003 Geocities page

Two anchors, one accent, a small set of semantic colours. The art-school waffle removed.

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Design · Definitive guide

Image file formats explained — when to use PNG, JPEG, WebP, AVIF, or SVG

The wrong format bloats your page or makes the picture look like a 1998 webcam. The modern defaults.

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Music & audio · Definitive guide

BPM, tempo, and time signature — a 3-minute primer for the rest of us

BPM, tempo, time signature, and the free tools on this site that tap, count, tune, and build chords for you.

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Astronomy · Definitive guide

How to read a star chart — and pick a telescope that is not a waste of money

The eyepiece math, the Dawes and Rayleigh limits, and the free tools on this site that will calculate magnification and exit pupil.

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Writing & business · Definitive guide

How to write a cover letter, resume, or business email that someone will actually read

The four-part structure, the two phrases that should never appear, and the free tools that will proofread, paraphrase, and tone-check the result.

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Wellbeing · Definitive guide

How to breathe, ground, and calm down — three techniques that work in under 5 minutes

Box breathing, 4-7-8 breathing, and the 5-4-3-2-1 grounding technique. The physiology, when to use which, and the free tools that pace you through them.

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