Guides — FocalMath

Each calculator's own page has a "how to read this result" section, but that's necessarily short — it explains your specific number, not the whole concept behind it. These guides go deeper: where a formula comes from, why it's shaped the way it is, and where the common misunderstandings actually happen, with real worked examples throughout.

Understanding Depth of Field covers the thin-lens math behind near and far sharp limits and why hyperfocal distance isn't just "a big number for landscapes." Understanding the Exposure Triangle explains why the three variables trade off the way they do, and why the metaphor of a "triangle" is useful but slightly misleading. Understanding Astro Shutter-Speed Limits walks through why the 500 rule is a rough approximation and what the NPF rule adds. Understanding Crop Factor and Lens Equivalence untangles field-of-view equivalence from depth-of-field equivalence — the single most commonly confused pair of numbers on this entire site. Understanding Print Resolution explains why the "right" DPI for a print depends entirely on how far away someone will stand to look at it.

None of these guides restate a calculator's own explainer section word for word — they're written to add the reasoning a results page doesn't have room for, and each one links back to its matching tool once you understand the concept well enough to want the number.

If you're new to photography math generally, Understanding Depth of Field is the best starting point — it introduces circle of confusion, which quietly underlies more of this site's calculations than any other single concept, and the reasoning there carries forward into how the astro and crop-factor guides are explained as well. Each guide stands on its own, so feel free to jump straight to whichever concept is actually giving you trouble right now, rather than reading front to back.