What this is

Ratio & Rule is a small toolkit for one connected problem: the relationship between pixels, proportions, resolution and physical dimensions. Nine calculators, each answering a question people actually arrive with, linked so you can follow a problem from one to the next without retyping anything.

Why it exists

Calculators for this material are plentiful and mostly frustrating. They bury the answer under explanation, assume a pixel density without saying so, round in ways they do not disclose, or attach confident quality verdicts to what is only a measurement. This site tries to be the opposite: answer first, show the geometry, explain the reasoning, and be honest about what it does not know.

How it works

  • Static pages, so they load immediately.
  • Calculations run in your browser. There is no server doing the arithmetic.
  • No account, no login, no uploads, no stored history.
  • Your inputs live in the URL, so refreshing keeps your work and a link reproduces it.
  • No advertising and no affiliate links.

Principles

  • Answer first. The calculator comes before the prose, not after it.
  • Never invent precision. Rounding is disclosed, and exact figures are shown alongside.
  • Distinguish fact from convention. An exact definition, a widely used working value and a calculated result are three different things.
  • Measure, do not judge. Density and dimensions are reported; quality verdicts are not.
  • Geometry is the illustration. Diagrams show relationships, not decoration.

Accuracy

The formulas used by each tool are printed on its own page, along with the assumptions they rest on. Where a value comes from outside the mathematics — the definition of an inch, ISO paper sizes, common print densities — the source is recorded on the methodology page.

If you find a result that looks wrong, the formula and assumptions on the relevant page are the fastest way to see what the calculator actually did.