Tools · canvas proportions · four catalogues, counted separately

Canvas Ratio

You have a rectangle: a canvas you are about to stretch, a frame, a photo crop, a screen. How common is that shape among real paintings? Type the two sides in any units and either order and this counts, in four open museum catalogues separately, how many catalogued paintings sit within your chosen tolerance of your proportion, whether that proportion is a crowded one or a gap between crowded ones, and the simplest whole-number ratio your rectangle matches. It is a lookup into the measurements themselves, done in your browser.

A percentage of catalogued paintings is not a percentage of paintings. These are four collections of what somebody chose to acquire, keep and measure. They lean European and American, three of them are single museums, and the fourth is crowd-sourced. The counts below are exact. What they are counts of is the thing to keep in view, and it is set out at the bottom of this page.
1 · what shape is it?
Understood: 76.2 x 101.6 cm · 24 by 36 in · 29 3/4 x 41 · 1920x1080 px · 3:2 · 1.618. Units cancel out of a ratio, so they are carried for display only. Order does not matter either: shape here is the long side over the short side, so a portrait and a landscape of the same proportions are one shape. The A4 button fills in 210 x 297 mm, the real ISO 216 size, which is 1.4143: a whole-millimetre rounding of the square root of 2 the A series is defined by, and not the square root of 2 itself.
A museum label that gives one object twice, 30 x 43 in. (76.2 x 109.2 cm), is read both ways and answered only if the two readings agree to within one per cent. Two different units inside one measurement, 30 in x 40 cm, is refused: thirty inches is 76.2 centimetres, so a long side over a short side taken across two rulers is not a ratio of anything, and guessing which ruler was meant would be a number you could not check.
2 · how close counts as the same shape?
± 0.50%
This is the whole argument in one control. A window of half a per cent around 4:3 is narrower than the rounding in a catalogue that recorded whole centimetres; a window of ten per cent will catch a tenth of everything, everywhere. The count you get is a fact about your window as much as about your shape, which is why the window is yours to set and is printed with every answer.

reading the measurements…

The URL grammar (every answer here is a link)
The whole state of this page lives in the address bar, so any answer can be linked to directly and will come back exactly as it was.
parametervaluesmeaning
ha positive numberone side
wa positive numberthe other side (order does not matter)
unitcm mm m in ft px ptdisplay only: units cancel out of a ratio
ra positive numbera bare proportion, used when h and w are absent; below 1 it is inverted
eps0.1 to 12the tolerance, as a percentage, plus or minus
two sides · /tools/canvas-ratio/?h=76.2&w=101.6&unit=cm&eps=0.5
a bare ratio · /tools/canvas-ratio/?r=1.618034&eps=1
a refusal about a shape is linkable · /tools/canvas-ratio/?r=2.9&eps=0.5 lands on the page saying why it will not give you a neighbour percentile there. That works because a shape and a window are what this grammar carries, and the three refusals of that kind (past 3:1, window past 3:1, neighbourhood past 3:1) are decided from them alone.
a refusal about what you typed is not · the twelve refusals the reader of the box can produce (mixed units, a frame, several panels, an oval, a depth, a contradiction, a negative side and the rest) are about a string, and there is no parameter here that carries a string. So when the box cannot be read this page empties the address bar instead of leaving it pointing at the answer before it, which would be a link to something you are not being shown.
Both forms are read by decodeQuery in ratio-engine.mjs, and encodeQuery writes them. The verifier round-trips a spread of states through both.