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…
no answer
your shape
Lift the hood: the exact window, the exact arithmetic
link copied
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.
parameter
values
meaning
h
a positive number
one side
w
a positive number
the other side (order does not matter)
unit
cm mm m in ft px pt
display only: units cancel out of a ratio
r
a positive number
a bare proportion, used when h and w are absent; below 1 it is inverted
eps
0.1 to 12
the 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.