The size of paintings.
When the artist has chosen the size of the painting, s/he will have thought about the effect that decision will make on the viewer. For example, a large canvas will make a more dramatic effect. Probably the viewer won't be able to take everything in at one view. They might even feel dwarfed by the canvas.
Joseph Wright of Derby probably wanted precisely that effect for some of his work.
Recent thinking about Monet's Water Lily canvases is that he wanted viewers to stand very close and be enveloped by the work.
Eruption of Vesuvius
120cm x 180cm
Joseph Wright of Derby
1775
When the patron (the person paying for the painting) chooses the size, a much more pragmatic factor comes into play:
"How much will it cost?"
This works both ways of course. If I have my portrait painted, life-size, by a leading artist then people will know I paid a lot for it. And full-length portraits cost more than half-portraits, which cost more than head and shoulders.
In the Renaissance, artists' contracts often stipulated the amount that would be paid per square metre of painting. Again, a larger painting displayed more wealth.
Water Lilies
200cmx 427cm
Claude Monet
post 1916
Ian McKellan
Clive Smith
2001
Lady with an Ermine
Leonardo da Vinci
1483
Mr and Mrs Andrews
Thomas Gainsborough
1750
Cocktail Party fact:
It was said that when Gainsborough found a sitter boring, he would introduce an animal into the painting to liven things up ...