I have a very nice loaf pan that I rarely use because of its size: 10 x 5 1/4". I'm never sure how to increase the proportions. If I follow the recipe exactly, the bread is too shallow.

Btw, Cakeometer is a nice app for round pans. I was surprised that it wouldn't allow me to change the shape. Thanks for all the answers and your common sense approaches.

I would use a baking pan volume chart (easily found online) and compare the volume of the 10 x 5.25" loaf pan to that of the prescribed pan, then multiply the recipe accordingly.
Since I couldn't find this size loaf pan on my chart, I figured its volume, first in cubic inches, then converted that to cups. I got 157.5 cu in (if height is est. 3") and 87.3 liquid oz, or about 11 cups.
As 8x4" loaf pan has about 6 cups capacity, and 9x5" loaf pan has 8 cups, adjust accordingly for the 11 cup pan if your recipe used one of those.
Or use the cakeometer, as rt21 suggested.

You really don't need to factor in the height, it'll just divide back out- the height of the loaves should be the same. It's really an easy calculation.

Oldunc - agree height not needed if moving between pans of sane shape.
But yes useful if moving between pans of different shapes (round, square, rectangle etc) and heights.

The depth will be a significant factor in the behavior of risen baked goods; if your pan is going to materially change the depth, you should either find another pan or adjust the recipe (which goes to the original question). Width can be a small factor, a round or square pan will bake slightly slower than a loaf, but isn't much of a worry. Also, of course, breads aren't bound by the depth of the pan, they'll usually rise above the top anyway.

The operative factor is the surface area, length x width. It should be simple to calculate the ratio of your pan to the pan called for in the recipe- you'll likely end up with some pretty odd fractions, but bread is very flexible and you only need to be fairly close. Your pan is 52.5 square inches. For example, if a recipe called for an 8 x 3 pan, the ratio would be 52.5 to 24, close enough to 2 to 1 not to worry about it.

Are you making yeast bread of quick bread? If yeast, I would double the recipe, fill the pan to your desired level and bake the rest in either another loaf pan or as free form loaves. After once or twice you can figure out if you need 1 1/2 or 1 3/4 times the recipe to fill your pan nicely.
With a quick bread you can't really do free form but can you bake the left over dough in a ramekin or some other oven safe pan? Good luck figuring it out.

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Since I couldn't find this size loaf pan on my chart, I figured its volume, first in cubic inches, then converted that to cups. I got 157.5 cu in (if height is est. 3") and 87.3 liquid oz, or about 11 cups.

As 8x4" loaf pan has about 6 cups capacity, and 9x5" loaf pan has 8 cups, adjust accordingly for the 11 cup pan if your recipe used one of those.

Or use the cakeometer, as rt21 suggested.

But yes useful if moving between pans of different shapes (round, square, rectangle etc) and heights.

With a quick bread you can't really do free form but can you bake the left over dough in a ramekin or some other oven safe pan? Good luck figuring it out.