Converting 1'x1'x1" would equal about .62 gallons.
as far as how deep the soil is watered is directly
related to you soil infiltration rate.
You can build your own double ring infiltrometer
or you can use these two links to estimate your soils I.R.

http://soils.usda.gov/technical/investigations/texture/

http://www.irrigation.org/certification/pdf/reference_golf_toro.pdf
(page 6)

remember this is per hour not per minute.

hope this helps.