Plumbing Math Practice Test

Plumbing mathematics is the most reliably scoreable section on any licensing exam because nothing in it is a matter of recall. Every answer can be checked by redoing the arithmetic. The topics are narrow and they repeat: right-triangle geometry for offsets, percentage and fraction work for grade, cylinder volume for pipe and tank capacity, and unit conversion threading through all of it.

Offset calculations are the signature plumbing math problem. A 45 degree offset has a travel equal to the offset multiplied by 1.4142, and the set-back equals the offset. The constants for the other common fitting angles are worth memorising as multipliers of the offset: 1.4142 for 45 degrees, 2.0 for 30 degrees, 1.1547 for 60 degrees, and 2.6131 for 22½ degrees. Rolling offsets add one step: find the true offset from the horizontal and vertical offsets with Pythagoras first, then apply the fitting constant to that.

Grade and fall questions convert between three expressions of the same thing: inches per foot, percent and total fall over a run. A quarter inch per foot is 2 percent; an eighth is 1 percent. Total fall is grade multiplied by run, so a 64 foot run at 1/8 inch per foot falls 8 inches. Reading the question for which of the three it wants is most of the work.

Volume questions come down to the cylinder: V = π r² L, with the answer usually wanted in gallons, so the 7.48 gallons per cubic foot and 231 cubic inches per gallon conversions have to be ready. For pipe capacity the useful shortcut is that gallons per foot equals the internal diameter in inches squared, divided by 24.5: a result you can derive on the spot if you remember where it comes from, which protects you when the question is set up slightly differently than you expect.