Pump Flow GPM Formula
Positive-displacement pump output is geometry times speed: Q(gpm) = D(in3/rev) x N(rpm) / 231, derated by volumetric efficiency. Use the working pump flow and horsepower calculator to get flow, shaft power and heat together.
The formula
231 cubic inches per gallon converts displacement-per-rev times speed into gpm; metric is Q(L/min) = D(cc/rev) x N / 1000:
Q = D * N / 231 [gpm, in3/rev, rpm]
Volumetric efficiency
Real pumps leak internally: multiply by eta_v (commonly 0.85-0.97, falling with pressure and wear). Flow loss at pressure is the classic wear signature.
Power follows
Shaft power is flow times pressure over efficiency - the working calculator returns gpm, hp and the heat the inefficiency becomes.
Frequently asked questions
Why 231?
There are exactly 231 cubic inches in a US gallon, so in3/rev times rev/min divided by 231 is gal/min.
Does pressure change pump flow?
Ideally no (positive displacement), practically yes - internal leakage grows with pressure, which is what volumetric efficiency captures.
Related pages
- Pump flow & HP calculator - flow, shaft power and efficiency together.
- Hydraulic motor torque calculator - the same equation driven backward.
- Cylinder speed calculator - where the flow ends up.