Well, after applying advanced reef fluid dynamics and displacement modeling, the net water volume of a reef aquarium can be approximated as:
V_net = ∭(Ω_wet) [1 − (ρ_rock + ρ_sand + ρ_equipment)] dV
− ΣV_plumbing
+ ∫(Q_RODI dt)
− ε_hanna
+ λ_reefkeeper
Where:
Ω_wet = the three-dimensional region actually containing water
ρ_rock = displacement density of “just a few pieces of live rock”
ρ_sand = displacement coefficient of the sand bed you promised would stay shallow
ρ_equipment = combined displacement factor of pumps, heaters, probes, frag racks,
magnetic cleaners, random clips, and mystery objects in the sump
ΣV_plumbing = cumulative water trapped in pipes, UV sterilizers, reactors, and fittings behind the stand
∫(Q_RODI dt) = total volume added during the initial fill (adjusted for membrane efficiency and snack breaks)
ε_hanna = alkalinity testing error after the second retest
λ_reefkeeper = hobbyist optimism correction factor
Boundary conditions:
Alk must be stable, ORP must be confusingly high,
and the reefer must have already ordered more coral.
OR: I would just go with 75-80% of manufacturer’s advertised volume.
However, I typically just round up to the nearest 100gal so I can be better than my neighbor Bob! lol