Pool Water Replacement Math: 4 Gallons per Bather and Dilution

The 2024 MAHC (5.6.7.4.2; check what your state adopted) requires at least 4 gallons per bather per day per venue to be discharged, or treated by an alternate system and reused. Backwash water counts toward that volume (5.6.7.4.2.1). Evaporation does not. Below: turning attendance into a gallon target, measuring backwash, and using the dilution formula to predict what a drain does to CYA, TDS and calcium.

What does the MAHC require, and what counts?

Annex 5.6.7.4 says 4 gallons is the minimum and 8 gallons per bather per day is recommended. Backwash counts. Evaporated water does not, because salts, metals and many organic contaminants stay behind and concentrate as water evaporates. In a pool system with several recirculation systems, replenishment must be proportional to the bathers in each system (5.6.7.4.3). Annex 4.7.4.1 says the 4 gallon figure is roughly half the 8 gallon number used abroad and is typically met by filter backwashing alone. It also says that "knowing pump GPM and knowing how much time one is backwashing" gives the volume discharged.

The daily attendance record (6.4.1.6 item 15) gives you the bather count. In pools where attendance is not ordinarily recorded, the Code allows a guest sign-in book.

How do you turn a week of attendance into a gallon target?

A made-up example: a 110,000 gallon HOA pool with two filters of 12.6 ft² each. The backwash rate must be at least 15 gpm per square foot unless the filter maker says otherwise (5.7.2.2.2), so 15 × 12.6 = 189 gpm per filter. Say we measure 190 gpm and backwash each filter for 4 minutes: 190 × 4 = 760 gallons per filter, 1,520 gallons for both. Both filters are backwashed on Wednesday and Sunday.

Day	Bathers	Required at 4 gal	Backwash gallons	Running balance
Mon	40	160	0	−160
Tue	55	220	0	−380
Wed	60	240	1,520	+900
Thu	75	300	0	+600
Fri	120	480	0	+120
Sat	260	1,040	0	−920
Sun	240	960	1,520	−360
Week	850	3,400	3,040	−360

The week is 360 gallons short at 4 gallons. At the Annex's 8 gallons, the target is 850 × 8 = 6,800 gallons, and the gap is 6,800 − 3,040 = 3,760 gallons, or 3.4 percent of the pool (3,760 ÷ 110,000). The Code says "per day," so Saturday alone is 1,040 gallons short. Whether your health department averages over a week is a question for them.

You can also measure an intentional drain from level. With 3,200 ft² of surface, each inch of level is 3,200 × (1/12) × 7.48 gallons per ft³ = 1,995 gallons.

What does the dilution formula predict?

When you remove a fraction f of the pool and refill with fill water, the new concentration is:

new = old × (1 − f) + fill × f

Draining 50 percent of a pool at 80 ppm CYA, refilled with CYA-free water, gives 80 × 0.5 + 0 × 0.5 = 40 ppm. The Annex 6.5.3.2.1 text agrees on the key point: draining alone changes nothing; the concentration falls only when fresh water goes in.

To find the fraction you need, rearrange: f = (old − target) ÷ (old − fill). Using the 110,000 gallon example, with these made-up readings:

Parameter	Pool	Fill	Target	f needed	After one 50% exchange
CYA	80 ppm	0	40	40 ÷ 80 = 50%	40 ppm
TDS	2,600 ppm	300	1,800	800 ÷ 2,300 = 34.8%	1,450 ppm
Calcium hardness	450 ppm	80	300	150 ÷ 370 = 40.5%	265 ppm

The TDS target comes from the Annex, which calls a TDS of 1,500 ppm above the fill water a generally accepted working figure (300 + 1,500 = 1,800). It says there is no scientific data for any maximum, and that TDS above 5,000 ppm might need a complete drain and refill or extra filtering, since a complete drain might damage some pools (Annex 5.7.4.6). The MAHC requires TDS testing quarterly (5.7.5.9). At 50 percent, the exchange moves 55,000 gallons. At an example water-and-sewer rate of 6 dollars per 1,000 gallons, that is 55 × 6 = 330 dollars.

Why does a partial drain never reach the fill-water level?

Each exchange removes the fraction f of whatever is left. After n equal exchanges of 10 percent each:

C(n) = fill + (old − fill) × 0.9ⁿ

For CYA 80 ppm with CYA-free fill, five weekly exchanges of 10 percent (11,000 gallons each, 55,000 in total) give 80 × 0.9⁵ = 80 × 0.5905 = 47.2 ppm. One 50 percent drain gives 40 ppm for the same 55,000 gallons. Smaller steps leave more behind because each later step drains water that already includes fresh fill. The (old − fill) gap shrinks every time but never reaches zero, and chemicals you add keep pushing it back up. Repeated small exchanges avoid a long closure; the one-time drain removes more per gallon.

The fill water sets the floor. Test it for calcium, alkalinity and TDS before you rely on the math. The Code requires fill water from a public water system, a source meeting the health department's rules, or an alternative the health department has approved (5.7.4.5). The Annex adds that municipal fill water may carry chloramines, and it recommends running the fill-water tests your jurisdiction requires once a year. If the fill is 250 ppm calcium, a 300 ppm target is almost out of reach and the Annex advises lowering pH or alkalinity to improve the saturation index instead (Annex 5.7.4.6). Makeup water must come through an air gap or other approved backpressure device (4.7.1.4.6.2), and the Code requires discharge through an approved air gap and in line with local rules (5.6.7.3.1 to 5.6.7.3.3).

Which problems does dilution fix?

Problem	Dilution fixes it?	Notes
High CYA	Yes, it is the only way	The Annex says CYA falls only by dilution. The MAHC limit is 90 ppm (5.7.3.1.3.2); at 300 ppm the pool closes (5.7.3.1.3.3). Stop adding stabilized products.
High TDS	Yes	The Annex says filters do not remove dissolved solids.
High calcium	Only down to fill-water level	If the fill is hard, work on pH and alkalinity
Chronic combined chlorine	Sometimes	Above 0.4 ppm the Code requires action, which may include superchlorination, water exchange or better bather hygiene (5.7.4.4.2). Compare costs.
Cloudy or dull water from suspended solids	No	That is a filtration problem; see cloudy water

For the combined chlorine row, compare the cost of the chemical fix with the water you would replace. Replace the example rate with your own bill, including sewer charges for what you discharge. Check where discharge may go under your local law.

How does this change by pool class, season and site count?

At the minimum rate, how fast does each class replace its water? Days to replace once = volume ÷ (daily bathers × 4). Example numbers:

Class (example)	Volume	Bathers per day	Gallons per day at 4	Days to replace once
Spa	600	25	100	6
Wading pool	1,500	30	120	12.5
Indoor lap pool	80,000	100	400	200
HOA pool (850 a week)	110,000	about 121	486	226

CDC's operating page advises draining and replacing all or part of hot tub water weekly to monthly, which roughly matches the spa row. Large pools take most of a year at the minimum. An outdoor pool that gets a seasonal drain resets itself. An indoor pool that never does keeps accumulating CYA, TDS and calcium, so plan its exchange on the calendar. Evaporation raises concentrations without removing anything. EPA's WaterSense page says pools lose water through evaporation, cleaning, leaks and splashing, and that a cover can prevent up to 95 percent of evaporation. See also leak versus evaporation.

Across 10, 30 or 60 pools, keep one sheet per pool with volume, weekly bathers, required gallons at 4 and 8, backwash gallons, last CYA, TDS and calcium readings, and the fill-water numbers. Sort by shortfall. In the logs, look for pools with high CYA or TDS and no discharge record. Add discharge volume to the daily log next to attendance and backwash time (6.4.1.6 items 9 and 15). Poolean lets lifeguards enter patron counts from a phone and lets you export logs as CSV. For chemical use planning, see usage forecasting and operating cost comparisons. To talk it through, book a 30-minute call.

The short version

• The MAHC minimum is 4 gallons per bather per day per venue, with 8 recommended in the Annex. Backwash counts; evaporation does not.
• Get gallons from bathers × 4 (or 8), and backwash gallons from gpm × minutes. The gap is your intentional drain.
• Dilution: new = old × (1 − f) + fill × f. The fraction needed is (old − target) ÷ (old − fill).
• Partial drains never reach the fill-water level, and the fill water's own calcium, alkalinity and TDS set the floor.
• Use dilution for high CYA and TDS. Treat calcium, combined chlorine and cloudy water on a case-by-case basis.