No black box. Here is the exact math behind every calculator on the site — volume, surface area, pump sizing, heating, cost — pulled straight from our calculation engine.
Every result on the site shows its own formula and a step-by-step walkthrough. This page collects them all in one place — and you can keep the PDF above as a reference. Figures are planning estimates, not engineering guarantees.
Every pool volume reduces to one idea: the area of the water surface times its average depth, converted to gallons.
All geometry is computed in feet and cubic feet; units convert only at the end. We use the precise 7.48051948 gal/ft³, not the rounded 7.5 (which over-estimates by ~0.26%).
Conversions used throughout:
| Cubic feet → gallons | 1 ft³ = 7.48051948 US gal |
| US → imperial gallons | 1 US gal = 0.83267384 imp gal |
| US gallons → litres | 1 US gal = 3.78541178 L |
| Cubic feet → cubic metres | 1 ft³ = 0.0283168466 m³ |
| Metric length → feet | 1 m = 3.28083989 ft |
| Water weight (heating) | 1 US gal = 8.34 lb |
| Water billing | 1 CCF = 748.051948 gal |
| Gas heating | 1 therm = 100,000 BTU |
Each shape computes the area of the water surface (the footprint), which then flows through the master formula with the mean depth below.
| Rectangle | Area = Length × Width |
| Round / circular | Area = π × (Diameter ÷ 2)² |
| Oval | Area = π × (Length ÷ 2) × (Width ÷ 2) |
| Triangle | Area = ½ × Base × Height |
| Kidney | Area = (Width A + Width B) × Length × 0.45Width A = widest bulge, Width B = narrowest. 0.45 is the industry-standard adjustment for the curved outline. |
| Roman | Area = Length × Width + π × (Width ÷ 2)²Rectangle plus the two semicircular ends (one full circle of diameter = width). |
| Grecian | Area = Length × Width − 2 × Cut²Rectangle with four 45° chamfered corners. |
| Surface area (direct entry) | Area = the surface area you enterFor plans/spec sheets that already list it — works on any shape. |
When you pick "I know my surface area", the number you enter replaces the shape formula above and feeds the master formula directly — so it works for any shape, from a plan or spec sheet.
The mean depth still comes from your floor profile (below): flat = depth; sloped = (shallow + deep) ÷ 2; hopper and spa as shown there.
The same result the calculator gives for a 385 sq ft pool with a shallow-to-deep floor.
The liner and solar-cover tools need the pool's interior surface — floor plus walls — not just the water surface. The walls use the perimeter, and a sloped floor covers more than its flat footprint.
Floor = the footprint area above. Walls = Perimeter × Wall height (the average water depth; for a spa, water-above-seats + footwell depth).
Perimeter drives the wall area:
| Rectangle | Perimeter = 2 × (Length + Width) |
| Round | Perimeter = π × Diameter |
| Oval | Perimeter = π(a+b) × [1 + 3h ÷ (10 + √(4 − 3h))]Ramanujan ellipse; a = L÷2, b = W÷2, h = ((a−b)÷(a+b))². |
| Triangle | Perimeter = Base + Height + √(Base² + Height²) |
| Roman | Perimeter = 2 × Length + π × Width |
| Grecian | Perimeter = 2 × (Length + Width) − 8 × Cut + 4 × Cut × √2 |
| Kidney | Perimeter ≈ Ellipse-perimeter(Length, avg width) × 1.1+10% for the concave waist. |
Run = pool length (or slope run on a hopper); Drop = Deep − Shallow. The floor follows the incline, so it covers more than its flat projection. Vinyl liner material = Interior surface × (1 + waste%).
The mean depth turns surface area into volume. Sloped and hopper floors are integrated properly, not approximated by a single number.
| Flat | Mean depth = Depth |
| Sloped | Mean depth = (Shallow + Deep) ÷ 2 |
| Hopper / deep-end | Mean depth = (S·d_s + T·(d_s+d_d)÷2 + D·d_d) ÷ (S + T + D)Flat shelf (run S), sloped transition (run T), flat deep bottom (run D), each weighted by its run. |
| Spa (seats) | Mean depth = Water-above-seats + FootwellFraction × Footwell-depthSeats displace the lower shell; footwell fraction defaults to 0.40. |
Unit-gallons: per 1,000 gal = 1000, per CCF = 748.052, per gallon = 1.
Default hose flow: ½" = 9 GPM, ⅝" = 12 GPM, ¾" = 18 GPM.
Defaults: 5,000-gal capacity, $350/load. Shows tap vs truck and flags the cheaper.
≤ 1/16" = evaporation; ≤ ¼" = possible leak; more = likely leak.
Cover-effect defaults to 0.95; evaporation defaults to 0.25"/day.
Heat reduction defaults to 0.50 (DOE quotes 50–70%).
Flow needed for a target turnover = Gallons ÷ (Target-hours × 60).
Motor efficiency defaults to 0.70. Monthly = ×30, yearly = ×365.
Per tier: Flow = Full-flow × Speed% ; Watts = Full-watts × Speed%³. Half speed → half flow but ~⅛ the power.
Equipment head defaults to 25 ft — often the largest term, and the one naive tools omit.
Q = GPM, d = pipe inside diameter (in). Pipe velocity (ft/s) = 0.4085 × GPM ÷ d² (flagged above ~5 ft/s).
Media rate (design / max GPM per ft², NSF 50): Sand 15 / 25 · D.E. 2 / 2.5 · Cartridge 0.375 / 1.
ΔT = temperature rise (°F). Loss factor defaults to 1.25. Gas cost = (BTU ÷ 100,000) × Price-per-therm.
Waste defaults to 10%. Gauge (lb/ft²): 20-mil 0.10 · 27-mil 0.135 · 28-mil 0.14.
Over-dig defaults to 1.5 ft. Swell: sand 12% · loam 22% · clay 30% · rock 50%. Truck trips = ⌈Loose ÷ 10–12 yd³⌉.
0.78 packing factor (circles can't tile a rectangle). Coverage target defaults to 75%.
Area per bather: shallow 15 ft² · deep 20 ft² · spa 10 ft². An estimate — your local health code governs.
Build cost is a low–high range. Resale value is deliberately not computed — it's too local to estimate honestly.
These are the exact formulas the calculators run, shown for transparency. Every result is a planning estimate — verify safety-critical or spending decisions (structural, chemical dosing, equipment) with a professional. Chemical dosing is intentionally not produced by these tools. See how it works for the reasoning behind each choice.