How We Calculate
This page lists the methods, constants and assumptions behind every calculator on Pool Calculus, so you can check our work or reproduce it.
Units and concentrations
All chemistry uses parts per million (ppm), which in pool water is the same as milligrams per litre. A dose in grams is ppm × litres ÷ 1,000. We convert with 1 US gallon = 3.785 litres, 1 cubic foot = 7.48 gallons and 1 lb = 453.6 g (NIST). Alkalinity and calcium hardness are counted “as calcium carbonate”, the standard used by pool test kits.
Chemical products
| Product | Strength we assume | Side effects we track |
|---|---|---|
| Liquid chlorine and bleach | Label % read as grams of available chlorine per 100 mL | About 1.65 ppm salt per 1 ppm chlorine |
| Cal-hypo | 65% or 73% available chlorine | 0.71 ppm calcium hardness per 1 ppm chlorine |
| Dichlor | 56% or 62% available chlorine | 0.91 ppm CYA per 1 ppm chlorine |
| Trichlor | 90% available chlorine | 0.61 ppm CYA per 1 ppm chlorine |
| Muriatic acid | 31.45% (density 1.16) or 14.5% (density 1.07) | Lowers alkalinity as well as pH |
| Dry acid | Sodium bisulfate, 93.2% | Adds sulfate |
| Baking soda, soda ash | 100% sodium bicarbonate, sodium carbonate | Both raise alkalinity |
| Calcium chloride | 77% flakes or 94% pellets | Adds chloride |
The side effects come from the molecules themselves. For example, trichlor carries three chlorines for each cyanuric acid, so each ppm of chlorine brings 129.07 ÷ (3 × 70.9) = 0.61 ppm of CYA. Orenda’s figure of 6 to 6.5 ppm CYA per pound of trichlor in 10,000 gallons matches this.
pH and alkalinity
Acid and soda ash doses come from the carbonate equilibrium, not a fixed rule of thumb. From your pH, total alkalinity, CYA and any borates, we work out how much carbonate is in the water, then how much acid or base moves it to the target pH. The equilibrium constants are the Plummer and Busenberg (1982) equations, adjusted for water temperature and for dissolved solids with the Davies equation. Cyanurate (pKa 6.88) and borate (pKa 9.24) buffering are included, which is why a pool with high CYA needs a little more acid for the same pH drop.
As a check, the model reproduces the standard figures: 25.6 fl oz of 31.45% muriatic acid lowers total alkalinity by 10 ppm in 10,000 gallons, and 1.4 lb of baking soda raises it by 10 ppm.
Chlorine targets
Recommended free chlorine levels come from the Trouble Free Pool FC/CYA chart, interpolated between its rows. Below 20 ppm CYA we use the CDC minimums (1 ppm without stabilizer, 2 ppm with it). The breakpoint shock target is free chlorine plus 10 times combined chlorine.
Saturation index
LSI = pH − pHs, with pHs = (9.3 + A + B) − (C + D), where A depends on dissolved solids, B on temperature, C on calcium and D on carbonate alkalinity. We subtract cyanurate alkalinity from the total alkalinity first, as Orenda and Taylor recommend. Our result for Orenda’s published example comes out within 0.01 of theirs.
Evaporation
Outdoor evaporation uses the equation fitted by Smith, Löf and Jones to measurements from an unoccupied outdoor pool, as reviewed by Shah in ASHRAE Transactions (2014): evaporation = (70.3 + 0.314 × air speed) × (vapour pressure at the water − vapour pressure in the air) ÷ latent heat. Its coefficients are 74% of the ASHRAE indoor equation. A cover is assumed to cut evaporation by 90% while it is on, the low end of the EPA’s figures.
Heaters and pumps
Heater size follows the U.S. Department of Energy: output in Btu per hour = surface area × temperature rise × 12, which assumes a 1 to 1¼°F rise per hour with 3½ mph of wind. Heating energy is 8.34 Btu per gallon per °F. Heat pumps use a coefficient of performance (the DOE gives 3 to 7). Pump savings use the affinity laws, the basis of ENERGY STAR’s note that halving pump speed cuts energy to one-eighth. Pipe limits use the CDC code’s 6 ft/s suction and 8 ft/s discharge velocities with schedule 40 PVC inside diameters.
Filters and salt cells
Residential filter rates come from manufacturer ratings (a 3.14 ft² Hayward sand filter rated at 62 gpm, a 420 ft² Pentair cartridge rated at 150 gpm, and 2 gpm per ft² for DE). Public pool rates come from the CDC code: 15 gpm/ft² for sand, 0.30 for cartridges, 2 for precoat. Salt cell sizing uses the 1×, 1.5× and 2× volume multipliers from Pool & Spa News, scaled up when the pump runs under 8 hours.
Hot tub running costs
Covered standby power starts from your spa’s rating, or the California limit of 5 × volume^(2/3) watts if you don’t know it, measured at 102°F water and 60°F air. We scale it to your temperatures and add the heat lost to evaporation and the jet pump while you soak.
How we test
Every formula on this site is written twice: once for the calculators and once, separately, in a different programming language for testing. Before each release we feed thousands of random inputs through both and through the live calculators in a browser, and they must agree. We also check that each worked example on the site matches the calculator.
Limits
These are estimates. Real pools vary: test kits have error bars, product strengths fade (liquid chlorine loses strength in heat), and weather changes evaporation and heat loss hour by hour. Add large doses in stages and retest. Always follow the label and safety directions on any chemical you use.
Sources
- Home Pool and Hot Tub Water Treatment and Testing. U.S. Centers for Disease Control and Prevention (CDC), reviewed May 10, 2024.
- Model Aquatic Health Code, 5th edition (2024). CDC.
- Understanding the Chlorine/CYA Chart. Trouble Free Pool.
- The solubilities of calcite, aragonite and vaterite in CO₂–H₂O solutions between 0 and 90°C (carbonate equilibrium constants). Plummer, L. N. and Busenberg, E., Geochimica et Cosmochimica Acta 46 (1982).
- Understanding LSI: The Langelier Saturation Index. Orenda Technologies.
- Langelier Saturation Index (LSI). Mountain Empire Community College, water technology course notes.
- What increases cyanuric acid (CYA) in a swimming pool?. Orenda Technologies.
- Methods for Calculation of Evaporation from Swimming Pools and Other Water Surfaces (reviews the Smith et al. outdoor-pool equation). M. M. Shah, ASHRAE Transactions, 2014.
- Pool Water Efficiency (WaterSense guide EPA-832-F-22-015), September 2022. U.S. Environmental Protection Agency.
- Gas Pool Heaters. U.S. Department of Energy, Energy Saver.
- Heat Pump Swimming Pool Heaters. U.S. Department of Energy, Energy Saver.
- ENERGY STAR Certified Pool Pumps. U.S. EPA, ENERGY STAR.
- Sizing Salt Chlorinators. Bob Harper, Pool & Spa News, July 29, 2011.
- ProSeries 24 in. sand filter (S244T2) specifications. Hayward.
- Pentair Clean & Clear Plus 420 cartridge filter. Leslie’s product listing.
- California Title 20 Section 1602 for portable electric spas and hot tubs. Hot Tub Insider.
- NIST Guide to the SI, Appendix B: Conversion Factors. U.S. National Institute of Standards and Technology.