Every number, and where it came from

Sourced figures

Each of these was fetched from the publisher on the date shown. A raw copy of the source as fetched — the page, file or API response — is kept in this project's evidence archive, which is not part of the published site. For 7 of them the raw copy of the original retrieval was not kept, and the copy on file is a later capture of the same source; the last column says so wherever that applies, with both dates.

What is wrong with each of them

Residential electricity price by state

A state average across every residential customer and every rate plan, for one past month. A pool on a tiered or time-of-use rate is very often paying a marginal rate well above it, because pool heating is added on top of an existing bill.

Residential natural gas price by state

An annual average that folds in the fixed monthly customer charge. Summer pool heating is close to pure commodity gas, so the true marginal price of a summer therm is usually lower than this figure.

U.S. residential propane price

A national figure, and the residential propane series is only collected October through March. Delivered propane prices vary by more between two neighbouring suppliers than this number varies across a year.

Natural gas heat content

A national average. A utility bill states the heat content actually billed, usually as a therm factor, and that is the number to prefer if you have it.

Air temperature, relative humidity, wind speed and surface irradiance

A reanalysis on a coarse grid, not a weather station reading. It resolves a metropolitan area, not a back yard, and a 20-year mean says nothing about the cold week that will actually decide whether you swim in April.

Independent cross-check on air temperature

Station normals cover a different 30-year window than the reanalysis and are measured at an airport. Where the two disagree the methodology page reports the gap rather than picking a winner.

Federal minimum thermal efficiency, gas-fired pool heaters

A floor, not a rating. It is used here as the default because it is the one gas-heater efficiency that is knowable without a model number, and any real unit meets or beats it.

A source limitation is not a disclaimer. It is the specific reason a figure might be wrong for your situation. Where a calculator takes the figure as an input, the fix is to replace it with your own number there: prices on the energy prices page and on the calculators that ask for a price, gas heater efficiency on the gas heater page, and air temperature, humidity, wind and sunlight on the heat-loss page. The natural gas heat content and the station cross-check have no control.

Assumptions

These are numbers no publisher supplies for a residential pool. All but one can be changed, or bypassed, on at least one page of this site, either directly or by picking a different option such as a cover type or a wind exposure; the "Where to change it" line under each one names the page. The controls are on the home page calculator and the heat-loss, heat-pump, sizing, solar heating, pool cover, season length and climate pages. A page that uses an assumption does not always offer a control for it: the home page calculator, for example, uses the default sunlight retention, heat-pump COP slope and sizing margin, which can be changed only on the heat-loss, heat-pump and sizing pages. The exception is the 12-hour daylight window used to split cover hours, which is fixed and cannot be edited anywhere; it is listed here with its reasoning and range so that it is visible rather than hidden.

The reasoning behind each

Freeform and kidney surface-area factor

A kidney or freeform pool inscribed in its own bounding rectangle covers roughly 80 to 90 percent of it. 0.85 is the midpoint. Rectangles, ovals and circles are computed exactly and do not use this. Where to change it: Not a setting. To bypass it, enter a measured surface area directly on the heat-loss or solar heating page; on a calculator that asks for length and width, pick rectangle where a shape is offered and enter a length and width that multiply to your measured area.

Share of regional wind that reaches the water

The climate record reports wind 2 metres above open ground. A pool sits behind a fence, beside a house wall, usually inside landscaping, and its water surface is roughly 0.3 metres below the reference height. Windbreak measurements consistently show a solid barrier cutting downwind speed to about a third to a half of the open-field value for five to ten barrier heights downwind, which is the zone a back-yard pool occupies. 0.35 is the middle of that for a typical suburban lot. This is the input the evaporation term is most sensitive to, so it is a visible control rather than a buried constant. Known weakness: The regional figure itself carries a large artefact. A reanalysis reports wind for a grid cell, and a cell dominated by water or open plain reads far higher than a cell dominated by forest or dense building, at the same real exposure. In this dataset the Miami cell reads about ten miles per hour and the Raleigh cell about half a mile per hour in the same month — a difference that is mostly surface roughness, not weather. Where the regional figure looks implausible for your site, override the exposure setting rather than trusting it. Where to change it: Wind exposure control on the home page, sizing, climate and solar heating calculators. The heat-loss page takes a wind speed directly instead. The pool cover, season-length and payback calculators use the default.

Pool shortwave absorptivity

A water surface reflects roughly 6 to 8 percent of incident sunlight at typical daily mean sun angles; the water column absorbs most of the remainder and a light plaster floor sends a little back out. Dark finishes sit higher, pale ones lower. Where to change it: Editable on the heat-loss page, for a single day's heat balance. Every other calculator on this site that counts sunlight, including the home page, uses the default.

Heat-pump capacity derate with air temperature

Pool heat-pump datasheets that publish two air conditions typically show roughly half of rated capacity once the air drops to about 50 F, which is 0.014 to 0.018 per degree from the 80.6 F rating point. This is a shape, not a specification for any particular unit. Where to change it: Editable on the heat-pump page. If your datasheet lists capacity at two air temperatures, the slope is the drop between them as a fraction of rated capacity, divided by the gap in degrees F.

Heat-pump COP derate with air temperature

COP falls with air temperature more gently than capacity does, because the compressor draws less power as it moves less heat. Roughly three quarters of the capacity slope. Where to change it: Editable on the heat-pump page.

Heat-pump low-air-temperature cutoff

Most pool heat pumps stop or are shut off by their own control somewhere between 45 and 55 F ambient. Below cutoff the model reports the demand as unserved instead of quietly pricing it, because a heater that is not running has no operating cost and also does not heat your pool. Where to change it: Editable on the heat-pump page.

Cover evaporation blocking

A physical cover removes the free water surface almost completely; what leaks past is edge gap and handling. A liquid cover is a monolayer that wind disrupts, and the published claims for it span a very wide range, so it is modelled conservatively. Where to change it: Cover type control on the cover page.

Cover sensible and radiant blocking

A cover floats near air temperature rather than water temperature, so it cuts the driving difference for both convection and sky radiation without eliminating them. Insulated covers cut more than bubble covers; a monolayer cuts essentially nothing. Where to change it: Cover type control on the cover page.

Cover solar transmittance

Clear bubble covers are designed to pass sunlight; opaque insulated covers block nearly all of it, which is exactly why leaving one on through a sunny day can cost more than it saves in a mild climate. Where to change it: Cover type control on the cover page.

Unglazed polymer collector curve

Unglazed polymer mats have a high optical intercept and a very steep loss slope, because there is no glazing between the absorber and the wind. Certified collector ratings publish both numbers for a specific product; these are representative of the unglazed class, not of any one mat. Where to change it: Both editable on the solar page.

Daylight window used to split cover hours

Sunlight is credited across a fixed 12-hour window, the annual mean, rather than a computed sunrise-to-sunset. A monthly mean climate record does not carry the hourly detail that a real solar geometry calculation would need, so a finer split would be false precision. Where to change it: Not exposed; documented here because it affects the covered-during-daylight case only.

Unheated water temperature above mean air temperature

An unheated outdoor pool settles a few degrees above the monthly mean air temperature because it absorbs sunlight all day and has enormous thermal mass. Used only to set the starting point of the heat-up calculation. Where to change it: Editable on the sizing page.

Sizing design margin

A margin over the computed peak, to cover the cold week the monthly mean hides, fouling on the heat exchanger, and the fact that nobody is measuring your actual wind. Not a code requirement; a judgement. Where to change it: Editable on the sizing page.

Published correlations used

Scope and limits of each

These are methods, not measurements: nothing here was looked up for your pool, so each is cited for what it computes and listed with the limit that matters for this site. The evaporation correlation, first below, matters most.

Evaporation correlation

Developed and validated for indoor pools where air velocity over the water is small. Applying it to an outdoor pool in wind is an extrapolation beyond the data it was fitted to, and it is the largest single uncertainty in every number this site produces. The ASHRAE Handbook is a paid standard; it is cited, not linked, because there is no free authoritative copy to link to.

Sensible-heat ratio

Used only to tie convective loss to the evaporation term: the convection coefficient shares the evaporation correlation's wind function, so it carries that correlation's outdoor-wind uncertainty as well.

Clear-sky radiant temperature

A clear-sky formula. Cloud is applied month by month from the ratio of all-sky to clear-sky surface sunlight, a daytime measurement standing in for cloud cover at every hour, so on a particular night the radiant loss can be well off the monthly figure.

Saturation vapour pressure

A curve fit for the saturation vapour pressure of water, evaluated here at the water temperature you set and, on the air side, at the month's mean air temperature and humidity, so the air side inherits the monthly-mean limit stated under what this model deliberately does not do.

Heat-pump rating point

This model uses that High Air Temperature - Mid Humidity condition as its reference. The same DOE table lists two other AHRI 1160-2014 conditions, High Air Temperature - High Humidity (80.6 F dry bulb, 75.8 F wet bulb) and Low Air Temperature - Mid Humidity (50.0 F dry bulb, 44.3 F wet bulb), and a manufacturer may publish COP at one or all of them. Check which condition the manufacturer states for the COP you enter, and match it to this reference condition before comparing results.

The arithmetic, end to end

Worked here on the site's default example — a 512 square foot pool, 19,150 gallons, held at 84 °F in Phoenix, AZ from April through October.

1. Geometry. Surface area is length × width × a shape factor (1 for a rectangle, π/4 for an ellipse or circle, 0.85 for freeform). Volume is area × average depth × 7.4805 gallons per cubic foot. Mass is volume × 8.3454 pounds per gallon = 159,815 lb.
2. Vapour pressures. Saturation pressure at the water surface and at the air temperature comes from the Buck equation, in kPa, converted to inches of mercury. Air-side pressure is the saturation value at air temperature multiplied by the month's relative humidity.
3. Evaporation. area × (95 + 0.425 × wind in ft/min) × (P_water − P_air), in BTU per hour. Wind is the month's 2 m climatological wind multiplied by the shelter factor you selected.
4. Convection. area × 0.010138 × (95 + 0.425 × wind) × (water − air) in °F. The coefficient is the Bowen ratio with the vapour-pressure term algebraically cancelled against the evaporation expression, which is what keeps it finite in saturated air.
5. Radiation. 0.95 × σ × area × (T_water⁴ − ε_sky × T_air⁴) in kelvin. Clear-sky emissivity from Swinbank; cloud fraction derived per month from the ratio of measured all-sky to clear-sky surface irradiance.
6. Solar gain. area × daily irradiance × 0.85, converted from kWh/m²/day to BTU/ft²/day at 3,412 BTU per kWh and 10.7639 ft² per m².
7. Cover. Covered and uncovered hours are evaluated separately and summed, never blended, because evaporation is strongly non-linear in cover state.
8. Month total. (losses − solar gain), floored at zero per day, times days in month. Season total is the sum: 196.18 million Btu for this example.
9. Maintain sizing. The largest night-time hourly deficit across the season's months: 110,594 BTU/h, in April.
10. Heat-up sizing. mass × 1 BTU/lb·°F × rise ÷ hours, plus the maintain load: 158,992 BTU/h over 36 hours.
11. Required output. The larger of the two, times (1 + margin): 182,840 BTU/h.
12. Cost. Season BTU ÷ (efficiency or coefficient of performance) × price, with the heat pump evaluated month by month because its coefficient tracks air temperature.

Two independent temperature records, and the gap between them

Air temperature is available from two unrelated sources, and they disagree. Rather than pick one silently, both are reported.

The two differ because they measure different things over different periods: a reanalysis grid cell covers a wide area including built-up land and water, while a station normal is a single instrument at an airport. The site runs on the reanalysis, because that is the only source that also supplies humidity, wind and irradiance on a consistent basis — mixing sources for a single energy balance would introduce errors larger than either source's own.

What this model deliberately does not do

• It does not model hours. Everything runs on monthly means. Real pool heating is decided by cold nights and cloudy weeks, and a monthly mean cannot see them. That is why sizing carries a margin.
• It does not model solar geometry. Irradiance is on a horizontal surface. Collector tilt, azimuth and shading are left out rather than approximated from data that cannot support them.
• It does not model conduction to the ground. For an in-ground pool this is small compared to the surface terms and highly dependent on soil moisture and construction. Including a made-up number would be worse than omitting it; treat the results as slightly optimistic for a pool in wet, cold ground.
• It does not model the pump. Circulation energy is a real cost and it is not pool heating cost. Adding it would make the heater comparison misleading.
• It does not forecast prices. Every operating-cost figure uses the historical energy prices this site has on file (state averages: electricity for May 2026, natural gas for 2025 annual; both dated on the energy prices page), with no escalation; install costs are your own quotes. The payback page offers a sensitivity table instead of an escalation assumption.

Review and correction

Every sourced figure is listed above with the date of the copy on file, and with its original retrieval date where that copy is a later capture. Energy prices move, and the natural gas series in particular is an annual figure that will be superseded. If a figure on this site is stale or wrong, the contact page is the route to say so; corrections are made to the figure registry, which is the only place any of these numbers exist.

Dates of the copies on file: 2026-08-06, 2026-08-24, 2026-09-04, 2026-10-05. Sourced figures: 11. Declared assumptions: 13. Published correlations: 5.