Where every number on this site comes from

The three labels, and why they are not decoration

sourced means the figure is quoted verbatim from the page cited beside it, and a snapshot carrying that exact quote sits in the evidence directory. The quote was matched against the captured bytes mechanically, not by eye. There are 105 of these.

derived means we did arithmetic over sourced values, and the arithmetic is printed below so you can redo it. There are 1.

assumed means nobody publishes it and we chose it. Every assumption is listed in full further down, each one is exposed as an editable input rather than buried, and each one is labelled on the page that uses it. There are 4 of them.

The distinction matters because the failure mode in this subject is not error, it is unearned confidence. A calculator that presents a guessed regional multiplier in the same typeface as a federal regulation has told you nothing about which parts of its answer to trust.

The derived arithmetic, written out

Therms in a thousand cubic feet of gas

Residential gas is priced per thousand cubic feet and burned per therm. One thousand cubic feet at the published heat content, divided by the Btu in a therm, gives 10.37 therms per thousand cubic feet. Every gas running-cost figure passes through that conversion.

Heat the water actually needs

Gallons drawn, times the weight of a gallon of water, times the temperature rise in degrees Fahrenheit, times 365. One British thermal unit raises one pound of water one degree, so no coefficient is needed beyond the weight itself. This is the only step with no appliance in it.

Fuel actually burned

Heat delivered divided by the uniform energy factor. That single division carries standby loss, combustion loss and everything else the rating captures, which is why the rating is a divisor rather than a multiplier and why a rating above 1.0 is possible for a heat pump and impossible otherwise.

Minimum efficiency by class

Federal standards state each minimum as a straight line in rated storage volume, selected by product class and usage bin. The engine evaluates that line rather than storing a lookup table, so the published coefficients are the thing in the code. The classes carried here:

• gas storage, 20 to 55 gallons: medium usage bin is 0.6483 minus 0.0017 times the rated volume.
• gas storage, 55.0001 to 100 gallons: medium usage bin is 0.7897 minus 0.0004 times the rated volume.
• electric storage, 20 to 55 gallons: medium usage bin is 0.9307 minus 0.0002 times the rated volume.
• electric storage, 55.0001 to 120 gallons: medium usage bin is 2.1171 minus 0.0011 times the rated volume. A minimum above 1.0 cannot be met by resistance heating, so every appliance in this class is a heat pump.
• gas tankless, 0 to 2 gallons: medium usage bin is 0.81 flat.
• electric tankless, 0 to 2 gallons: medium usage bin is 0.91 flat.

Heat pumps at or below fifty-five gallons

In that size range the federal electric storage minimum is the resistance floor and does not describe a heat pump at all. So the site multiplies that floor by 2 and by 3, using the published statement that a heat pump is two to three times as efficient as resistance, takes the midpoint for the headline figure, and shows the whole band beside it. Labelled derived, because it is our multiplication rather than anybody’s measurement.

Installed cost anchor

Every line the scope answers turn on contributes its own published low and high. The low total is the sum of the lows, the high total the sum of the highs, and the headline figure is the midpoint of those two rounded to the nearest twenty-five dollars. There is no multiplier anywhere in that chain.

Assumptions — the complete list

These are ours. No source states them. Each is editable in the tool that uses it, so you can replace our judgement with your own figure and watch the answer move.

• inlet water f: 55 °F assumed — A mid-latitude municipal supply figure. The tool exposes it as an input precisely because it is not sourced, and a reader in Minnesota or Florida should change it.
• setpoint f: 120 °F assumed — The setting most manufacturers ship. The federal Energy Saver pages warn that 140 degrees raises scald risk; they do not prescribe a number for this calculation.
• tankless annual service usd: 150 USD/yr assumed — No source we checked publishes a descaling price. It is exposed as an editable input and defaults to a figure we chose; set it to zero to see the payback without it.
• difficult access hours: 2 hours assumed — The per-hour premium is sourced; how many hours a given closet costs is not. The tool lets the visitor set the hours.

Known limitations, stated rather than hidden

A discrepancy inside the federal sizing worksheet

The worked example on the federal sizing page lists three showers, one shave and one hand dishwashing, then prints a total of 66 gallons. Those line items sum to 65. We add the line items, because the per-use gallons are the operative data. Anyone checking this site against that page will find the one-gallon difference, so it is recorded here rather than left to look like our error.

Efficiency ratings are measured on a laboratory schedule

A uniform energy factor is measured against one of four standard draw patterns, not against your household. Two appliances rated in different bins are not directly comparable at all. The running cost figures on this site are therefore a comparison instrument on fixed assumptions, not a prediction of your bill, and they exclude the standing charge you pay regardless of usage.

Installed-cost bands are commercial, not primary

The physics, the efficiency standards, the draw-pattern bins and every energy price here come from federal primary sources. The installed-cost bands do not — they come from commercial cost guides that aggregate contractor estimates and do not publish their sample. Two independent publishers are used and their figures overlap, which is worth something, but it is weaker evidence than the rest of this page and should be read that way.

There is no regional cost adjustment, on purpose

Labor plainly costs more in some metros than others. No source we could verify publishes a defensible state-by-state installed-cost index for this trade, and the federal wage tables refuse automated retrieval. Rather than invent a multiplier that would look authoritative and be fabricated, the installed-cost tool prices awkward access by the hour from a published hourly premium and lets you set the hours. Energy prices, by contrast, are genuinely state-specific and are treated that way.

Service life sources disagree

Federal guidance gives a tankless unit more than 20 years and a storage tank 10 to 15. A commercial guide starts its ranges at 15 and 8. Both are shown wherever service life affects an answer, and the payback verdict uses the longer figure, which makes a payback claim harder to establish rather than easier.

Freshness

Every figure carries a refresh date six months past the day it was checked, listed in the table above. A stale figure blocks a new deployment rather than silently ageing on the page. Energy prices move fastest and are the reason that horizon is short.