Hot-water House Boiler Interactive Calculator
Compare heat-rate arithmetic using explicitly assumed constant efficiencies. Results do not establish boiler input ratings, output capacities or equipment selection.
Equation Used
For this exercise, the entered percentages are assumed constant heat-output/input ratios. Input scenario = entered heat rate divided by efficiency. Comparison output = comparison input times its assumed efficiency. The percentage tile compares that arithmetic output with the entered heat rate; it is not a boiler oversizing assessment.
- The entered heat rate is a scenario value; no building heat-loss calculation is performed.
- Efficiency is entered as a percent and treated as constant over the comparison.
- Comparison input multiplied by an assumed constant efficiency is an illustrative heat rate, not a verified nameplate output.
- Distribution losses, pickup factors, and domestic hot water loads are not included.
Heating water and circulating heat
In a hydronic heating system, a heat source warms water, piping carries it to emitters, and cooler water returns. A pumped system includes a circulator; the detailed connections, expansion provisions, controls and protective devices depend on its design.
The illustration follows Hiscox’s entry 1551: a house hot-water vessel connected to a stove water-back by two circulation pipes. The cold supply extends down inside the vessel, hot water is drawn from the top, and a lower draw-off is shown. The connection layout is historical; it is not a modern installation diagram.
The animation shows the direction of natural circulation: cooler water returns to the water-back and heated water rises toward the vessel. Marker speed, flame motion and colors are qualitative. The heat-rate inputs change the calculator results, not the vessel geometry or a predicted circulation rate.
Hydronic heat distribution
Water-based heating can serve radiators, baseboard emitters, radiant panels or other heat exchangers. Their required temperatures, flows and capacities vary with the installation.
The arithmetic exercise can compare assumed heat-input and output rates using a clearly stated constant efficiency. It cannot choose a boiler, circulator, expansion tank or control setting, and it does not assess domestic hot-water demand.
Constant-efficiency arithmetic
Let Q be an entered heat rate and η an assumed constant efficiency expressed as a fraction. The input scenario is I = Q/η. The calculator converts that value from Btu/h to kW by dividing by 3,412.142.
For comparison input Ic and assumed efficiency ηc, comparison output is Oc = Icηc. The displayed difference is 100(Oc/Q − 1). A positive result only means that this arithmetic output exceeds the entered Q.
AFUE describes annual output energy relative to annual fuel-input energy. Substituting an AFUE rating into this steady heat-rate exercise does not establish peak boiler capacity, cycling performance or an appropriate replacement size.
Illustrative arithmetic example
Enter Q = 62,000 Btu/h and assume a constant efficiency of 95%. Then I = 62,000/0.95 = 65,263.16 Btu/h, or 19.13 kW.
For a separate comparison input of 100,000 Btu/h and an assumed constant efficiency of 80%, the arithmetic output is 80,000 Btu/h. It is 29.03% above the entered 62,000 Btu/h.
These are products and quotients of the entered assumptions. They do not establish the capacity of a particular boiler, its AFUE at a particular operating point, annual fuel use, payback or suitability for a home.
Equipment comparison needs more information
A heating-system comparison needs a building load assessment, applicable equipment output ratings, emitter performance, distribution losses and control behavior. Operating costs additionally need climate, use patterns, tariffs and equipment performance over the season.
Fuel boilers, electric boilers and heat pumps use different energy-conversion processes and rating methods. A single assumed percentage and heat-rate quotient cannot rank their installed costs, comfort, service life or seasonal economics.
Frequently asked questions
Can I divide design heat loss by AFUE to select a boiler?
This calculator cannot support that selection. AFUE is an annual energy ratio. Peak-load selection requires applicable equipment output ratings and an assessment of the building and heating system.
What do the efficiency sliders mean here?
They are assumed constant output/input heat-rate ratios for an arithmetic comparison. They are not a prediction of seasonal or part-load performance.
Does the difference percentage prove that the existing boiler is oversized?
No. It compares an assumed output with an entered heat rate. It does not know the boiler’s rated output, minimum firing rate, zoning or control behavior.
Does it calculate household heat loss?
No. Heat rate is an input. The calculator includes no building dimensions, insulation, air leakage or outdoor design temperature.
Does the drawing prescribe water temperature or relief pressure?
No. It is a schematic heat-distribution illustration. Operating limits and protective-device settings are equipment-specific.
Can it diagnose a leaking valve, cold zone or cycling burner?
No. Those symptoms can have several causes. They require assessment of the actual equipment and system; this arithmetic model does not provide a repair procedure.
Sources and scope
U.S. Department of Energy: Purchasing Energy-Efficient Boilers defines AFUE as a measure of fuel-to-heat efficiency over a typical year. It is distinct from assuming a constant efficiency in this heat-rate comparison.
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 1551, depicts the historical hot-water vessel and circulation arrangement. It is not an installation instruction for a modern heating system.
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