Heat loss and heating load calculations

Grace Lin's first visit to the bungalow on Oakland Avenue was not about the boiler at all. She walked around the outside with a tape measure, counted the windows, looked into the attic hatch and asked the owners, Hana and Peter, what the house felt like on the coldest days. The old boiler in the basement was rated at 140,000 Btu/h of input, almost three times what Grace guessed the house needed. "Before we pick any equipment," she told Maya, "we find out how much heat this house actually loses on a cold day. Everything else, the boiler size, the water temperature, the flow, the pipe sizes, comes from that one number."

The heating load of a building is the rate at which it loses heat to the outdoors at the design condition, the cold temperature the system is sized for. A heating system sized to that load keeps the building comfortable on all but the rarest coldest hours. This lesson explains how heat is lost, how the load is calculated room by room, which standards set the method, and why oversizing, the most common mistake in residential heating, causes so many problems.

How buildings lose heat

A building loses heat in two ways. Transmission is heat conducted through the walls, windows, doors, roof, basement and floor, from the warm inside to the cold outside. Air leakage, also called infiltration, is heat carried out by warm air escaping through cracks while cold outdoor air leaks in to replace it. Mechanical ventilation, such as bathroom fans, range hoods and heat recovery ventilators, adds a third, deliberate air exchange that must also be heated.

Transmission through each surface depends on its area, how well it resists heat flow and the temperature difference across it:

U is the overall heat transfer coefficient of the assembly, the heat that passes through one square foot for each degree Fahrenheit of temperature difference, in Btu/(h·ft²·°F). Insulation values are often given as thermal resistance instead, written as an R-value in US units, and U is simply one divided by the total resistance. A wall rated R-12 overall has a U value of about 0.083. Windows have much higher U values than walls, often 0.30 to 0.55, which is why a house with large old windows loses so much heat through them.

Air leakage is estimated from the volume of air that leaks out each hour, expressed as air changes per hour (ACH) at natural conditions. The heat needed to warm that air in Btu per hour is about 0.018 times the air changes per hour, times the house volume in cubic feet, times the temperature difference in degrees Fahrenheit. A blower door test, which depressurizes the house with a calibrated fan, measures leakage directly and is far better than guessing.

Design temperatures

The outdoor design temperature comes from climate data. ACCA Manual J uses the ASHRAE 99 percent heating design temperature, the temperature that is colder only about 1 percent of the hours in a year. For Columbus it is about 2 °F. Manual J uses an indoor design temperature of 70 °F. The design temperature difference for the bungalow's above-grade walls is therefore 70 − 2 = 68 °F.

Not every surface sees the full outdoor temperature. The basement floor sits on ground that stays around 50 °F even in winter, so its temperature difference is much smaller. An attached garage or a crawl space is somewhere between indoor and outdoor. Using the right temperature difference for each surface is part of doing the calculation properly.

Room-by-room calculation

ACCA Manual J, Residential Load Calculation, in its eighth edition, is the method most US codes reference for sizing heating and cooling equipment in houses. The residential code requires heating and cooling equipment to be sized from a Manual J or equivalent calculation, and many jurisdictions ask to see it with a permit application. Software that follows the method is normal practice.

The calculation is done room by room, not just for the whole house. Each room's walls, windows, ceiling and floor are measured, their U values are taken from the construction, and the room's share of air leakage is assigned. The room loads add up to the building load, and they also tell the designer how much emitter each room needs, which is exactly what a hydronic designer needs to size baseboard, radiators or floor loops.

The table shows the bungalow's story clearly. The walls, windows and ceiling together lose less than the air leaking through the old house. Grace's whole-house total is about 45,100 Btu/h, a little below her first estimate of 48,000 Btu/h and about a third of the old boiler's input.

# Whole-house heat loss: transmission (U x A x dT) plus air leakage
parts = [("walls", 1020, 1 / 12, 68), ("windows", 150, 0.50, 68), ("doors", 43, 0.35, 68),
         ("ceiling", 1180, 1 / 40, 68), ("basement walls", 650, 0.09, 68), ("basement floor", 1180, 0.05, 22)]
def loss(ach, volume=21200, dt=68):
    trans = sum(a * u * d for _, a, u, d in parts)
    leak = 0.018 * ach * volume * dt
    return trans, leak

for ach in (1.0, 0.6, 0.3):
    t, l = loss(ach)
    print(f"{ach:.1f} ACH: transmission {t:,.0f} + leakage {l:,.0f} = {t + l:,.0f} Btu/h")

1.0 ACH: transmission 19,185 + leakage 25,949 = 45,134 Btu/h
0.6 ACH: transmission 19,185 + leakage 15,569 = 34,755 Btu/h
0.3 ACH: transmission 19,185 + leakage 7,785 = 26,970 Btu/h

The script shows why Grace recommended air sealing before buying any equipment. Sealing the attic, the rim joists and the basement windows to bring the leakage down to about 0.6 air changes per hour cuts the load to about 36,800 Btu/h. Every Btu per hour saved here is capacity of boiler, emitter and fuel the owners never have to pay for.

Checking against fuel use

For an existing house, past fuel bills are a valuable check on the calculation. Heating degree days measure how cold a season was: each day contributes the number of degrees by which its average temperature fell below 65 °F. A house's fuel use divided by the degree days gives its heat loss per degree, which can be scaled to the design temperature difference. If the calculation and the bills disagree by a lot, one of them is wrong, and it is worth finding out which before choosing equipment.

Why oversizing causes problems

It is tempting to add a generous safety factor and buy a bigger boiler, but oversizing hurts. An oversized boiler or heat pump reaches the thermostat setting quickly and shuts off, then starts again a few minutes later. This short cycling wastes fuel, because every start and stop has losses, and it wears out ignition parts and compressors. Condensing boilers and heat pumps reach their best efficiency when they run long and low, at part load; a unit that is too big rarely gets there. Oversized equipment also costs more to buy.

Modern equipment helps by modulating: a modulating boiler can turn its burner down to a fraction of its maximum input, and a variable-speed heat pump can slow its compressor. But every unit has a minimum firing rate. If the house's load on a mild day is smaller than the unit's minimum output, the unit will still cycle. The right choice is equipment whose maximum output matches the design load with a modest margin, and whose minimum output is as low as possible.

Grace recommended sizing the new heat source for about 37,000 Btu/h after air sealing, with a minimum output below 10,000 Btu/h. On a typical January day, when the outdoor temperature is around 23 °F rather than the design 2 °F, the house will need only about 25,000 Btu/h, and a well-chosen modulating unit will run almost continuously at that rate.

Loads in larger buildings

A building like Kingsway is sized by a mechanical engineer using commercial load methods, which account for many floors, internal heat from people and equipment, ventilation air and the diversity between suites. The plumber does not do that calculation, but needs to understand it, because the engineer's load schedule sets the flow and temperature drop of every riser and fan coil the plumber installs. When a tenant wants to add a coil or change a zone, someone has to check the change against that design.

Ventilation, heat recovery and thermal bridges

Air sealing a house raises a fair question from owners: if the leaks are closed, where does fresh air come from? The answer is mechanical ventilation. Tight houses need a controlled supply of outdoor air for health and moisture control, and current codes require a ventilation system in new houses. That deliberate airflow is part of the heating load too, and a full load calculation includes it.

A heat recovery ventilator (HRV) or energy recovery ventilator (ERV) reduces that cost. It exhausts stale air from bathrooms and the kitchen area and brings in the same amount of fresh outdoor air, passing the two streams through a heat exchanger so that the outgoing air warms the incoming air. A good unit recovers well over half the heat that would otherwise be lost. In the load calculation, the ventilation airflow is multiplied by one minus the recovery efficiency before its heat is added to the total.

Thermal bridges are the other detail that simple calculations miss. Wherever framing, concrete or steel passes through the insulation, such as studs, rim joists, balcony slabs and window frames, heat bypasses the insulation. In a wood-frame wall, studs and plates can make up a fifth or more of the wall area, so the effective resistance of the whole wall is lower than the insulation's rating. The standard methods handle this by using effective assembly values rather than the nominal insulation value, and Grace used the effective values for the bungalow's walls.

Grace also wrote down what the owners told her: the back bedroom was always cold, and the living room window fogged on cold mornings. Both observations matched the calculation, which showed the back bedroom with two outside walls and a large window. Listening to occupants is part of a load survey; it often points straight to the room that needs the most attention.