Introduction
Heat pump sizing and running-cost estimates often start from a single number: design heat loss in watts at a stated outdoor temperature. That coefficient describes conductive loss through the fabric. The annual heat the heat pump must deliver is different. It is the integral of net demand over the year: conductive loss minus solar gain through glazing, minus heat from people and standby electrical loads inside the house.
The Solar Butter simulation software was run for the geographical area around Gloucester under different property heat loss scenarios ranging from 1 to 16 kW. Space-heating thermal output rises from 425 kWh/year at 1 kW to 52,033 kWh/year at 16 kW. Total heat-pump electricity (space heating plus hot water) rises from 946 kWh to 11,965 kWh. The increase is far from linear at low heat loss and approaches a doubling each time fabric loss doubles at the high end.
These reports were modelled using our solar calculator: open the free Solar Butter solar calculator, which is free to use with no sign up required.
Methods and assumptions
Study design
Five historic heat-pump-only simulations were run in Solar Butter for one UK site across calendar year 2025. Site, design outdoor and indoor temperatures (−3.0 °C / 20.5 °C), weather-compensated flow temperatures, SCOP, floor area, occupancy, standby power, and domestic hot water settings are fixed. Only design heat loss at the design outdoor temperature changes. Maximum heat pump power at design is set equal to that heat loss so the heat pump’s maximum output equals design heat loss and does not limit delivered heat below what the fabric would require.
| Parameter | Value |
|---|---|
| Site location | UK-Gloucester (51.89, −2.19), 2025 historic year |
| Design outdoor / indoor temperature | −3.0 °C / 20.5 °C |
| Design / minimum flow temperature | 43.0 °C / 30.0 °C, weather compensation enabled |
| SCOP | 3.77 at 45 °C reference flow temperature |
| Property | 100 m² floor area; thermal mass 160 kJ/°C/m²; solar glazing g-factor 0.6 |
| Heat added inside the house (not from the heat pump) | Solar gain through glazing (g-factor 0.6; total window area split N/E/S/W); 3 occupants at 80 W each; 100 W standby electrical heat |
| Hot water | 200 L cylinder; 55 °C set; 50 L/person/day; present in every run (reported only in total heat-pump electricity) |
| Varied parameter | Design heat loss (and matching max power): 1, 2, 4, 8, 16 kW |
Modelling
Heat balance
Design heat loss defines a fabric heat-loss coefficient. With design indoor temperature Tin,des and design outdoor temperature Tout,des:
k = Pdesign / (Tin,des − Tout,des)
Instantaneous conductive loss is then k × (Tin − Tout). Conductive loss scales with k. Solar gain through glazing, occupant body heat, and standby electrical heat do not: they offset (subtract from) conductive loss when forming the net space-heating load. When those gains exceed conductive loss in a half-hour, net space-heating load is zero. Annual space-heating thermal energy is the integral of that net load over the year. When the gains are large relative to conductive loss, doubling k multiplies annual space heat by more than 2× (Table 3: 6.74×, 3.28×, then 2.53× as design heat loss steps from 1 to 8 kW). When conductive loss dominates, doubling k multiplies annual space heat by about 2× (8 to 16 kW: 2.19×).
Half-hourly simulation
Solar Butter advances the house and heat pump on a half-hourly historic weather timeline. The house has thermal mass, so indoor temperature evolves from net heat flows rather than jumping to the setpoint. Weather compensation sets flow temperature from outdoor conditions between the design and minimum flow temperatures. Coefficient of performance (COP) is derived from a Carnot-style model calibrated to the stated SCOP, with outdoor temperature and flow temperature as the main drivers. Hysteresis controls on/off cycling. Domestic hot water is modelled with cylinder volume, set temperature, draw-off, and standing loss.
Solar gain through glazing
Solar gain is the heat delivered indoors by sunlight that passes through glazing, not sunlight warming the outside of walls or the roof. At each half-hour, Solar Butter computes how much solar radiation strikes vertical windows, multiplies by glazed area and by the g-factor, and subtracts that power from the conductive fabric loss when forming the net space-heating load. On a bright day the solar term can exceed fabric loss and the indoor temperature can rise with the heat pump off; on a dull winter day it is small and the heat pump must cover almost all of the fabric loss (after occupant and standby heat).
Window area
Window area is the total glazed area of the property, in square metres. It is the aperture through which solar radiation can enter. The model does not require a separate drawing of each façade: it splits the total window area equally across four vertical orientations (north, east, south, and west) and computes incident irradiance on each façade from the site location and the historic weather (direct and diffuse). That is a deliberate simplification: a south-heavy house would admit more winter sun than an equal four-way split, and a north-heavy house less. The equal split is a neutral default when detailed window orientation is unknown.
Solar gain at a given time is then the sum over those four orientations of:
solar gain (W) = Σ irradianceorientation (W/m²) × (window area / 4) × g-factor
If window area is set to zero, solar gain is identically zero and only occupant and standby heat remain as non-heat-pump inputs.
Solar glazing g-factor
The g-factor (solar transmittance, sometimes called the solar heat gain coefficient) is the fraction of solar radiation incident on the outside of the glass that ends up as heat inside the room. It is a property of the glazing, not of the weather. Clear single glazing can be near 0.8–0.9; typical double glazing is often around 0.5–0.7; solar-control glass can be lower. These reports use a g-factor of 0.6, a mid-range double-glazing value. Raising the g-factor scales solar gain linearly for the same window area and irradiance; lowering it does the opposite. It does not change the fabric heat-loss coefficient derived from the heat-loss survey.
Occupancy
Number of occupants is used in two separate places. They are not the same calculation.
Space heating: always-on body heat. Each occupant is modelled as a constant 80 W heat source in every half-hour of the year. There is no weekday/weekend presence schedule and no “away at work” reduction: three occupants contribute 240 W continuously, which is 240 W × 8,760 h ≈ 2,100 kWh/year of heat added to the house. That power is subtracted from conductive fabric loss when the net space-heating load is formed, in the same way as solar gain through glazing. Raising the occupant count therefore cuts annual space-heating energy even if the heat-loss survey is unchanged.
Hot water: daily volume from head count, drawn on a fixed timetable. Daily hot-water consumption in litres is:
daily draw (L/day) = number of occupants × litres per person per day
These reports use 3 occupants and 50 L/person/day, so 150 L/day. That daily volume is not drawn uniformly. By default the model puts 40% of the day’s draw in the morning hours 06:00–08:00 and 60% in the evening hours 18:00–21:00, split evenly across those hours and then across the half-hour timesteps. Outside those windows the draw is zero. Each litre drawn is replaced by cold water at the stated cold-water temperature (here 10 °C); the thermal energy removed from the cylinder is litres × (tank temperature − cold-water temperature) × the specific heat of water. The heat pump then reheats the 200 L cylinder toward the 55 °C set temperature, subject to hysteresis and charge ΔT. Occupancy therefore scales how much hot water is used each day and when that energy is taken from the tank; it does not change the fabric heat-loss coefficient or the solar-gain calculation.
Standby electrical heat
Standby power contribution is the heat from always-on electrical loads that ends up in the heated volume (routers, fridge waste heat, standby electronics, and similar). These reports use 100 W continuous (about 876 kWh/year of heat). Like occupant body heat, it is subtracted from conductive fabric loss when computing net space-heating load. It is not heat-pump electricity; it is an assumed internal heat input from other appliances.
How non-heat-pump heat affects the heat-loss comparison
Design heat loss only sets the fabric coefficient k. Solar gain (window area × orientation irradiance × g-factor), always-on occupant body heat (80 W × head count), and standby heat (here 100 W) are independent. Together, for three occupants and 100 W standby, the non-solar internal heat alone is 340 W in every timestep. At 1 kW design heat loss that is already a large fraction of typical fabric loss in mild weather; add solar gain through glazing and the heat pump may deliver almost no space heat for long stretches. At 16 kW the same 340 W plus solar is a small correction on a large conductive term, which is why doubling design heat loss from 8 to 16 kW multiplies annual space heat by 2.19×.
Results
| Scenario | Detail | Report |
|---|---|---|
| 1 | 1 kW design heat loss Low fabric coefficient; solar, occupants, and standby leave little net space-heating demand. | Download PDF |
| 2 | 2 kW design heat loss Gains still offset a large share of conductive loss (space heat rises 6.74× from 1 kW, not 2×). | Download PDF |
| 3 | 4 kW design heat loss Space-heating electricity (2,149 kWh) exceeds hot-water electricity in the total. | Download PDF |
| 4 | 8 kW design heat loss High fabric loss; gains are a smaller share of conductive loss. | Download PDF |
| 5 | 16 kW design heat loss From 8 kW: space-heating thermal output rises 2.19×. | Download PDF |
| Design heat loss | Space heat thermal (kWh) | Space heat electricity (kWh) | Total heat pump electricity (kWh) | Space COP |
|---|---|---|---|---|
| 1 kW | 425 | 116 | 946 | 3.66 |
| 2 kW | 2,865 | 701 | 1,597 | 4.09 |
| 4 kW | 9,391 | 2,149 | 3,106 | 4.37 |
| 8 kW | 23,774 | 5,182 | 6,145 | 4.59 |
| 16 kW | 52,033 | 10,952 | 11,965 | 4.75 |
Total heat-pump electricity includes domestic hot water as well as space heating. When design heat loss doubles, space-heating thermal output multiplies by 6.74×, 3.28×, 2.53×, then 2.19×, approaching a factor of two as fabric loss comes to dominate.
Discussion
When design heat loss is low, solar gain, occupant heat, and standby heat offset most of the fabric loss
Net space-heating load is conductive fabric loss minus solar gain through glazing, occupant body heat, and heat from standby electrical loads. Those three contributions do not scale with design heat loss. At 1 kW design heat loss, they offset most of the fabric term for much of the year, so the heat pump delivers only 425 kWh of space heat. Total heat-pump electricity is then mostly hot water (946 kWh total versus 116 kWh for space heating). Doubling design heat loss to 2 kW raises space-heating thermal output to 2,865 kWh (6.74×), not 2×, because the same solar, occupant, and standby heat is subtracted from a larger conductive base and the residual therefore grows faster than the fabric coefficient.
When design heat loss is high, annual space heat scales nearly with the fabric coefficient
From 8 kW to 16 kW, space-heating thermal output rises by 2.19×. Solar gain through glazing, occupant body heat, and standby electrical heat are unchanged in absolute terms, so they are a smaller fraction of the conductive loss; net space-heating load therefore tracks the fabric coefficient more closely. Space-heating electricity follows the same pattern (5,182 kWh to 10,952 kWh), scaled by COP.
Why average space-heating COP rises with design heat loss
Table 3 shows space-heating COP rising from 3.66 at 1 kW to 4.75 at 16 kW. That is not because a leakier house makes the machine more efficient at the same outdoor conditions. The average COP in Table 3 is energy-weighted: annual space thermal output divided by annual space electricity. Instantaneous COP depends mainly on outdoor temperature and flow temperature.
At 1–2 kW, solar gain, occupant heat, and standby heat offset most conductive loss for much of the year, so the heat pump runs mainly in the coldest spells: low outdoor temperature, poorer COP, and more time near defrost conditions. That small annual space-heating load is concentrated in those hours, which pulls the average down. At 8–16 kW the heat pump also runs through milder weather, where outdoor and weather-compensated flow temperatures are more favourable. Those higher-COP hours dominate the annual energy total and lift the average.
The mix of operating hours changes. This is not a reason to under-insulate: absolute electricity use still rises sharply with fabric heat loss.
Hot-water electricity is almost unchanged across heat-loss scenarios
Every run uses the same occupancy and domestic hot-water settings, so hot-water electricity stays near constant. At 1 kW design heat loss, total heat-pump electricity is 946 kWh, of which only 116 kWh is space heating (about 830 kWh is hot water). Total heat-pump electricity therefore stays near 900 kWh/year in this study even when space heating is tiny. As design heat loss rises, space-heating electricity grows and becomes most of the total: at 16 kW it is 10,952 kWh of 11,965 kWh.
Limitations
- Results are modelled estimates for one location and one historic year (Gloucester, 2025).
- Solar gain through glazing, occupant count, standby electrical heat, and glazing assumptions are fixed. Real homes differ.
- These reports are heat-pump-only: no rooftop PV, battery, or tariff is included in the energy totals.
- Design heat loss must be estimated from a heat-loss survey or metered performance; the stepped values here are controlled scenarios, not a claim about a specific dwelling.
- Hot-water electricity is not listed separately in Table 3; only total heat-pump electricity (space plus hot water) is shown alongside space-heating metrics.
Conclusion
Design heat loss sets the fabric heat-loss coefficient. Annual space-heating energy is the integral of conductive fabric loss minus solar gain through glazing, occupant body heat, and standby electrical heat. When the fabric coefficient is small, those three heat inputs offset most of the conductive term, so net load is far below what annual demand would be if it scaled in direct proportion to design heat loss. When the fabric coefficient is large, the same three inputs are a smaller fraction of conductive loss, and net load scales nearly with design heat loss.
For this Gloucester 2025 model, a 2× change in design heat loss at the low end changes space-heating thermal output by 6.74× (1↔2 kW). From mid to high heat loss, space heat changes by nearly the same factor as the fabric coefficient (8 to 16 kW: 2.19×), so absolute savings from insulating a high-loss home remain large. Average space-heating COP can look better on a leakier home only because the heat pump runs more often in milder weather; absolute electricity use remains much higher.
References
- Solar Butter. Historic heat pump energy reports: design heat loss 1–16 kW, UK-Gloucester, 2025.
- Are heat pumps still worth it for old properties? : fabric heat loss and running cost across property ages.
- How much does it cost to run a heat pump? : location comparison with solar and battery.
- Octopus Flux or Cosy for a heat pump home with a battery? : tariff choice once heat demand is known.
