Cold-Climate Heat Pump Sizing Calculator

Key inputs (and where to find them)

Effective Envelope UA (Btu/hr·°F)

UA represents how readily heat flows out of the building by conduction through walls, windows, ceilings, floors, etc. It’s the sum of each component’s U-value × Area. You may see UA in an energy audit report, modeling output, or you can approximate it from assemblies and window specs. As a rough feel (very home-dependent): older leaky homes can be several hundred Btu/hr·°F; deep-retrofit/high-performance homes can be much lower.

Outdoor design temperature (°F)

Use a code/ASHRAE-style winter design temperature (often the 99% or 99.6% heating design condition). This is not the record low; it’s a temperature that’s cold but occurs often enough to design around.

Blower-door ACH50

ACH50 is air changes per hour at 50 Pascals from a blower-door test. This tool converts ACH50 to an estimated “natural” infiltration rate (ACH_n) using a simple factor (see formulas below). If you already have a better site-specific conversion (from an auditor/model), use that instead by adjusting inputs/expectations.

Continuous ventilation (CFM)

Enter continuous mechanical outdoor air in CFM (e.g., ERV/HRV supply or exhaust, or a supply fan). For simplicity, this calculator treats ventilation air as outdoor air that must be heated to indoor temperature (i.e., it does not explicitly model heat-recovery effectiveness).

HSPF (Region V) and heating season hours

HSPF is a seasonal efficiency metric. This tool uses HSPF and an hour estimate to produce a rough seasonal energy figure. For equipment selection in cold climates, always check the manufacturer’s low-ambient capacity and COP tables at your design temperature.

Formulas and units

The calculator uses standard steady-state heat-loss relationships at the design condition.

1) Temperature difference

ΔT = T_indoor − T_outdoor (°F)

2) Conduction (envelope) heat loss

Q_cond = UA × ΔT (Btu/hr)

3) Infiltration heat loss (from ACH50)

First estimate building volume from floor area and ceiling height:

V = Area × Height (ft³)

Convert blower-door ACH50 to an estimated natural ACH (ACH_n). A common rough factor used for cold climates is:

ACH_n ≈ ACH50 × 0.02

Then convert ACH_n to infiltration airflow (CFM):

CFM_inf = (ACH_n × V) / 60

Finally compute infiltration heat loss using the air heat capacity constant (1.08):

Q_inf = 1.08 × CFM_inf × ΔT (Btu/hr)

4) Ventilation heat loss

Q_vent = 1.08 × CFM_vent × ΔT (Btu/hr)

5) Total design heating load and sizing factor

Q_total = Q_cond + Q_inf + Q_vent

Apply a sizing safety factor:

Q_target = Q_total × (1 + SafetyFactor/100)

MathML summary

Where A is floor area (ft²) and H is average ceiling height (ft). Constants and conversion factors are approximations; see limitations below.

How to interpret the results

• Design heating load (Btu/hr): Estimated heat required to hold the indoor setpoint at the outdoor design temperature. This is the number you compare to heat-pump delivered capacity at that temperature.
• Heat pump sizing target: The design load multiplied by your safety factor. In cold climates, it’s common to size near the load and rely on variable-speed modulation (and sometimes backup) rather than oversizing heavily.
• Backup requirement: If your heat pump can’t deliver the full design load at the design temperature, you need supplemental heat (electric resistance, boiler, etc.). Your entered backup kW is compared to the remaining shortfall.
• Nominal “tons” vs. cold-weather capacity: A “3-ton” label is typically based on ~47°F conditions, not your design temperature. Always confirm capacity at 5°F, 0°F, −5°F, etc. from submittals.

If the calculator suggests a capacity target that’s close to a piece of equipment’s rated low-ambient output, that’s a good sign. If it’s far above, investigate envelope improvements, duct losses, zoning, or a different equipment class.

Worked example (using the default inputs)

Assume:

• Area = 2000 ft², Ceiling height = 8.5 ft → Volume V = 17,000 ft³
• UA = 350 Btu/hr·°F
• Outdoor design = −5°F, Indoor = 70°F → ΔT = 75°F
• ACH50 = 4.0 → ACH_n ≈ 4.0 × 0.02 = 0.08
• Ventilation = 60 CFM
• Safety factor = 10%

Conduction:

Q_cond = 350 × 75 = 26,250 Btu/hr

Infiltration airflow:

CFM_inf = (0.08 × 17,000) / 60 ≈ 22.7 CFM

Infiltration loss:

Q_inf = 1.08 × 22.7 × 75 ≈ 1,840 Btu/hr

Ventilation loss:

Q_vent = 1.08 × 60 × 75 = 4,860 Btu/hr

Total design load:

Q_total ≈ 26,250 + 1,840 + 4,860 = 32,950 Btu/hr

With 10% safety factor:

Q_target ≈ 32,950 × 1.10 = 36,245 Btu/hr

That target is the number to compare against a candidate heat pump’s capacity at −5°F (not just its nominal tonnage).

Quick comparisons (what changes the load most)

Assumptions and limitations (important)

• Not a full Manual J: This estimate does not model room-by-room loads, window orientation/solar gains, internal gains, duct losses, foundation edge effects, or detailed assembly takeoffs.
• ACH50 to natural infiltration is simplified: Using ACH_n ≈ ACH50 × 0.02 is a rough rule-of-thumb. True infiltration varies with wind, stack effect, shielding, height, terrain, and leakage distribution.
• Ventilation heat recovery is not credited: If you have an HRV/ERV, actual ventilation heating load may be lower than shown depending on effectiveness, defrost behavior, and airflow balance.
• Steady-state at design condition: The load is computed at a single outdoor temperature. Real weather is dynamic; equipment controls, thermal mass, and setbacks can change performance.
• Equipment capacity must be checked at temperature: Heat pumps have temperature-dependent capacity. Always verify delivered capacity and minimum/maximum modulation at your design temperature.
• Distribution and delivery losses not included: Duct leakage in attics/crawlspaces, hydronic distribution losses, or poor airflow can increase required capacity.
• Energy estimate is coarse: HSPF-based seasonal estimates are simplified and may differ from utility bills due to occupant behavior, thermostat settings, solar gains, and regional weather.

If you’re near the edge of capacity (or in very cold/windy sites), use this tool to narrow options, then confirm with a Manual J (or equivalent) and manufacturer performance data.

CSV download: Use the CSV to share your inputs, intermediate values, and outputs with an energy auditor or HVAC contractor for review.