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Heat Loss Calculator
Computes the steady-state conductive heat loss through a building element from its area, its thermal transmittance (U-value, or an SI or imperial R-value) and the inside–outside temperature difference, with the daily and monthly energy and the cost at an electricity price.
When to use
You want the heat flow through a specific wall, window, roof or floor at a given insulation level, or the energy an insulation upgrade would save.
Do not use when: You need a room's equipment size (use hvac-btu-sizing) or ventilation losses (use air-changes-per-hour); the formula ignores air leakage, solar gain and thermal mass.
Formula
heat_loss_w = U × area_m2 × temperature_difference_k, with U = u_value_w_m2k, or 1 / r_value_si, or 1 / (r_value_imperial / 5.678); heat_loss_btu_per_hour = heat_loss_w × 3.412142; energy_per_day_kwh = heat_loss_w × hours_per_day / 1000; energy_per_month_kwh = energy_per_day_kwh × 30; cost_per_month = energy_per_month_kwh × electricity_price_per_kwh
Fourier conduction through a plane element under steady conditions (ASHRAE Fundamentals). The U-value must include surface films, as published U-values do; whole-assembly R-values differ from the nominal insulation R because of studs and bridging.
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
area_m2 | number | m² | yes | Area of the wall, roof, floor or window in square metres. Range: > 0, ≤ 1000000 |
u_value_w_m2k | number | W/(m²·K) | no | Thermal transmittance, e.g. 0.3 for an insulated cavity wall, 1.4 for double glazing, 5.8 for single glazing. Give exactly one of u_value_w_m2k, r_value_si or r_value_imperial. Range: > 0, ≤ 20 |
r_value_si | number | m²·K/W | no | Thermal resistance in SI units (RSI), the reciprocal of the U-value; alternative to u_value_w_m2k. Range: > 0, ≤ 100 |
r_value_imperial | number | ft²·°F·h/BTU | no | Thermal resistance as printed on North American insulation (e.g. R-19); converted with R_SI = R / 5.678. Alternative to u_value_w_m2k. Range: > 0, ≤ 500 |
temperature_difference_k | number | K | yes | Inside minus outside temperature in kelvin (identical to °C difference), e.g. 20 for 21 °C inside and 1 °C outside. Range: ≥ 0, ≤ 100 |
hours_per_day | number | h | default 24 | Hours per day the temperature difference applies. Range: ≥ 0, ≤ 24 |
electricity_price_per_kwh | number | per kWh | no | Optional price per kWh in your currency, used to cost the loss as if replaced by electric resistance heating (1 kWh heat per kWh electricity). Range: ≥ 0, ≤ 100 |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
heat_loss_w | number | W | U × area × temperature difference. |
heat_loss_btu_per_hour | number | BTU/h | Heat loss in BTU per hour (1 W = 3.412142 BTU/h). |
energy_per_day_kwh | number | kWh | heat_loss_w × hours_per_day / 1000. |
energy_per_month_kwh | number | kWh | Daily energy × 30 days. |
cost_per_month | number | Monthly energy × electricity_price_per_kwh, for electric resistance heating (divide by the COP for a heat pump); only when a price is given. | |
u_value_used | number | W/(m²·K) | Thermal transmittance used in the calculation. |
r_value_si | number | m²·K/W | 1 / U-value. |
r_value_imperial | number | ft²·°F·h/BTU | R-value (SI) × 5.678. |
Example
20 m² wall, U 0.3, ΔT 20 K, price 0.30: {"area_m2":20,"u_value_w_m2k":0.3,"temperature_difference_k":20,"electricity_price_per_kwh":0.3} → {"heat_loss_w":120,"heat_loss_btu_per_hour":409.5,"energy_per_day_kwh":2.88,"energy_per_month_kwh":86.4,"cost_per_month":25.92,"r_value_si":3.333,"r_value_imperial":18.93}
15 m² of R-19 insulation, ΔT 25 K: {"area_m2":15,"r_value_imperial":19,"temperature_difference_k":25} → {"r_value_si":3.346,"u_value_used":0.2988,"heat_loss_w":112.1,"energy_per_day_kwh":2.69}
GET https://tttkmbb.com/api/v1/calculate/heat-loss?area_m2=20&u_value_w_m2k=0.3&temperature_difference_k=20&electricity_price_per_kwh=0.3
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/heat-loss(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/heat-loss · Markdown: https://tttkmbb.com/energy/heat-loss.md · JSON definition: https://tttkmbb.com/energy/heat-loss.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="heat-loss" - OpenAPI operationId:
calculate_heat_loss - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- Wikipedia – Thermal transmittance (U-value) (reference)
- Wikipedia – R-value (insulation) (reference)
- U.S. DOE Energy Saver – Insulation (R-value) (government)
FAQ
How do I convert between R-value and U-value?
U = 1 / R_SI. Imperial R (ft²·°F·h/BTU) divided by 5.678 gives R_SI (m²·K/W); e.g. R-19 ≈ RSI 3.35 ≈ U 0.30 W/(m²·K).
Which temperature difference should I use?
For a design load use the indoor setpoint minus the local design outdoor temperature; for seasonal energy use the average difference over the heating period, or run the calculator per month.
Does the cost apply to gas heating?
The cost assumes 1 kWh of electricity per kWh of heat. For gas divide by the boiler efficiency and use the gas price per kWh; for a heat pump divide by its seasonal COP.
Related calculators
- HVAC BTU Sizing Calculator — Equipment size for the whole room.
- Specific Heat Calculator — Energy to raise the temperature of a mass, the other side of the heat balance.
- Electricity Cost Calculator — Cost of running the heater that replaces this loss.