# 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.

- Calculator id: `heat-loss` · Category: Home Energy & Electrical (`energy`) · Tool name: `calculate_heat_loss`
- Canonical page: https://tttkmbb.com/energy/heat-loss · This document: https://tttkmbb.com/energy/heat-loss.md · JSON definition: https://tttkmbb.com/energy/heat-loss.json

## Purpose

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.

**Use when:** 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.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `area_m2` | number | m² | required | Area of the wall, roof, floor or window in square metres. (> 0, max 1000000) |
| `u_value_w_m2k` | number | W/(m²·K) | optional | 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. (> 0, max 20) |
| `r_value_si` | number | m²·K/W | optional | Thermal resistance in SI units (RSI), the reciprocal of the U-value; alternative to u_value_w_m2k. (> 0, max 100) |
| `r_value_imperial` | number | ft²·°F·h/BTU | optional | 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. (> 0, max 500) |
| `temperature_difference_k` | number | K | required | Inside minus outside temperature in kelvin (identical to °C difference), e.g. 20 for 21 °C inside and 1 °C outside. (min 0, max 100) |
| `hours_per_day` | number | h | optional, default 24 | Hours per day the temperature difference applies. (min 0, max 24) |
| `electricity_price_per_kwh` | number | per kWh | optional | 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). (min 0, max 100) |

## Output

| Field | 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. |

## 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.

## Data Sources

- Wikipedia – Thermal transmittance (U-value) — https://en.wikipedia.org/wiki/Thermal_transmittance (reference, retrieved 2026-09-24)
- Wikipedia – R-value (insulation) — https://en.wikipedia.org/wiki/R-value_(insulation) (reference, retrieved 2026-09-24)
- U.S. DOE Energy Saver – Insulation (R-value) — https://www.energy.gov/energysaver/insulation (government, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/heat-loss?area_m2=…&temperature_difference_k=…`
- `POST https://tttkmbb.com/api/v1/calculate/heat-loss` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/heat-loss · OpenAPI operationId `calculate_heat_loss` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "heat-loss", "inputs": {…}}`

## Example

- 20 m² wall, U 0.3, ΔT 20 K, price 0.30: inputs `{"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: inputs `{"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
```

## Limitations

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. 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. All values are computed from the formula above; no measurement or live data is involved.

## 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

- [HVAC BTU Sizing Calculator](https://tttkmbb.com/energy/hvac-btu-sizing.md) — Equipment size for the whole room.
- [Specific Heat Calculator](https://tttkmbb.com/physics/specific-heat.md) — Energy to raise the temperature of a mass, the other side of the heat balance.
- [Electricity Cost Calculator](https://tttkmbb.com/everyday/electricity-cost.md) — Cost of running the heater that replaces this loss.