{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"heat-loss"},"result":{"entity_type":"calculator","id":"heat-loss","calculator_id":"heat-loss","canonical_url":"https://tttkmbb.com/energy/heat-loss","name":"Heat Loss Calculator","title":"Heat Loss Calculator – Watts and BTU/h through a Wall, Roof or Window from U-value or R-value","category":"energy","category_name":"Home Energy & Electrical","tool_name":"calculate_heat_loss","featured_mcp_tool":false,"description":"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.","inputs":[{"name":"area_m2","label":"Element area","type":"number","unit":"m²","required":true,"max":1000000,"exclusive_min":0,"description":"Area of the wall, roof, floor or window in square metres.","example":20},{"name":"u_value_w_m2k","label":"U-value","type":"number","unit":"W/(m²·K)","required":false,"max":20,"exclusive_min":0,"description":"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.","example":0.3},{"name":"r_value_si","label":"R-value (SI)","type":"number","unit":"m²·K/W","required":false,"max":100,"exclusive_min":0,"description":"Thermal resistance in SI units (RSI), the reciprocal of the U-value; alternative to u_value_w_m2k."},{"name":"r_value_imperial","label":"R-value (imperial)","type":"number","unit":"ft²·°F·h/BTU","required":false,"max":500,"exclusive_min":0,"description":"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."},{"name":"temperature_difference_k","label":"Temperature difference","type":"number","unit":"K","required":true,"min":0,"max":100,"description":"Inside minus outside temperature in kelvin (identical to °C difference), e.g. 20 for 21 °C inside and 1 °C outside.","example":20},{"name":"hours_per_day","label":"Hours per day","type":"number","unit":"h","required":false,"default":24,"min":0,"max":24,"description":"Hours per day the temperature difference applies.","example":24},{"name":"electricity_price_per_kwh","label":"Electricity price","type":"number","unit":"per kWh","required":false,"min":0,"max":100,"description":"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).","example":0.3}],"outputs":[{"name":"heat_loss_w","label":"Heat loss","type":"number","unit":"W","decimals":1,"description":"U × area × temperature difference."},{"name":"heat_loss_btu_per_hour","label":"Heat loss (BTU/h)","type":"number","unit":"BTU/h","decimals":1,"description":"Heat loss in BTU per hour (1 W = 3.412142 BTU/h)."},{"name":"energy_per_day_kwh","label":"Energy per day","type":"number","unit":"kWh","decimals":3,"description":"heat_loss_w × hours_per_day / 1000."},{"name":"energy_per_month_kwh","label":"Energy per month","type":"number","unit":"kWh","decimals":2,"description":"Daily energy × 30 days."},{"name":"cost_per_month","label":"Cost per month","type":"number","decimals":2,"description":"Monthly energy × electricity_price_per_kwh, for electric resistance heating (divide by the COP for a heat pump); only when a price is given."},{"name":"u_value_used","label":"U-value used","type":"number","unit":"W/(m²·K)","decimals":4,"description":"Thermal transmittance used in the calculation."},{"name":"r_value_si","label":"R-value (SI)","type":"number","unit":"m²·K/W","decimals":3,"description":"1 / U-value."},{"name":"r_value_imperial","label":"R-value (imperial)","type":"number","unit":"ft²·°F·h/BTU","decimals":2,"description":"R-value (SI) × 5.678."}],"input_schema":{"type":"object","properties":{"area_m2":{"description":"Area of the wall, roof, floor or window in square metres. Unit: m².","type":"number","maximum":1000000,"exclusiveMinimum":0,"examples":[20],"x-unit":"m²"},"u_value_w_m2k":{"description":"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. Unit: W/(m²·K).","type":"number","maximum":20,"exclusiveMinimum":0,"examples":[0.3],"x-unit":"W/(m²·K)"},"r_value_si":{"description":"Thermal resistance in SI units (RSI), the reciprocal of the U-value; alternative to u_value_w_m2k. Unit: m²·K/W.","type":"number","maximum":100,"exclusiveMinimum":0,"x-unit":"m²·K/W"},"r_value_imperial":{"description":"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. Unit: ft²·°F·h/BTU.","type":"number","maximum":500,"exclusiveMinimum":0,"x-unit":"ft²·°F·h/BTU"},"temperature_difference_k":{"description":"Inside minus outside temperature in kelvin (identical to °C difference), e.g. 20 for 21 °C inside and 1 °C outside. Unit: K.","type":"number","minimum":0,"maximum":100,"examples":[20],"x-unit":"K"},"hours_per_day":{"description":"Hours per day the temperature difference applies. Unit: h.","type":"number","minimum":0,"maximum":24,"default":24,"examples":[24],"x-unit":"h"},"electricity_price_per_kwh":{"description":"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). Unit: per kWh.","type":"number","minimum":0,"maximum":100,"examples":[0.3],"x-unit":"per kWh"}},"additionalProperties":false,"required":["area_m2","temperature_difference_k"]},"output_schema":{"type":"object","properties":{"heat_loss_w":{"description":"U × area × temperature difference. Unit: W.","type":"number","x-unit":"W"},"heat_loss_btu_per_hour":{"description":"Heat loss in BTU per hour (1 W = 3.412142 BTU/h). Unit: BTU/h.","type":"number","x-unit":"BTU/h"},"energy_per_day_kwh":{"description":"heat_loss_w × hours_per_day / 1000. Unit: kWh.","type":"number","x-unit":"kWh"},"energy_per_month_kwh":{"description":"Daily energy × 30 days. Unit: kWh.","type":"number","x-unit":"kWh"},"cost_per_month":{"description":"Monthly energy × electricity_price_per_kwh, for electric resistance heating (divide by the COP for a heat pump); only when a price is given.","type":"number"},"u_value_used":{"description":"Thermal transmittance used in the calculation. Unit: W/(m²·K).","type":"number","x-unit":"W/(m²·K)"},"r_value_si":{"description":"1 / U-value. Unit: m²·K/W.","type":"number","x-unit":"m²·K/W"},"r_value_imperial":{"description":"R-value (SI) × 5.678. Unit: ft²·°F·h/BTU.","type":"number","x-unit":"ft²·°F·h/BTU"}}},"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","method":"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.","sources":[{"name":"Wikipedia – Thermal transmittance (U-value)","url":"https://en.wikipedia.org/wiki/Thermal_transmittance","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – R-value (insulation)","url":"https://en.wikipedia.org/wiki/R-value_(insulation)","type":"reference","retrieved_at":"2026-09-24"},{"name":"U.S. DOE Energy Saver – Insulation (R-value)","url":"https://www.energy.gov/energysaver/insulation","type":"government","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"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},"expected":{"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},"url":"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"},{"name":"15 m² of R-19 insulation, ΔT 25 K","inputs":{"area_m2":15,"r_value_imperial":19,"temperature_difference_k":25},"expected":{"r_value_si":3.346,"u_value_used":0.2988,"heat_loss_w":112.1,"energy_per_day_kwh":2.69},"url":"https://tttkmbb.com/api/v1/calculate/heat-loss?area_m2=15&r_value_imperial=19&temperature_difference_k=25"}],"faq":[{"q":"How do I convert between R-value and U-value?","a":"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)."},{"q":"Which temperature difference should I use?","a":"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."},{"q":"Does the cost apply to gas heating?","a":"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."}],"tags":["heat loss","u-value","r-value","thermal transmittance","insulation","heat loss through wall"],"related":[{"calculator_id":"hvac-btu-sizing","reason":"Equipment size for the whole room."},{"calculator_id":"specific-heat","reason":"Energy to raise the temperature of a mass, the other side of the heat balance."},{"calculator_id":"electricity-cost","reason":"Cost of running the heater that replaces this loss."}],"links":{"html":"https://tttkmbb.com/energy/heat-loss","markdown":"https://tttkmbb.com/energy/heat-loss.md","json":"https://tttkmbb.com/energy/heat-loss.json","api":"https://tttkmbb.com/api/v1/calculate/heat-loss","schema":"https://tttkmbb.com/api/v1/calculators/heat-loss","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:48:10Z","next_actions":[{"tool":"run_calculator","calculator_id":"heat-loss","reason":"Run Heat Loss Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/energy/heat-loss.md"}}