Heating
Radiators and baseboard heaters: output, length and ΔT
A radiator rated at one temperature gives a different output at another. Once you know the ΔT rule, sizing emitters for a room and a boiler for the house is straightforward.
Emitters: where the heat leaves the system
A hydronic heating system heats water in a boiler and pumps it through pipes to emitters in each room: cast-iron or steel panel radiators, fin-tube baseboard, or tubing in the floor. An electric system skips the water and uses resistance elements in baseboard or wall heaters. Either way, the room’s heat loss sets how much emitter it needs, and the per-square-foot heating figures by climate zone give the first estimate. A 168 sq ft bedroom in climate zone 4, at 38 BTU per hour per square foot, loses 6,384 BTU per hour on the design night.
Why output depends on temperature
A radiator gives off heat in proportion to the difference between its surface and the room, raised to a power of about 1.3, because hotter surfaces also drive more convection. Manufacturers rate panels at a standard difference, ΔT 50 °C in the European standard EN 442, which corresponds to water averaging about 160 °F in a 68 °F room. At any other temperature the output changes:
| Average water temperature | ΔT (room 68 °F) | Output as a share of rating |
|---|---|---|
| 180 °F | 62 °C | 132% |
| 160 °F | 51 °C | 103% |
| 140 °F | 40 °C | 75% |
| 120 °F | 29 °C | 49% |
| 110 °F | 23 °C | 37% |
This is why lowering a boiler’s water temperature, which a condensing boiler needs in order to condense and reach its rated efficiency, means the radiators must be larger or the house better insulated. It is also the central question when replacing a boiler with an air-to-water heat pump, which works best at 120 °F or below: at that temperature a radiator gives about half its rated output. The radiator BTU output calculator applies the correction for any water temperature.
Radiators, worked
A modern panel and an old cast-iron radiator
A type 22 double-panel radiator, 24 in high and 40 in long, at the standard condition:
- Face area: 0.610 × 1.016 = 0.619 m²
- Output: 0.619 × 3,200 W per m² = 1,982 W, or 6,763 BTU/hr
- Room it can heat in zone 4: 6,763 ÷ 38 = 178 sq ft
A cast-iron radiator with 12 sections 25 in high, on a boiler running 180 °F water (ΔT 61 °C):
- Rated output at ΔT 50: 6,000 BTU/hr
- Correction: (61 ÷ 50)^1.3 = 1.295
- Output: 6,000 × 1.295 = 7,770 BTU/hr, enough for 149 sq ft in zone 6
Old cast-iron systems were often sized generously for houses that had no insulation. After insulation and new windows, the same radiators can heat the house at a lower water temperature, which suits a condensing boiler or a heat pump.
Baseboard length
Baseboard is rated per foot. Standard electric baseboard gives 250 watts per foot at 240 V; hot-water fin-tube baseboard gives around 450 to 600 BTU per hour per foot at typical water temperatures, falling at lower temperatures in the same way as a radiator. The baseboard heater calculator divides the room’s load by the rating:
Electric and hot-water baseboard
A 168 sq ft bedroom in zone 4 with electric baseboard:
- Room load: 168 × 38 = 6,384 BTU/hr, or 1,871 W
- Length: 1,871 ÷ 250 = 7.5, so 8 ft, one 2,000 W unit drawing 8.3 A at 240 V
A 220 sq ft room in zone 6 with fin-tube at 160 °F average water:
- Room load: 220 × 52 = 11,440 BTU/hr
- Length: 11,440 ÷ 450 = 25.4, so 26 ft
Baseboard goes under windows and along outside walls, where the cold is. If the room does not have that much free wall, high-output baseboard, a panel radiator or a kickspace heater does the job in less length.
Space heaters and floors
A plug-in space heater is limited to about 1,500 W by the 15 A household circuit, which is about 5,100 BTU per hour. That is enough to top up a 150 sq ft room but not to heat a cold one on its own; the space heater size calculator says when a room needs a hardwired 240 V heater instead.
Radiant floors work at a much lower surface temperature, typically 80 to 85 °F, and give about 2 BTU per hour per square foot for each degree the floor is above the room. A 200 sq ft tile floor at 80 °F in a 70 °F room gives 4,000 BTU per hour, about half a zone 4 living room’s load. The radiant floor heat output calculator shows how much of the room a floor can cover and the water temperature it needs.
Sizing the boiler behind them
A boiler is sized from the house’s heat loss, or from the total radiation connected to it, plus a small allowance for warming up the system:
Eight radiators on a cast-iron boiler
Eight radiators averaging 6,000 BTU/hr each, 15% pickup, an 85% AFUE boiler.
- Net load: 8 × 6,000 = 48,000 BTU/hr
- Gross output: 48,000 × 1.15 = 55,200 BTU/hr
- Input: 55,200 ÷ 0.85 = 64,941 BTU/hr, so a 70,000 BTU/hr boiler
The boiler size calculator sizes from either the radiation or the house, and asks the question that matters: do the radiators represent the house’s real heat loss? If they are generous, as they often are in older homes, a smaller boiler running cooler water serves the house better. Input, output and AFUE work exactly as for a furnace, which the guide to furnace input and output explains.
Heat pumps and low water temperatures
Air-to-water heat pumps run most efficiently at low water temperatures. A house with radiators sized for 180 °F water will usually need some larger radiators, or better insulation, to be heated at 120 °F. Work through each room: its load at the design temperature, from the guide to BTU per square foot by climate zone, against its radiator’s output at the lower temperature. Rooms that come up short are the ones to upgrade. The guide to heat pumps in cold climates covers the other half of the question, the heat pump’s own output in cold weather.