Heat output from water flow — P = q · c · ΔT

In a water-based heating or cooling system the energy is carried by the water. How much power is transferred depends on how much water flows and by how many degrees it is cooled (or heated) along the way.

For water near room temperature the formula reduces to a handy rule of thumb: P[kW] ≈ q[l/s] · 4.19 · ΔT. A ΔT of 20 K means, for example, 70/50 °C flow/return.

A flow of 0.2 l/s with ΔT = 20 K gives P = 0.2 · 4.19 · 20 ≈ 16.8 kW. If you want to move more power through the same pipe, you must either increase the flow (= higher velocity) or increase ΔT.

• 01c and ρ for water vary slightly with temperature — the common values near room temperature are used here.
• 02Applies to pure water. For glycol mixtures and other fluids, the relevant material constants must be entered.

The formula is based on the mass flow ṁ [kg/s], but on site you usually measure and balance the volume flow q [l/s or m³/h]. The two are linked via the density: ṁ = q · ρ. For cold water ρ ≈ 1000 kg/m³ (1 kg/l), but hot water takes up more space: at 70 °C ρ ≈ 978 kg/m³, at 90 °C ≈ 965 kg/m³. In heating systems the difference is a few percent and often disappears in the rule of thumb P[kW] ≈ q[l/s] · 4.19 · ΔT, but for precise balancing and for domestic hot water you must use the actual density.

A radiator's rated output is not a fixed number — it applies at specific temperatures. All European radiators are measured according to DS/EN 442 at 75 °C supply, 65 °C return and 20 °C room, which gives a logarithmic mean temperature difference of 50 K. If the system runs colder (e.g. combined with a heat pump), the radiator emits less.

The shares are calculated with n = 1.3 and logarithmic ΔT per EN 442. The point is striking: at low-temperature operation for a heat pump, a given radiator delivers only a third to a quarter of its catalogue output — which is why heat pump conversion often requires larger radiator surfaces or underfloor heating. (Source: DS/EN 442; REHVA Journal — indicative calculation.)