This calculator works out the temperature of water after a hot and a cold stream are mixed, as in a mixing valve or a bath. Enter each temperature and flow rate; you get the mixed temperature, the total flow and the share of hot water.
Formula
Heat balance: the mixed temperature is the flow-weighted average, Tm = (Th × Qh + Tc × Qc) ÷ (Qh + Qc). It assumes both streams are water and no heat is lost. To hit a target temperature, the hot share is (Tm − Tc) ÷ (Th − Tc).
- Th, Tc: hot and cold temperatures
- Qh, Qc: hot and cold flow rates in the same unit
Worked Example
4 L/min at 60 °C mixed with 6 L/min at 10 °C.
- 60 × 4 = 240; 10 × 6 = 60; sum 300
- Total flow = 4 + 6 = 10.00 L/min
- Tm = 300 ÷ 10 = 30.0 °C = 30 × 9 ÷ 5 + 32 = 86.0 °F
- Hot share = 4 ÷ 10 = 40.0%
Limits and common mistakes
- Works with °F too, as long as both inputs use the same scale.
- Very hot water scalds quickly; thermostatic mixing valves exist to cap the outlet temperature, and their setting follows local plumbing rules.
- Pipe runs cool the hot water, so the real outlet is often a little cooler.
Formula used
in th | Hot water temperature | °C | 60 | 0 | 100 in qh | Hot water flow | L/min | 4 | 0 in tcold | Cold water temperature | °C | 10 | 0 | 100 in qc | Cold water flow | L/min | 6 | 0 out tm | Mixed temperature | °C | (th * qh + tcold * qc) / (qh + qc) | 1 out q | Total flow | L/min | qh + qc | 2 out tf | Mixed temperature | °F | tm * 9 / 5 + 32 | 1 out hs | Hot water share of the flow | % | qh / (qh + qc) * 100 | 1
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.
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