LMTD Calculator
LMTD is the logarithmic average of the end temperature differences: a counter-flow exchanger with hot 150 → 100 °C and cold 30 → 70 °C has LMTD = 74.8888 °C.
With U, gives the area needed; 0 to skip.
74.8887568941862 °C
Full answer, then cut to fewer decimals (not rounded):
- 74.8887568941862 °C
- 74.888756894186 °C
- 74.88875689418 °C
- 74.8887568941 °C
- 74.888756894 °C
- 74.88875689 °C
- 74.8887568 °C
- 74.888756 °C
- 74.88875 °C
- 74.8887 °C
- 74.888 °C
- 74.88 °C
- 74.8 °C
- ΔT₁
- 80 °C
- ΔT₂
- 70 °C
- Arithmetic mean ΔT (for comparison)
- 75 °C
- Area needed A = Q/(U·LMTD)
- 5.34126 m²
Step-by-step solution
- Counter-flow: ΔT₁ = Th,i − Tc,o = 80, ΔT₂ = Th,o − Tc,i = 70
- LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂) = 10 ÷ ln(1.14286) = 74.8888 °C
LMTD Formula
LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂)
counter-flow ΔT₁ = Th,i − Tc,o, ΔT₂ = Th,o − Tc,i
Worked Example
Counter-flow: hot 150 → 100 °C, cold 30 → 70 °C, Q = 200 kW, U = 500 W/m²·K:
- Counter-flow: ΔT₁ = Th,i − Tc,o = 80, ΔT₂ = Th,o − Tc,i = 70
- LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂) = 10 ÷ ln(1.14286) = 74.8888 °C
ΔT₂: 70 °C · Arithmetic mean ΔT (for comparison): 75 °C · Area needed A = Q/(U·LMTD): 5.34126 m²
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Frequently asked questions
Why is counter-flow LMTD higher than parallel flow?
The temperature difference stays more even along the exchanger, so for the same terminal temperatures counter-flow needs less area.
What if ΔT₁ = ΔT₂?
The formula becomes 0/0, and the LMTD equals that common difference.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). LMTD Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/lmtd-calculator/
IEEE
Scientific Converters, "LMTD Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/lmtd-calculator/