Enter the two end-point temperature differences (ΔT₁ and ΔT₂) into the calculator to determine the logarithmic mean temperature difference (LMTD).

Logarithmic Mean Temperature Difference (LMTD) Calculator

Enter any 2 values to calculate the missing variable

LMTD Formula

The following formula is used to calculate a logarithmic mean temperature difference (LMTD) from the two end-point temperature differences in a heat exchanger. 

LMTD = (\Delta T_1 - \Delta T_2) / \ln(\Delta T_1/\Delta T_2)
  • Where LMTD is the logarithmic mean temperature difference
  • ΔT₁ is the temperature difference (hot − cold) at one end of the heat exchanger
  • ΔT₂ is the temperature difference (hot − cold) at the other end of the heat exchanger

To calculate LMTD, divide the difference between the two end-point temperature differences (ΔT₁ − ΔT₂) by the natural log of their ratio ln(ΔT₁/ΔT₂). In practice, ΔT₁ and ΔT₂ are typically used as positive temperature differences (or you can use absolute values).

Any consistent temperature-difference unit can be used (°C, K, °F, or °R), as long as ΔT₁ and ΔT₂ are in the same unit.

LMTD Definition

What is LMTD?

LMTD, short for logarithmic mean temperature difference, is a metric used in thermodynamics to represent the average temperature-driving force for heat transfer in a heat exchanger.

For a heat exchanger operating at steady state with (approximately) constant heat-transfer area A and overall heat-transfer coefficient U, a larger LMTD corresponds to a larger heat-transfer rate (since Q = U·A·LMTD), and a smaller LMTD corresponds to a smaller heat-transfer rate.

Example Problem

How to calculate LMTD?

Assume a counterflow heat exchanger where the hot fluid enters at 150 °C and leaves at 100 °C, while the cold fluid enters at 60 °C and leaves at 90 °C.

First, determine the end-point temperature difference at one end (for counterflow, a common choice is hot inlet minus cold outlet):

ΔT₁ = Th,in − Tc,out = 150 − 90 = 60 °C

Next, determine the end-point temperature difference at the other end (hot outlet minus cold inlet):

ΔT₂ = Th,out − Tc,in = 100 − 60 = 40 °C

Finally, calculate LMTD using the formula above:

LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)

LMTD = (60 − 40) / ln(60/40)

LMTD ≈ 49.33 °C

FAQ

What are the practical applications of calculating LMTD in real-world scenarios?
LMTD is widely used in designing and evaluating heat exchangers (power plants, chemical processing, HVAC, refrigeration, etc.). When combined with the overall heat-transfer coefficient and area (Q = U·A·LMTD), it helps estimate heat-transfer rates and informs sizing and performance checks.

Can LMTD be used for all types of heat exchangers?
The LMTD method applies directly to simple parallel-flow and counterflow exchangers when the inlet and outlet temperatures are known. It is also commonly applied to multipass shell-and-tube and crossflow exchangers by using an LMTD correction factor. If outlet temperatures are unknown (design problems), the effectiveness–NTU method is often more convenient.

How does the choice of temperature units (Fahrenheit, Celsius, Kelvin) affect the LMTD calculation?
LMTD is computed from temperature differences, so you may use °C, K, °F, or °R as long as ΔT₁ and ΔT₂ are in the same unit. The result will be in that same temperature-difference unit.