LMTD Calculator (Log Mean Temperature Difference)

What this calculator does

The log mean temperature difference, or LMTD, is the correct average temperature gap to use when sizing a heat exchanger, because the gap between the hot and cold fluid rarely stays constant along its length. A simple arithmetic average of the two end temperatures overstates the true driving force whenever the gap narrows sharply from one end to the other, which is why engineers use the logarithmic form instead.

This LMTD calculator takes the temperature difference at each end of the exchanger and returns the log mean value, alongside the plain arithmetic mean for comparison. The gap between the two shows how much error a simple average would introduce for a given pair of end temperatures.

The formula

FormulaLMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

LMTD equals (ΔT1 − ΔT2) divided by the natural log of (ΔT1 ÷ ΔT2), where ΔT1 and ΔT2 are the temperature differences between the two fluid streams at each end of the exchanger. When ΔT1 and ΔT2 are equal, this formula divides by ln(1), which is zero, so it is undefined by direct substitution; the mathematical limit as ΔT2 approaches ΔT1 is simply that common value, so this calculator returns ΔT1 directly in that case rather than showing an error.

Term	Meaning
ΔT1	The temperature difference between the two fluids at one end of the exchanger.
ΔT2	The temperature difference between the two fluids at the other end of the exchanger.
LMTD	The log mean temperature difference: the effective average driving temperature gap along the exchanger.

The inputs explained

Field	What to enter
Temperature difference at end 1 (ΔT1) (°C)	The temperature difference between the hot and cold stream at whichever end you label the first end.
Temperature difference at end 2 (ΔT2) (°C)	The temperature difference between the hot and cold stream at the other end.

When to use it

Sizing a shell-and-tube heat exchanger

LMTD is combined with the overall heat transfer coefficient and required duty to work out the heat transfer area a shell-and-tube or plate exchanger needs.

Comparing counterflow and parallel-flow arrangements

For the same inlet and outlet temperatures, a counterflow arrangement produces a higher LMTD than a parallel-flow one, which is one reason counterflow exchangers are usually more compact for the same duty.

Checking a vendor's exchanger sizing

Recomputing LMTD independently from the quoted end temperatures is a quick way to check that a vendor's sizing calculation used the temperatures you actually specified.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How LMTD compares to a simple arithmetic average as the end temperatures diverge

A fixed 80°C gap at one end, against a range of gaps at the other end.

ΔT1 held at 80°C

ΔT2	Log mean temperature difference (LMTD)	Arithmetic mean of the two, for comparison
80°C	80.00 °C	80.00 °C
60°C	69.52 °C	70.00 °C
40°C	57.71 °C	60.00 °C
20°C	43.28 °C	50.00 °C
10°C	33.66 °C	45.00 °C
5°C	27.05 °C	42.50 °C

When the two end differences are equal the log mean and the arithmetic mean coincide exactly at 80°C; as the gap at one end shrinks relative to the other, the log mean pulls further below the simple average, understating the driving force less than a plain average would overstate it.

LMTD for a range of typical shell-and-tube end conditions

Several ΔT1 values against a ΔT2 fixed at 15°C, a common tighter approach temperature.

A spread of end-temperature pairs

ΔT1	Log mean temperature difference (LMTD)
15°C	15.00 °C
30°C	21.64 °C
50°C	29.07 °C
80°C	38.83 °C
120°C	50.49 °C
200°C	71.42 °C

A wider gap between the two end differences pulls the LMTD progressively closer to the smaller of the two values rather than to their midpoint, which is why using a plain average in place of LMTD tends to overstate the effective driving temperature the further apart the two ends are.

Questions

Why not just average the two end temperature differences?

A straight arithmetic average overstates the true driving force whenever heat transfer along the exchanger is not linear, which is the normal case. The logarithmic form correctly weights the way the temperature gap actually changes along the length of the exchanger, and the two only coincide exactly when ΔT1 equals ΔT2.

What happens when ΔT1 and ΔT2 are equal?

The formula (ΔT1 − ΔT2) ÷ ln(ΔT1 ÷ ΔT2) becomes 0 ÷ 0 by direct substitution, since ln(1) is zero. Taking the mathematical limit shows LMTD equals that common temperature difference, and this calculator applies that limit directly rather than returning an error.

Does it matter which end I call ΔT1 and which I call ΔT2?

No. The formula is symmetric in the two values, so swapping them gives the same LMTD result either way.

Is LMTD different for counterflow versus parallel-flow exchangers?

The formula itself is the same, but the ΔT1 and ΔT2 values you feed into it differ, because the two fluids meet at opposite ends in a counterflow arrangement. Working out ΔT1 and ΔT2 correctly for the actual flow arrangement is what changes, not the LMTD formula.

For the heat transfer rate itself once you have a temperature driving force, see the thermal conductivity calculator.