LMTD Calculator – Log Mean Temperature Difference

Enter the hot and cold fluid inlet/outlet temperatures and the flow arrangement to get the log mean temperature difference (LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2)) used to size heat exchangers.

Quick Facts

LMTD formula
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
The true driving temperature difference between two fluids exchanging heat.
Counter-flow ΔTs
ΔT1 = Th,in − Tc,out; ΔT2 = Th,out − Tc,in
Fluids flow in opposite directions through the exchanger.
Parallel-flow ΔTs
ΔT1 = Th,in − Tc,in; ΔT2 = Th,out − Tc,out
Fluids flow the same direction; always less efficient than counter-flow.
Sizing equation
Q = U × A × LMTD
Combines LMTD with the overall heat transfer coefficient U and area A to size an exchanger.

Your Results

Calculated
LMTD
-
Log mean temperature difference
ΔT at End 1
-
Temperature difference at one exchanger end
ΔT at End 2
-
Temperature difference at the other exchanger end
Arithmetic Mean ΔT
-
(ΔT1 + ΔT2) / 2, for comparison with LMTD

Ready

Enter the four exchanger temperatures, choose a flow arrangement, then press Calculate.

Formula and Method for the LMTD Calculator – Log Mean Temperature Difference

In a heat exchanger, the temperature difference between the hot and cold fluids is rarely constant along the length of the unit — it shrinks (or grows) as heat transfers from one stream to the other. Using a simple arithmetic average of the inlet and outlet temperature differences overstates the true driving force for heat transfer, because the temperature gap changes exponentially, not linearly, along the flow path. The Log Mean Temperature Difference (LMTD) is the correct, exact average to use: LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the hot and cold streams at the two ends of the exchanger. Multiplying LMTD by the overall heat transfer coefficient U and the heat transfer area A gives the total heat duty: Q = U × A × LMTD.

How the calculation works

First choose the flow arrangement. In counter-flow (counter-current) exchangers the hot and cold fluids move in opposite directions, so the end-point differences are ΔT1 = Th,in − Tc,out and ΔT2 = Th,out − Tc,in. In parallel-flow (co-current) exchangers both fluids move the same direction, so ΔT1 = Th,in − Tc,in and ΔT2 = Th,out − Tc,out. Once ΔT1 and ΔT2 are found, the calculator applies LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2). If ΔT1 and ΔT2 happen to be equal, that formula is a 0/0 indeterminate form; the mathematical limit shows LMTD simply equals ΔT1 in that special case, which this calculator handles automatically. The calculator also reports the arithmetic mean ΔT — (ΔT1 + ΔT2) / 2 — so you can see how much the true log mean differs from the naive average.

Common mistakes

  • Pairing the wrong temperatures: mixing up the counter-flow and parallel-flow ΔT definitions is the most common error — double-check which outlet pairs with which inlet for your actual flow direction.
  • Ignoring a temperature cross: if ΔT1 or ΔT2 comes out zero or negative, the hot stream is not staying warmer than the cold stream at that end — the log mean formula is undefined there, and the arrangement needs to be re-examined (or a multi-pass design considered).
  • Skipping the correction factor: the plain LMTD formula is exact only for true single-pass counter-flow or parallel-flow. Shell-and-tube and multi-pass exchangers need a correction factor F (F ≤ 1) applied as Q = U × A × LMTD × F.
  • Substituting the arithmetic mean: (ΔT1 + ΔT2) / 2 is only a close approximation of LMTD when ΔT1 and ΔT2 are within about 40% of each other; for larger spreads it noticeably overstates the true driving temperature difference.

Real-world applications

  • Sizing shell-and-tube, plate, and double-pipe heat exchangers for process plants, using Q = U × A × LMTD × F to solve for the required surface area A.
  • Designing HVAC coils, radiators, and condensers where hot and cold streams exchange sensible heat.
  • Comparing counter-flow versus parallel-flow layouts for the same duty — counter-flow always yields an LMTD greater than or equal to parallel-flow for identical terminal temperatures.
  • Rating and troubleshooting existing exchangers by back-calculating U from measured temperatures, flow rates, and known area.

Frequently Asked Questions

What is the LMTD formula?
The log mean temperature difference is LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the hot and cold streams at each end of the heat exchanger. It gives the true average driving temperature difference for heat transfer, which is always less than or equal to the simple arithmetic average (ΔT1 + ΔT2) / 2.
What is the difference between counter-flow and parallel-flow LMTD?
In counter-flow (counter-current) exchangers the two fluids move in opposite directions, so ΔT1 = Th,in − Tc,out and ΔT2 = Th,out − Tc,in. In parallel-flow (co-current) exchangers both fluids move the same direction, so ΔT1 = Th,in − Tc,in and ΔT2 = Th,out − Tc,out. For the same inlet and outlet temperatures, counter-flow always produces an LMTD greater than or equal to parallel-flow, making it more thermally efficient.
What happens when ΔT1 equals ΔT2?
When ΔT1 and ΔT2 are equal, the formula (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2) becomes 0/0. The mathematical limit shows that LMTD simply equals ΔT1 (or ΔT2) in that case, and this calculator applies that limit automatically instead of dividing by zero.
How do I use LMTD to size a heat exchanger?
Heat exchanger sizing uses Q = U × A × LMTD × F, where Q is the heat duty (W), U is the overall heat transfer coefficient (W/m²·K), A is the heat transfer area (m²), and F is a correction factor (F = 1 for true counter-flow or parallel-flow; F < 1 for shell-and-tube or multi-pass exchangers). Once Q and U are known, solve for the required area with A = Q / (U × LMTD × F).

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