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LMTD Calculator (Heat Exchangers)

Calculate the log mean temperature difference (LMTD) that drives heat transfer in a heat exchanger, and optionally its heat duty. Enter the temperature differences at each end of the exchanger, plus an overall coefficient and area if you want the duty Q.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

How to use this calculator

  1. Enter the temperature difference at end 1 (dT1) and at end 2 (dT2) of the exchanger in kelvin or degrees Celsius.
  2. Optionally enter the overall heat transfer coefficient U (W/m2.K) and the heat transfer area A (m2) to also get the heat duty.
  3. Read the log mean temperature difference and, if provided, the exchanger heat duty Q.

How it works

The LMTD is the correct average temperature driving force for an exchanger with exponentially varying temperature profiles: LMTD = (dT1 - dT2) / ln(dT1 / dT2), where dT1 and dT2 are the hot-to-cold temperature differences at the two ends. When dT1 and dT2 are equal the formula is indeterminate, so the LMTD simply equals that common value. If an overall coefficient U and area A are supplied, the heat duty follows from Q = U * A * LMTD.

Worked example

Worked example. With dT1 = 50 K and dT2 = 20 K: LMTD = (50 - 20) / ln(50 / 20) = 30 / 0.9163 = 32.74 degC. Adding U = 500 W/m2.K and A = 3 m2 gives Q = 500 * 3 * 32.74 = 49,111.05 W.

Common mistakes

  • Applying plain LMTD to a cross-flow or multi-pass exchanger without the F correction factor, which overstates the driving force.
  • Confusing the end temperature differences with the individual stream temperatures; each dT is a hot-minus-cold difference at one end.
  • Assigning the ends inconsistently between counter-flow and parallel-flow, which changes both dT values.

Frequently asked questions

What happens when dT1 equals dT2?

The logarithmic formula becomes 0/0, so the LMTD is taken as the limit, which is exactly that shared temperature difference. This calculator returns dT1 in that case.

When do I need the F correction factor?

Plain LMTD is exact only for pure counter-flow or parallel-flow. Shell-and-tube (multi-pass) and cross-flow exchangers use Q = U * A * F * LMTD, where F (0 to 1) accounts for the less-ideal flow arrangement.

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