LMTD Calculator
The log mean temperature difference, or LMTD, is the effective temperature difference that drives heat across a heat exchanger when the difference between the hot and cold streams changes from one end to the other. Because the temperature gap narrows or widens along the exchanger, a simple average overstates the driving force; the logarithmic mean gives the correct value to use in the heat exchanger duty equation. The LMTD is the difference between the two end temperature differences divided by the natural logarithm of their ratio. This calculator takes the temperature difference at each end of the exchanger, the hot-to-cold gap at the inlet and at the outlet, and returns the LMTD to two decimal places. It applies to both parallel-flow and counter-flow arrangements as long as you supply the correct end differences. When the two end differences are equal the formula reduces to that common value, which the tool handles smoothly. The method is the standard textbook approach to heat exchanger analysis. Thermodynamics and environmental science references are published by US federal agencies including the National Oceanic and Atmospheric Administration. Every figure is computed deterministically from the formula, shown below, with a worked example that reconciles exactly to the calculator so you can verify each step yourself.
The log mean temperature difference is (dT1 - dT2) / ln(dT1 / dT2). With end differences of 50 K and 20 K, the LMTD is 32.74 K, the effective driving temperature for the exchanger.
LMTD formula
LMTD = (dT1 - dT2) / ln(dT1 / dT2)
LMTD = log mean temperature difference (K)
dT1 = hot-to-cold gap at one end
dT2 = hot-to-cold gap at the other end
Subtract the smaller end difference from the larger, then divide by the natural logarithm of their ratio. The logarithmic mean correctly weights a driving force that changes along the exchanger. When dT1 equals dT2, the LMTD simply equals that shared value.
Worked example
A heat exchanger has a temperature difference of 50 K between the streams at one end and 20 K at the other end.
- Subtract the end differences: 50 - 20 = 30
- Take the ratio: 50 / 20 = 2.5
- Natural log of the ratio: ln(2.5) = 0.9163
- Divide: 30 / 0.9163 = 32.74 K
So the log mean temperature difference is 32.74 K. These are the calculator's default inputs, so the result above matches the widget exactly.
LMTD Calculator: frequently asked questions
How do you calculate LMTD?
The log mean temperature difference is (dT1 - dT2) / ln(dT1 / dT2), where dT1 and dT2 are the hot-to-cold temperature differences at the two ends of the exchanger. With dT1 = 50 K and dT2 = 20 K, the LMTD is 30 / ln(2.5) = 32.74 K.
Why use a logarithmic mean instead of a simple average?
The temperature difference between the streams changes along the exchanger, usually not linearly. The logarithmic mean is the exact effective difference for the heat duty equation; a plain arithmetic average would overstate the true driving force and oversize the exchanger.
Does LMTD work for both parallel and counter flow?
Yes, provided you use the correct end differences for each arrangement. Counter-flow generally yields a larger LMTD for the same inlet and outlet temperatures, which is why counter-flow exchangers transfer heat more effectively.
What happens when the two end differences are equal?
When dT1 equals dT2 the ratio is one and its logarithm is zero, so the formula is taken in the limit and the LMTD equals that common end difference. This calculator returns that value directly.
What is the LMTD formula?
The log mean temperature difference is LMTD = (dT1 - dT2) / ln(dT1 / dT2).
Official sources
- Thermodynamics and environmental science reference: US National Oceanic and Atmospheric Administration (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.