Drawing No. EH–TH–028 // Thermal Engineering & HVAC
LMTD Calculator
Reviewed August 2026
Find the log-mean temperature difference for a counterflow or parallel-flow heat exchanger from its four terminal temperatures, and heat duty if UA is known.
What problem does this solve?
Simple average temperature difference doesn't correctly represent the driving force for heat transfer in a heat exchanger, because the temperature difference between the two streams changes continuously along the exchanger's length. The log-mean temperature difference (LMTD) is the correct effective average to use with Q = UA × LMTD.
Inputs
Hot stream
Cold stream
Results
Background
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂), where ΔT₁ and ΔT₂ are the temperature differences between the two streams at each end of the exchanger. For counterflow, ΔT₁ = Th,in − Tc,out and ΔT₂ = Th,out − Tc,in. For parallel flow, both ends are measured with hot and cold entering together: ΔT₁ = Th,in − Tc,in and ΔT₂ = Th,out − Tc,out.
The temperature difference between hot and cold streams shrinks continuously along a heat exchanger's length (in counterflow) or from one profile to another (in parallel flow), and heat transfer rate depends on the local ΔT at every point. The logarithmic mean is the exact effective average that, combined with UA, correctly reproduces the total heat duty — a simple arithmetic average of the two end ΔTs always overstates LMTD (and thus overstates predicted duty for a given UA).
For the same four terminal temperatures, counterflow arrangement produces a higher LMTD than parallel flow, because it maintains a more even temperature difference along the exchanger's length — this is why counterflow exchangers need less heat transfer area for the same duty, and why they're generally preferred when the application allows it.
Frequently asked questions
Practical questions about inputs, assumptions and interpretation.
When ΔT₁ equals ΔT₂ (or very nearly), the logarithm formula becomes indeterminate (0/0) — in that limit, LMTD simply equals ΔT₁ (=ΔT₂), since the temperature difference is constant along the exchanger. The calculator handles this automatically.
The LMTD formula assumes pure counterflow or pure parallel flow. Multi-pass shell-and-tube and crossflow exchangers have more complex flow patterns partway between these idealized cases, so a correction factor F (looked up from standard charts based on the exchanger geometry and temperature ratios, typically 0.75–0.95) is applied: Q = UA × F × LMTDcounterflow.
The calculator checks that hot-side temperatures stay above cold-side temperatures at both ends, which LMTD requires. If your design has a temperature cross, standard counterflow/parallel-flow LMTD doesn't apply directly and you likely need a multi-pass configuration analysis instead.