Heat Exchanger LMTD Calculator
Calculate the log mean temperature difference (LMTD) for a parallel-flow or counter-flow heat exchanger from its four terminal temperatures, apply a correction factor for multi-pass/cross-flow arrangements, and optionally estimate the required heat-transfer area from a duty and overall heat-transfer coefficient.
Input
Flow Arrangement
Terminal Temperatures
Applies to all four temperatures below. LMTD is a difference, so it comes out in the same unit.
Area Estimate (optional)
W/(m²·K). Leave blank to skip the area estimate.
kW. Leave blank to skip the area estimate.
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/heat-exchanger-lmtd-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"arrangement": "counter",
"temperatureUnit": "c",
"hotIn": "150",
"hotOut": "100",
"coldIn": "20",
"coldOut": "80",
"overallCoefficient": "500",
"duty": "250"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `heat-exchanger-lmtd-calculator` tool (Heat Exchanger LMTD Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/heat-exchanger-lmtd-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Heat Exchanger LMTD Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
The driving force behind heat transfer in an exchanger isn't a single temperature difference — it changes continuously along the exchanger as both streams heat or cool. The log mean temperature difference (LMTD) is the single effective ΔT that, multiplied by the overall heat-transfer coefficient and the area, gives the correct total duty: Q = U × A × LMTD.
This calculator works out the LMTD from the four terminal temperatures for a parallel-flow or counter-flow exchanger, applies a correction factor for other arrangements, and — given a duty and an overall coefficient — estimates the area you'd need.
How to use it
- Pick the flow arrangement: counter-flow (the two streams run in opposite directions — the standard, most efficient configuration), parallel flow (co-current — both streams enter at the same end), or Other for a multi-pass shell-and-tube or cross-flow exchanger.
- Enter the four terminal temperatures: hot fluid inlet/outlet and cold fluid inlet/outlet, all in the same unit.
- For Other, enter a correction factor F between 0 and 1. Multi-pass and cross-flow exchangers aren't purely counter-current, so their true mean ΔT is less than the equivalent counter-flow value — by how much depends on the specific configuration and the ratio of the temperature changes, and is normally read off a Bowman or TEMA correction-factor chart for that geometry. This calculator can't derive F for you; it applies whatever value you supply.
- Optionally enter an overall heat transfer coefficient (U) and a heat duty (Q) to get an estimated required area.
The formulas
Counter-flow: ΔT1 = Th,in − Tc,out, ΔT2 = Th,out − Tc,in
Parallel flow: ΔT1 = Th,in − Tc,in, ΔT2 = Th,out − Tc,out
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2). When ΔT1 and ΔT2 are (nearly) equal, this ratio has a removable singularity and the LMTD is simply ΔT1 — the calculator handles that case directly rather than dividing by ln(1) = 0.
Corrected LMTD (Other mode) = F × LMTD, where LMTD here is computed with the counter-flow terminal-difference convention — that's the baseline the correction factor is defined against.
Required area: A = Q / (U × LMTD_corrected), with Q converted from kW to W.
Why counter-flow beats parallel flow
For the same four terminal temperatures, counter-flow always gives a larger LMTD than parallel flow — meaning less area is needed for the same duty. Parallel flow also has a hard physical limit that counter-flow doesn't: the cold outlet can never exceed the hot outlet, because both temperatures are converging toward each other along the same direction of flow. Counter-flow has no such ceiling; the cold stream can in principle leave hotter than the hot stream leaves, since they're moving past each other in opposite directions.
Temperature cross
If either ΔT1 or ΔT2 comes out zero or negative, the calculator reports a temperature cross instead of a number — that combination of temperatures and arrangement is thermodynamically impossible for a simple two-stream exchanger (most often caused by picking the wrong flow arrangement for the temperatures given, or a cold outlet that overshoots the hot outlet in parallel flow).
Privacy
Everything runs in your browser. No temperatures or duties are sent anywhere.
Related tools
Working out the Reynolds number for the flow that goes through this exchanger? See the Reynolds Number Calculator. Converting between temperature units before you start? Use the Temperature Converter.