# LMTD Calculator (Log Mean Temperature Difference)

URL: https://speedycalculator.com/calculators/physics/lmtd/
Last updated: 2026-10-30

> The LMTD calculator finds the log mean temperature difference of a parallel-flow or counter-flow heat exchanger from the four terminal temperatures, with an optional correction factor for cross-flow or shell-and-tube designs.

## Inputs

- Flow arrangement
- Hot inlet (°C, °F, K)
- Hot outlet (°C, °F, K)
- Cold inlet (°C, °F, K)
- Cold outlet (°C, °F, K)
- Correction factor F
- UA (W/K, optional)

## Results

- ΔT₁
- ΔT₂
- LMTD
- Corrected LMTD (F·LMTD)
- Heat duty U·A·F·LMTD

## Formula

```
Counter: ΔT₁ = T_h,in − T_c,out, ΔT₂ = T_h,out − T_c,in · Parallel: ΔT₁ = T_h,in − T_c,in, ΔT₂ = T_h,out − T_c,out
LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂),  q = U·A·F·LMTD
```

## Explanation

The temperature difference between two fluids varies along a heat exchanger. The log mean temperature difference is the correct average to use in q = UA·ΔT when sizing exchangers.

### How to use the LMTD Calculator

- **Flow arrangement**
- **Hot inlet**
- **Hot outlet**
- **Cold inlet**
- **Cold outlet**
- **Correction factor F**
- **UA (W/K, optional)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the flow arrangement and enter the inlet and outlet temperatures of both fluids, the correction factor F (1 for pure counter or parallel flow) and optionally UA.

### Inputs explained

FieldWhat to enterFlow arrangementChoose one: Parallel flow, Counter flowHot inletUnits: °C, °F, KHot outletUnits: °C, °F, KCold inletUnits: °C, °F, KCold outletUnits: °C, °F, KCorrection factor FA numberUA (W/K, optional)A number

### What each result means

- **Corrected LMTD (F·LMTD)** = [Correction factor F]×[LMTD]
- **Heat duty U·A·F·LMTD** = [UA (W÷K, optional)]×[Correction factor F]×[LMTD]÷1000

### Example values

How the main result changes when **Hot inlet** changes and everything else stays at the example values above:

Hot inlet (°C)LMTD (K)4515.41767.531.09949042.0551112.551.494113560.088418075.7415

## Worked example

Inputs — Flow arrangement: Counter flow; Hot inlet: 90 °C; Hot outlet: 50 °C; Cold inlet: 15 °C; Cold outlet: 40 °C; Correction factor F: 1; UA (W/K, optional): 1,000.

Results — ΔT₁ = 50 K; ΔT₂ = 35 K; **LMTD = 42.0551 K**; Corrected LMTD (F·LMTD) = 42.0551 K; Heat duty U·A·F·LMTD = 42.0551 kW.

## Key terms

- **LMTD**: Log mean temperature difference.

## FAQ

**Why use a logarithmic mean?**
The temperature difference decays exponentially along the exchanger.

**Why is counter-flow better?**
It keeps a more uniform temperature difference and allows temperature cross.

**What if ΔT₁ = ΔT₂?**
The LMTD equals that common value.

**What is the F factor?**
A correction for multi-pass and cross-flow exchangers.


## Sources

- [Incropera – Fundamentals of Heat and Mass Transfer (reference text)](https://www.wiley.com/en-us/Fundamentals+of+Heat+and+Mass+Transfer%2C+8th+Edition-p-9781119320425)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)