LMTD Calculator (Log Mean Temperature Difference & HX Area)
By Santaji GadepatilinUpdated November 5, 2026
The log mean temperature difference is the true average driving force for heat transfer between two fluids in a heat exchanger. This LMTD calculator works out the LMTD from the four terminal temperatures for counterflow or parallel flow, then sizes the exchanger with Q = U·A·LMTD — see the types of heat exchangers and how a plate heat exchanger works.
How to use the LMTD calculator
Choose counterflow or parallel flow and enter the inlet and outlet temperatures of both fluids. The calculator returns ΔT₁, ΔT₂ and the LMTD. Enter the overall heat transfer coefficient U and the heat duty Q to get the required area — or clear Q and enter an area to find how much heat an existing exchanger can transfer.
LMTD formula
LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂) · Q = U × A × LMTD
Worked example
Hot oil cools from 150 °C to 90 °C, water heats from 30 °C to 70 °C, counterflow, U = 500 W/m²·K, duty 250 kW:
- ΔT₁ = 150 − 70 = 80 K, ΔT₂ = 90 − 30 = 60 K
- LMTD = (80 − 60) ÷ ln(80 ÷ 60) = 69.52 K
- A = 250,000 ÷ (500 × 69.52) = 7.19 m²
In parallel flow the same temperatures give ΔT₁ = 120 K, ΔT₂ = 20 K and LMTD = 55.81 K, so 8.96 m² would be needed.
LMTD vs arithmetic mean
| ΔT₁ | ΔT₂ | Arithmetic mean | LMTD |
|---|---|---|---|
| 80 K | 60 K | 70 K | 69.52 K |
| 60 K | 40 K | 50 K | 49.33 K |
| 50 K | 10 K | 30 K | 24.85 K |
| 40 K | 20 K | 30 K | 28.85 K |
| 30 K | 15 K | 22.5 K | 21.64 K |
| 20 K | 5 K | 12.5 K | 10.82 K |
| 100 K | 50 K | 75 K | 72.13 K |
| 10 K | 9 K | 9.5 K | 9.49 K |
The arithmetic mean always overstates the driving force; the error is small only when ΔT₁ and ΔT₂ are close.
Notes
- If ΔT₁ = ΔT₂ the formula is 0 ÷ 0 — the LMTD then equals that common ΔT.
- A temperature cross (ΔT ≤ 0 at one end) is impossible for the chosen arrangement — check the temperatures.
- Typical U values: water–water plate exchanger 2,000–6,000 W/m²·K, shell-and-tube water–water 800–1,500, oil–water 100–400, gas–gas 10–50.
Frequently asked questions
What is the LMTD formula?
LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂), where ΔT₁ and ΔT₂ are the hot-to-cold temperature differences at the two ends of the exchanger.
How are ΔT₁ and ΔT₂ defined for counterflow?
For counterflow, ΔT₁ = hot inlet − cold outlet and ΔT₂ = hot outlet − cold inlet. For parallel flow, ΔT₁ = hot inlet − cold inlet and ΔT₂ = hot outlet − cold outlet.
Why is counterflow better than parallel flow?
With the same terminal temperatures counterflow gives a larger LMTD, so it needs less area, and it lets the cold outlet temperature rise above the hot outlet temperature.
What about shell-and-tube exchangers with several passes?
Multiply the counterflow LMTD by a correction factor F (usually 0.75–1.0 from TEMA charts) — Q = U·A·F·LMTD. Designs with F below about 0.8 are normally avoided.