Core Formulas

How to Calculate Heat Exchanger, Coil, and Radiator Manufacturing Metrics

The five core calculations a coil engineer runs before cutting metal, worked end to end with real units and numbers.

Sizing a fin-and-tube coil starts with the duty equation Q = U x A x LMTD. If a condenser must reject 90 kW (307,000 BTU/h) with an overall U of 35 W/m2K and a log-mean temperature difference of 12 K, required area A = 90,000 / (35 x 12) = 214 m2, or about 2,300 sq ft. Because braze fillet shadowing, fin-tube contact resistance, and fouling all steal surface, build gross rather than theoretical area. The Heat Transfer Area calculator applies a yield factor: at 85 percent, 2,300 / 0.85 = 2,706 sq ft gross. Always confirm your per-tube area already includes fin surface times fin efficiency, not bare tube.

Fin density (FPI) sets air-side surface and pressure drop, and you verify it by counting, not by trusting the drawing. Count fins across a measured gauge span and divide: 100 fins over a 4 inch gauge is 100 x (1/4) = 25 FPI. The Fin Density calculator adds a usable-fin multiplier for damage, so 25 x 0.95 for a 5 percent crushed pack yields 23.75 effective FPI. Fin pitch is the inverse: 1/25 = 0.040 in spacing. Typical targets run 14 to 22 FPI on automotive radiators, 10 to 18 FPI on comfort-cooling evaporators, and 18 to 25 FPI on condensers where cleanability allows.

Tube footage to purchase is not the footage in the core. Multiply tube count by finished cut length, then divide by usable yield to cover saw kerf, end crop, and bend rejects. For 500 tubes at 8 ft each: theoretical is 500 x 8 = 4,000 ft, but at 85 percent yield the Tube Length Usage calculator returns 4,000 / 0.85 = 4,706 ft, a 706 ft scrap allowance. Straight-cut work commonly holds 92 to 97 percent yield; tight-radius hairpin bending drops to 80 to 88 percent. Keep the in-core length in cut length and let yield absorb trim so you do not double-count and over-order.

Coil pressure drop is the acceptance metric on the test bench, and it scales with roughly the square of flow, not linearly. A clean liquid coil might read 8 psi at rated 40 gpm; push flow to 48 gpm and drop climbs by (48/40)^2 = 1.44, to about 11.5 psi. The Coil Pressure Drop calculator normalizes a measured baseline by a flow or fouling correction factor: a 100 psi baseline at a 1.2 factor gives 120 psi adjusted. That linear factor only holds near the reference flow it was derived at, so keep bench flow within about 10 percent of rated when you apply it.

Refrigerant charge for a coil-only shipment comes from internal volume, not a rule of thumb. Internal tube volume equals cross-sectional bore area times total tube length: a 3/8 in OD tube with 0.315 in bore has a bore area of pi/4 x 0.315^2 = 0.0779 sq in, so 400 ft (4,800 in) of pass length holds 0.0779 x 4,800 = 374 cu in, about 6.1 liters. Add header and distributor volume, then multiply by a fill factor for the operating state. The Refrigerant Charge Estimate calculator combines those terms to set trapped-charge and leak-test acceptance limits before the coil ships.

Line pacing ties the thermal and fabrication math to a clock. Assembly takt equals net available time divided by required units: a 450-minute staffed shift building 90 cores gives 450 / 90 = 5.0 minutes per core. Every station, fin press, hairpin bender, expander, braze load, and leak booth, must beat that takt or it gates output. The Assembly Takt calculator returns the pace target so you can compare it against Brazing Furnace Load and Leak Test Capacity. If the braze furnace delivers a good core every 5.7 minutes, it is 0.7 minutes over takt and caps the cell.

Chain these together and each number feeds the next. Heat Transfer Area sets tube count and rows; that count drops into Tube Length Usage for footage and into Fin Density for the fin pack; internal volume from the tube geometry drives Refrigerant Charge Estimate; and takt from build volume sizes the furnace and leak booth. Carry consistent units throughout: convert kW to BTU/h at 3,412, sq m to sq ft at 10.76, and always express yield and fill as decimals inside the formula. A single unit slip on U or LMTD can undersize a core by 20 to 30 percent and turn into a warranty return.

Before releasing a build, run a quick sanity loop. Recompute A from Q, U, and LMTD; confirm gross area exceeds theoretical by your 15 to 18 percent fouling allowance; verify counted FPI is within plus or minus one fin of print; and check that purchased footage equals in-core footage divided by measured yield. If gross area shows near-zero allowance, the core carries no fouling reserve and will lose rating within a cleaning cycle. These five calculations, area, fin density, tube footage, pressure drop, and charge, are the arithmetic that decides whether a coil holds its rating or comes back.

Published 2026-07-01.