PCB Copper Pour Thermal Resistance Calculator

How to use the copper pour calculator

1. Pick the package (its junction-to-pad θjc and pad area fill in; edit them for a custom part), type the power and the ambient.
2. Type the pour's width and height and how much bare board continues beyond it; choose the copper weight, the board thickness, the airflow and the junction target in the menu row.
3. Add the thermal vias under the pad and, with Both sides switched on, the back pour's size. The junction temperature, the margin, θja and the pour that meets the target appear; the Pour table tab compares square pours from 5 to 75 mm.

The pour as a fin

L = √(k t / h)    η = tanh(l/L) / (l/L)    θ_top = 1 / (h · [pad + η (A − pad)])

Heat enters the pour at the pad and has two things it can do: travel outward through the copper, or leave through the face into the air. The copper's conductance per length is k t (385 W/m·K times the foil's thickness), the face's loss per area is h (about 10 W/m²·K in still air, convection and radiation together), and their ratio sets a spreading length L: about 36.6 mm for 1 oz copper in still air, √2 more for 2 oz. Copper within L of the pad works almost fully; copper several L away sits near ambient and does little. The fin-efficiency formula turns that into the share η of the pour that counts, so the top face's resistance is 1 / (h × effective area). It is why a 1 in² pour is the standard recommendation and a 4 in² pour is not four times better.

Three ways out

The hot copper under the package sheds heat by three parallel routes. The top face of the pour is the obvious one. The bare FR-4 around the pour is a far poorer fin (its conductivity is a thousand times lower, so its spreading length is only a few millimetres), but it has two faces and often a lot of area, and in still air it can carry a surprising share; this is why a datasheet's θja, measured on a 76 × 114 mm test board, is better than a small pour alone would give. The third route goes down through the board, through the FR-4 under the pour and through any thermal vias, to the back face: a mirror pour if there is one, otherwise bare FR-4 that only works directly beneath. The three resistances add in parallel, the package's θjc goes in series in front, and the junction rise is the power times the total.

Thermal vias and the back pour

A via's plated barrel, 25 µm of copper around a 0.3 mm hole, is about 190 °C/W through a 1.6 mm board; a 3 × 3 grid under a pad is about 21 °C/W. That sounds poor until you compare the FR-4 it bypasses: under a small exposed pad the FR-4 alone is over 100 °C/W, so the vias carry most of the heat to the back. Under a large top pour the FR-4 beneath the whole pour already conducts well and vias change little, which the calculator will show you. A back pour the same size as the top one adds little for the same reason, since bare FR-4 under a hot pour sheds heat from that footprint anyway; the gain is in making the back pour larger, because the bottom of a board is usually free, so the vias and the FR-4 feed a second fin that spreads well beyond the top pour. On a two-layer board that is the cheapest heatsink there is. On a multilayer board the same vias feed an inner ground plane, which spreads the heat over the whole board and usually beats any pour.

What the model leaves out

This is a rule-of-thumb estimate, good to perhaps ±30 %. The pour is treated as round, the board as isolated, h as one number for both convection and radiation and all orientations; a vertical board convects better than a horizontal one, solder mask radiates better than bare copper, an enclosure traps the warm air, and neighbouring parts add their own heat. Use it to compare layouts and to size a pour with margin, not to sign off a design within a few degrees; for that, measure the real board, or run a thermal simulation.

Worked example: 1.5 W in a DPAK on a 25 × 25 mm pour

A DPAK regulator dissipates 1.5 W at 40 °C on a 25 × 25 mm 1 oz pour (35 µm), with 20 mm of bare 1.6 mm FR-4 around it, nine 0.3 mm vias under the tab, no back pour, still air (h = 10 W/m²·K), and the junction must stay under 110 °C. The spreading length is √(385 × 0.000035 / 10) = 36.6 mm; the pour's edge is 10.5 mm from the 40 mm² tab, so η = 97% and the top face is 164.1 °C/W. The bare board around it, a poor fin with two faces, adds 67.4 °C/W, and the path through the FR-4 and the vias to the bare back face 170.3 °C/W. In parallel that is 37.3 °C/W; with θjc 2.5 °C/W, θja = 39.8 °C/W, in the range datasheets quote for a DPAK on a square inch of copper. The junction reaches 99.7 °C, +10.3 °C under the target, and the layout would allow 1.76 W. A 40 × 40 mm back pour under the tab brings θja to 30.9 °C/W and the junction to 86.4 °C; 2 oz copper on the top alone gives 39.6 °C/W.

Questions

How big should a pour be?

Out to about one spreading length from the pad: a square of two to three centimetres for 1 oz copper in still air, more for heavier copper. Beyond that, add a back pour, vias to a plane, airflow or heavier copper rather than more area.

Why is my datasheet's θja better than this?

JEDEC θja figures are measured on a 76 × 114 mm test board, often with internal planes, whose whole area sheds heat; the bare-board term here is a modest version of that. A small real board with the pour near its edge will be worse than the datasheet, which is exactly what the margin input is for.

Do thermal vias need to be filled?

Not for the thermal path: the plated barrel does the conducting. Filling or tenting stops solder wicking down the holes during reflow, which can leave the pad starved of solder; that is a manufacturing reason, and a good one for vias in a pad.

Does solder mask on the pour matter?

For the heat, barely: mask is thin and radiates better than bare copper, so a masked pour runs slightly cooler in still air. Leave the pad itself open for the solder joint.