How much current melts a PCB trace

Onderdonk's equation, where it stops being true, how it compares against IPC's continuous rating, and why a resettable fuse can be slower than the copper.

There are two questions here and they have very different answers. How much current can this trace carry? is a temperature-rise problem answered by IPC-2221 or IPC-2152. How much current melts it? is an energy problem answered by Onderdonk’s equation. For a 20 mil trace in 1 oz copper at 25 °C:

continuous, 10 °C rise      1.46 A     IPC-2221, external layer
continuous, 50 °C rise      2.97 A     IPC-2221, external layer
melts in 1 s                5.14 A     Onderdonk
melts in 100 ms            16.3  A     Onderdonk
melts in 10 ms             51.4  A     Onderdonk

The gap between “carries” and “melts” is not a fixed safety factor — it is a function of how long the fault lasts, and it closes fast. At one second the melting current is only 3.5 times the continuous rating. The fusing current calculator computes both directions of that, and the trace width calculator answers the other question; this article is about which one to ask, and where the answers stop being trustworthy.

A single current axis for one trace width, marking the continuous rating for a ten degree rise, the rating for a fifty degree rise, and the currents that melt the same trace in one second and in ten milliseconds. The melting currents are many times the continuous rating. — Fig 1 — One 20 mil trace in 1 oz copper, and five different answers depending on the question. Notice how close the 1 second figure is to the continuous rating, and how far the 10 ms one is: the gap between "carries" and "melts" is not a factor, it is a function of time.

Onderdonk, and the assumption inside it

The equation, in the form the calculator implements, is

$I = A_{cmil}\sqrt{\frac{\log_{10}\!\left(\dfrac{T_m - T_a}{234 + T_a} + 1\right)}{33\,t}}$

with the area in circular mils, $t$ in seconds, and copper’s melting point $T_m = 1083$ °C. The 234 is copper’s inferred zero-resistance temperature — extrapolate its resistivity down and it reaches zero at about −234.5 °C — so the logarithm’s argument is really the ratio of the copper’s absolute resistivity at melting to its resistivity at ambient. The 33 is copper’s heat capacity and resistivity rolled into circular-mil units; in this repository it is re-derived from those properties in the unit tests, so a mistyped constant cannot ship.

The assumption is in the word adiabatic: none of the heat leaves the copper. All the energy delivered goes into raising the conductor’s own temperature until it melts. Rearranged, that says the melting threshold is a single number per cross-section:

$I^2 t = \text{constant}$

which is why every line on a log-log plot of fusing current against time has a slope of exactly −½, and why a fault that clears in microseconds does no damage at all.

Fusing current against fault duration on log axes, one curve for each of several trace widths. Every curve is a straight line of slope minus one half, so halving the time multiplied the survivable current by the square root of two. — Fig 2 — Onderdonk's relation for 1 oz copper at 25 °C ambient. The straight lines are the signature of the assumption behind it: no heat leaves the copper, so only the delivered energy matters, and current × √time is constant for each width. The red dots are where each line drops below the current the same trace carries indefinitely (the 10 mil line does so at 0.89 A, under the axis floor) — past which the model is not merely conservative, it is contradicting itself.

Put the two families on the same axes and the shapes differ as well as the values. Melting scales with the cross-sectional area; heating scales with area to the power 0.725. The ratio between them therefore slides with width — 2.9 at 10 mil, 3.5 at 20 mil, 5.5 at 100 mil — so “twice the rating is safe” is a statement that is wrong at some width, and you have to know which.

Current against trace width on log axes, comparing the continuous ratings from IPC-2221 for ten and fifty degree rises against the currents that melt the same trace in one hundred milliseconds, one second and ten seconds. The two families are separated by roughly an order of magnitude. — Fig 3 — The two families of curve on the same axes. Their slopes differ as well as their values — melting scales with the area and heating with area to the 0.725 — so the ratio between them is not a constant, and a safety factor derived at one width is wrong at another.

Where the equation stops being true

The adiabatic assumption is excellent for a short fault and progressively worse as the fault lengthens, because a trace on laminate is bonded to a heat sink the whole time. The usual way this is stated — “conservative beyond a few seconds” — undersells how badly it fails, and there is a way to see exactly where.

Ask the equation for the current that melts a 20 mil trace in 10 seconds and it answers 1.62 A. But IPC-2221 says the same trace carries 1.46 A indefinitely at a 10 °C rise. The two answers have collided: a model that says a trace melts at 1.62 A in ten seconds cannot be reconciled with a trace that carries 1.46 A forever. Setting the two expressions equal gives the duration at which the contradiction appears, and it is not far out:

trace width    crosses at (10 °C rise)   crosses at (50 °C rise)
   5 mil              5.7 s                    1.4 s
  20 mil             12.3 s                    3.0 s
 100 mil             29.8 s                    7.2 s
 500 mil             72.2 s                   17.5 s

The practical rule that follows: use Onderdonk for faults measured in milliseconds, and stop trusting it somewhere in the low single-digit seconds. Past that it is not conservative in a useful way — it is describing a conductor that loses no heat, and yours does. For long-duration cases the formula catalog points at Preece’s wire equation instead, and even that under-predicts a trace on laminate, because the substrate is a heat sink the free wire did not have.

The duration beyond which the adiabatic melting model predicts a lower current than the trace carries continuously, plotted against trace width for two definitions of the continuous rating. The boundary rises with width but stays inside a minute. — Fig 4 — Where Onderdonk stops being believable, computed by asking when its answer falls below the IPC continuous rating for the same trace. A 20 mil trace crosses at 12 s against a 10 °C rise and at 3 s against a 50 °C one. Use the equation for faults measured in milliseconds; past a second or two it is telling you about a conductor that is not losing heat, and yours is.

The continuous rating, and which standard says what

The other question has its own history. IPC-2221 gives a closed form,

$I = k\,\Delta T^{0.44} A^{0.725}$

with $k = 0.048$ on an external layer and $k = 0.024$ on an internal one, $\Delta T$ in °C and $A$ in mil². The factor of two between layers came from an assumption that buried copper cannot get rid of heat.

IPC-2152 measured the case properly and found otherwise. It is chart data rather than a formula, and the variable that actually matters turns out to be how far away the nearest copper plane is — a plane within about a millimetre roughly halves the temperature rise, and the internal-versus-external difference is much smaller than IPC-2221 implied. At the 10 °C rise plotted below, the catalog’s closed-form fit of its universal chart lands between the two IPC-2221 curves for anything wider than about 10 mil. It does not stay there: the fit’s exponents are shallower in area (0.653 against 0.725) and steeper in temperature rise (0.545 against 0.44), so on narrow traces and at larger rises it climbs above the external curve — at 5 mil it is already 0.56 A against 0.54 A, and at a 50 °C rise it exceeds IPC-2221’s external rating for everything narrower than about 100 mil. That is a property of two curve fits, not of the standards, and it is one more reason to treat either fit as ±10 % at best.

At 50 mil and a 10 °C rise the three models give 2.84 A, 2.53 A and 1.42 A. A factor of two, from the same width of the same copper, depending on which document is on the desk. Both IPC standards are paid, so neither is quoted here beyond its published closed forms; the practical position is that IPC-2221’s external curve is optimistic for a buried trace with no plane nearby, its internal curve is pessimistic for anything on a modern stackup, and the honest answer needs the chart.

Continuous current against trace width for three models: IPC-2221 on an external layer, IPC-2221 on an internal layer at half the constant, and the closed-form fit of the IPC-2152 universal chart, which runs between them for traces wider than about 10 mil and slightly above the external curve below that. — Fig 5 — The continuous rating depends on which standard is asked. IPC-2221 halves its constant for an internal layer; IPC-2152 measured the case and found the difference much smaller, with the real variable being how far away the nearest copper plane is. Fit curves, not the charts themselves — treat them as ±10 %.

Ambient temperature does opposite things to the two answers

This is worth internalising because it decides which failure a hot enclosure produces.

The melting current barely moves with ambient. The copper has to climb to 1083 °C whichever end it starts from, so raising the ambient from −40 °C to 125 °C reduces the one-second fusing current by only 18 %.

The continuous rating collapses. It is defined as an allowed rise on top of the ambient, against a fixed limit for what the laminate tolerates. The figure below uses 105 °C as an illustrative conductor limit; the real number is the laminate’s rated maximum operating temperature, which comes from its datasheet and not from either IPC formula. As the ambient approaches that limit the permitted rise goes to zero and so does the rating. One caveat on the curve itself: IPC-2221’s closed form is stated for rises of up to 100 °C, so with a 105 °C limit the part of the curve below a 5 °C ambient is extrapolation — the formula keeps producing numbers there, but they are not the standard’s.

So a trace in a hot box does not become more likely to melt. It becomes more likely to cook the board it is on, which is the same mechanism behind θJA being a property of the test board rather than yours and the reason thermal vias stop helping past a point.

Fusing current against ambient temperature, falling gently and almost linearly from minus forty degrees to a hundred and twenty-five, alongside the continuous rating, which falls to zero as the ambient approaches the allowed conductor temperature. — Fig 6 — Ambient temperature affects the two questions completely differently. The melting current barely moves, because the copper has to climb to 1083 °C either way. The continuous rating collapses, because it is set by an allowed rise on top of the ambient and there is a maximum laminate temperature at the top — 105 °C here, an illustrative figure rather than one from either standard. IPC-2221's fit is stated for rises up to 100 °C, so left of a 5 °C ambient the continuous curve is extrapolation and is drawn dimmer.

The protection is slower than the copper

This is the part that changes designs. A resettable PTC fuse is not fast. Bourns’ Multifuse solutions guide publishes a maximum time to trip for each part at a stated fault current, and for the surface-mount MF-SM series at 8 A the numbers run:

MF-SM075   hold 0.75 A    trips within  0.30 s at 8 A
MF-SM100   hold 1.10 A    trips within  0.50 s
MF-SM125   hold 1.25 A    trips within  2.0  s
MF-SM150   hold 1.50 A    trips within  5.0  s
MF-SM200   hold 2.00 A    trips within 12.0  s
MF-SM250   hold 2.50 A    trips within 25.0  s

Now ask Onderdonk how long the trace behind that fuse survives the same 8 A. A 20 mil trace lasts 0.41 s. A 50 mil trace lasts 2.6 s. A 100 mil trace lasts 10 s. The narrowest trace that outlives an MF-SM250’s worst-case 25 seconds is about 156 mil.

Two caveats keep this honest. Those long-duration trace figures are in exactly the region the previous section says not to trust — the real trace, losing heat into the laminate, survives longer than the equation claims. And the fuse’s number is a maximum, not a typical. But for a protection argument the conservative reading is the right one, and the conclusion survives it: on an ordinary board the trace is the fast protective element and the PTC is the slow one, which is the reverse of what the schematic implies.

Time plotted against hold current for a family of resettable fuses at a fixed eight amp fault, with horizontal lines showing how long several trace widths survive the same fault. The larger fuses take longer to trip than a narrow trace survives. — Fig 7 — The coordination question nobody asks. Bourns publishes a maximum time to trip at 8 A for each of the MF-SM parts plotted; Onderdonk says how long a trace survives the same 8 A. Where a fuse's point sits above a trace's line, the copper opens first — and a resettable fuse that trips after the trace has melted has protected nothing.

And the fuse derates harder than the trace does

The same guide’s thermal derating chart makes the coordination worse in a warm enclosure. A MF-R050 is a 0.5 A hold, 1.0 A trip part at 23 °C. Across its own operating range:

ambient    −40 °C    0 °C    23 °C    50 °C    85 °C
hold        0.78    0.60     0.50     0.36     0.20  A
trip        1.56    1.20     1.00     0.72     0.40  A

A 60 % loss of hold current between the headline temperature and the top of the part’s range. Meanwhile the trace it protects lost 18 %. Coordination checked at 23 °C is not coordination checked, and the direction of the drift is at least benign — the fuse becomes more sensitive, not less — but a design that relies on the fuse not nuisance-tripping at 0.4 A has just failed at 85 °C.

Hold and trip current of a resettable fuse plotted against ambient temperature, both falling by roughly sixty per cent between minus forty and eighty-five degrees, with the room-temperature rating marked. — Fig 8 — Bourns' published thermal derating for one MF-R part. The hold current falls from 0.78 A at −40 °C to 0.20 A at 85 °C — a 0.5 A fuse is a 0.2 A fuse in a warm enclosure. The trace it protects barely notices the same temperature change, so the coordination shifts as the box heats up.

The threshold is energy, so specify current and time together

Because $I^2t$ is the whole model, each trace width has a single number:

  5 mil      1.6 A²·s
 10 mil      6.59
 20 mil     26.4
 50 mil    165
100 mil    659
200 mil   2640

A 20 mil trace melts at 10 A after 0.26 s, or at 100 A after 2.6 ms, or at 1000 A after 26 µs — the same 26 A²·s each time. That is the useful way to read a supply’s specification: a current limit is meaningless without the time it takes to act, and the two together are one number that can be compared directly against the copper.

It is also the reason a bench supply set to a 3 A limit will happily destroy a trace that survives a dead short from a coin cell. The coin cell cannot deliver the energy; the bench supply can, for as long as you leave it there.

The energy delivered to a trace plotted as current squared times time, shown as a constant for each width: the melting threshold. Faults below the line do nothing and faults above it open the copper, regardless of how the current and time divide. — Fig 9 — Onderdonk restated as an energy threshold. Because no heat escapes, only the product I²t matters, and each width has a single number. That is what makes the model useful for a fault and useless for a steady load: a real trace carrying current for minutes is losing heat the whole time.

The via is usually the narrower conductor

A trace sized carefully for fault current is often fed through a via nobody sized at all. The barrel’s cross-section is

$A_{via} = \pi\left(d\,t - t^2\right)$

for a drill diameter $d$ and plating thickness $t$ , and with the drills used under a fine-pitch part that is not much copper:

0.2 mm drill, 20 µm plating      17.5 mil²
0.3 mm drill, 20 µm plating      27.2 mil²
0.5 mm drill, 25 µm plating      57.9 mil²
20 mil trace, 1 oz               27.6 mil²
40 mil trace, 1 oz               55.1 mil²

A 0.3 mm via is almost exactly a 20 mil trace, and a 0.2 mm one is a good deal less. Since fusing goes as the area and the via is short — so it is more adiabatic than the trace, not less, having less copper either side to conduct into — the via is very often where a fault opens the net. The via current calculator converts the barrel to an equivalent conductor for exactly this comparison, and the answer on a power net is nearly always more vias rather than a bigger one.

A cross-section of a plated through hole beside a trace, with their copper cross-sectional areas compared as bars. A small via with typical plating has less copper than the trace it joins. — Fig 10 — Where the copper actually runs out. A plated barrel's cross-section is π(d·t − t²) for a drill diameter d and plating thickness t, and for the drills used under a fine-pitch part that is less copper than the trace arriving at it. The via is the fuse you did not intend to fit.

Don’t use a trace as a fuse

The idea is tempting: neck a trace down and let it be the protection. It is a bad fuse for reasons that are all quantifiable.

The tolerance is enormous. Etch tolerance is a fixed number of mils, so on a narrow neck it is a large fraction of the width. Stack ±1.5 mil of etch, ±10 % of copper weight and the −40 to +85 °C ambient range on a nominal 8 mil neck and it opens somewhere between 1.4 A and 2.9 A — a 2.1:1 spread, wider than any cartridge fuse you could buy.

It does not clear cleanly. A wire fuse is designed to break an arc inside a sand-filled body with a stated breaking capacity. A trace melting on FR-4 sprays molten copper, carbonises the laminate underneath into something conductive, and may or may not actually open the circuit. There is no breaking capacity on the drawing because nobody characterised one.

It is not resettable and not replaceable. The board is scrap.

Deliberate fuse traces do exist in production — usually in mains-adjacent designs where the neck is over a routed slot, characterised by test, and approved by a safety agency. That is a different activity from narrowing a trace on a schematic review.

A narrowed section of trace intended as a deliberate fuse, drawn beside the spread of currents it could open at once every uncertainty is stacked, showing a range of more than two to one. — Fig 11 — Why a deliberately narrowed trace is a poor fuse. Etch tolerance alone moves the width by a few mils, and on a narrow trace that is a large fraction of it; copper weight, ambient and the plating add more. The result opens somewhere inside a range wider than any fuse you could buy.

Sizing a power trace, in order

Three questions to answer in order for a power trace: what it carries continuously, what the protection lets through and for how long, and whether the copper outlives that. Each box names the model that answers it. — Fig 12 — The three currents, in the order they constrain the width. Only the first is what most people size for, and only the third involves this article's equation. A trace sized for the continuous rating alone is a trace whose fault behaviour nobody has checked.

Continuous. What the load draws, at the worst-case ambient, against the temperature rise the board tolerates. Nearly always the binding constraint; the trace width calculator does this one.
Let-through. What the upstream protection allows and for how long. This comes from the supply’s current-limit behaviour or the fuse’s own time-to-trip curve, and if neither is specified there is no protection argument to make.
Survival. Whether the copper outlives step 2, with margin, at the temperature the enclosure actually reaches. The fusing current calculator does this one, and it tells you when the duration has left the model’s valid range.

Then check the vias on the same net, because they are frequently narrower than the trace, and check the protection’s derating at the real ambient rather than at 23 °C. Most of the time step 1 sets the width and the rest is confirmation — but the cases where it does not are exactly the ones worth catching before the board exists.