GaugePass

Welding math

Dilution Percentage

Every weld pass is a mixture of filler metal and melted base metal, and dilution is the fraction that came from the base plate, which is what determines the composition the deposit actually ends up with.

The formula

Dilution% = 100 x (base metal melted / total weld pass)

Dilution is the amount of base metal melted into a pass divided by the total amount of that pass, expressed as a percentage, and the resulting composition is the dilution-weighted average of base metal and filler.

What each symbol means

SymbolMeaningUnits
DDilution, the base metal share of the passpercent
A_baseBase metal melted into the pass, as area on a macro or as weightin^2 or lb
A_totalWhole pass, base metal plus filler, in the same unitsin^2 or lb
X_depElement content of the mixed depositweight percent

Why it works

Filler metal never arrives in the joint undiluted. The arc melts base metal along with the electrode, and the puddle is whatever the two make together. Dilution measures that mixing as the base metal's share of the pass. On a polished and etched macro section the two contributions are visibly distinct, so dilution is usually measured as the area below the original plate surface divided by the total pass area.

The composition follows as a weighted average. If a pass is thirty percent diluted, the deposit is thirty percent base metal chemistry and seventy percent filler chemistry, element by element. That simple mixing rule is what makes dilution actionable: it tells you in advance whether a nickel filler will still be nickel-rich enough after mixing, or whether a low-carbon deposit will be pulled up by carbon out of the plate.

Where this bites hardest is dissimilar joints and overlays. A corrosion-resistant overlay only performs if the alloy survives dilution, which is why such work is often deposited in two layers, the second diluted mainly by the first rather than by the base metal. In dissimilar welds the mixed composition can land in a range that is brittle or crack-prone even though neither parent material has any such tendency alone.

Worked examples

A single pass measured on a macro section

Base metal area melted
0.045 in^2
Total pass area
0.150 in^2
Base metal carbon
0.25 percent
Filler carbon
0.06 percent
  1. Dilution fraction: 0.045 / 0.150 = 0.30, so 30 percent dilution.
  2. The deposit is 30 percent base and 70 percent filler by composition.
  3. Deposit carbon: 0.30 x 0.25 + 0.70 x 0.06 = 0.075 + 0.042.

Result: 30 percent dilution, deposit carbon 0.117 percent
The deposit carries almost twice the carbon of the filler wire. Any assumption about weld metal properties based on the filler certificate alone would be wrong for this pass.

A low-dilution overlay pass

Base metal area melted
0.018 in^2
Total pass area
0.120 in^2
Base metal carbon
0.30 percent
Filler carbon
0.08 percent
  1. Dilution fraction: 0.018 / 0.120 = 0.15, so 15 percent dilution.
  2. Deposit composition is 15 percent base and 85 percent filler.
  3. Deposit carbon: 0.15 x 0.30 + 0.85 x 0.08 = 0.045 + 0.068.

Result: 15 percent dilution, deposit carbon 0.113 percent
Halving the dilution against a carbon-richer plate lands in almost the same place, which shows how strongly the technique that controls dilution governs the outcome relative to the plate chemistry itself.

In practice

  • Technique moves dilution more than anything else. Weaving, a shorter arc, positive electrode extension, and stringer beads placed to overlap the previous bead all reduce it; a hot digging arc into flat plate raises it.
  • Overlays are commonly deposited in two layers precisely so the surface layer is diluted by the first layer rather than by the base metal.
  • Dilution measured on one macro section describes that section only. Root passes are diluted very differently from fill passes on the same joint.
  • For a dissimilar joint, work out the mixed composition before welding, not afterwards. Some mixtures are brittle in ways neither parent metal predicts.

Related topics

Carbon Equivalent (IIW)Carbon equivalent rolls a steel's whole alloy content into one carbon-like number so two very different chemistries can be compared for how hard their heat affected zones will get when a weld cools fast.Pcm Cracking ParameterPcm is a carbon equivalent tuned for modern low-carbon steels, where the older expression penalises manganese so heavily that a perfectly weldable plate can be flagged as difficult.Arc Energy and Arc EfficiencyNot all the energy an arc produces ends up in the steel, and the fraction that does depends heavily on the process, which is why the same gross heat input means different things under a flux blanket and under an open tungsten arc.Deposition RateDeposition rate measures how fast a process puts metal in the joint while the arc is actually burning, which is only half the productivity picture and often the less important half.

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