Welding math
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.
The formula
CE = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15
The carbon equivalent is carbon plus manganese over six, plus the sum of chromium, molybdenum, and vanadium over five, plus the sum of nickel and copper over fifteen.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| CE | Carbon equivalent, a single hardenability index on the carbon scale | weight percent |
| C | Carbon content of the base metal | weight percent |
| Mn | Manganese content | weight percent |
| Cr, Mo, V | Chromium, molybdenum, and vanadium, grouped by similar potency | weight percent |
| Ni, Cu | Nickel and copper, the weakest contributors in this expression | weight percent |
Why it works
Carbon is the strongest hardener in steel, but it is not the only one. Manganese, chromium, molybdenum, vanadium, nickel, and copper all slow the transformation from austenite, which means they all make it easier for a fast-cooling heat affected zone to end up as hard martensite instead of something tougher. The carbon equivalent expresses each of them as the amount of carbon that would have the same effect.
The divisors carry the story. Manganese is divided by six, so it takes six times as much manganese as carbon to do the same job. Chromium, molybdenum, and vanadium share a divisor of five and are therefore slightly more potent per point than manganese. Nickel and copper are divided by fifteen, which is why a copper-bearing weathering steel can look unalarming on this index despite its alloy content.
What the number is for is comparison and screening, not acceptance. A high carbon equivalent says a steel will form hard microstructures readily and therefore deserves attention to preheat, to consumable hydrogen level, and to cooling rate. It does not say what preheat to use. That comes from the engineering for the specific job and from qualified procedures, and it depends on thickness, restraint, and hydrogen as much as on chemistry.
Worked examples
An ordinary structural carbon steel
- Carbon
- 0.20 percent
- Manganese
- 0.90 percent
- Chromium, molybdenum, vanadium
- 0.10, 0.02, 0.01 percent
- Nickel and copper
- 0.05 and 0.20 percent
- Manganese term: 0.90 / 6 = 0.15.
- Chromium plus molybdenum plus vanadium: (0.10 + 0.02 + 0.01) / 5 = 0.13 / 5 = 0.026.
- Nickel plus copper: (0.05 + 0.20) / 15 = 0.25 / 15 = 0.016667.
- Add the carbon and the three terms: 0.20 + 0.15 + 0.026 + 0.016667.
Result: 0.393
Under four tenths is unremarkable territory for a structural steel. Attention still belongs on hydrogen control and on thick sections, but the chemistry itself is not raising a flag.
A higher-hardenability alloy plate
- Carbon
- 0.30 percent
- Manganese
- 1.20 percent
- Chromium, molybdenum, vanadium
- 0.50, 0.20, 0.05 percent
- Nickel and copper
- 0.30 and 0.10 percent
- Manganese term: 1.20 / 6 = 0.20.
- Chromium plus molybdenum plus vanadium: 0.75 / 5 = 0.15.
- Nickel plus copper: 0.40 / 15 = 0.026667.
- Sum with carbon: 0.30 + 0.20 + 0.15 + 0.026667.
Result: 0.677
This chemistry will form martensite readily in a fast-cooling heat affected zone. It is the kind of number that makes preheat, low hydrogen consumables, and controlled cooling engineering requirements rather than good practice.
In practice
- Use a mill certificate for the actual heat, not the specification's maximum limits. A grade that permits 0.26 carbon is often supplied nearer 0.18, and calculating from the limit overstates the problem.
- Several carbon equivalent formulas exist and they do not agree. Always say which one a number came from, because the IIW expression and the Pcm parameter can rank two steels in opposite order.
- Carbon equivalent says nothing about thickness, restraint, or hydrogen, and all three matter as much as chemistry does. A moderate number on a heavily restrained thick joint is not a licence to skip preheat.
- For weld metal rather than base metal the same arithmetic works, but the answer describes the deposit, which on a diluted first pass is neither the plate nor the filler.
Related topics
Practise the arithmetic under pressure
The welding-math domain in the question bank is where these formulas get tested the way they get tested on paper — with distractors built from the mistakes people actually make.