Whether a weld cracks is settled by two things: how fast the joint cools, and how much the steel wants to harden when it does. The arc governs the first. The mill certificate governs the second. Neither number is a verdict on its own, and that is the lesson.

$H = \dfrac{\eta V I}{S}$ — read aloud H equals eta V I over S, with $\eta$ the Greek letter eta. $H$ is the heat input, the arc energy delivered into every millimetre of joint, quoted in kJ/mm. $V$ is the arc voltage in volts — at the ARC, not at the machine's meter. $I$ is the welding current in amperes. $\eta$ is the arc efficiency, the bare fraction of the arc's power that actually enters the plate: roughly 0.6 for GTAW, 0.8 for SMAW, 0.85 for GMAW, 0.95 for submerged arc. $S$ is the travel speed, how fast the arc walks the joint. In shop form, with $S$ in mm/min, $H = \dfrac{60\,\eta V I}{1000\,S}$ gives kJ/mm directly.

Two cautions. The unit matters more than the number: 1.17 kJ/mm and 29.75 kJ/in are the SAME weld, differing by 25.4, and a procedure sheet reading “30” could be either. And heat input decides nothing by itself — what governs the microstructure is the cooling time through the transformation range, which also depends on plate thickness, joint geometry and preheat. The same heat input on 6 mm plate and on 40 mm plate gives two welds with nothing metallurgical in common.

The steel's half is the carbon equivalent: $CE = C + \dfrac{Mn}{6} + \dfrac{Cr + Mo + V}{5} + \dfrac{Ni + Cu}{15}$ — every alloying element converted into the amount of carbon that would harden the steel as much, then added up. $CE$ and every symbol in it are weight per cent off the mill certificate, and the answer comes out on the same scale. The three divisors are the whole content of the formula: a per cent of manganese is worth a sixth of a per cent of carbon, chromium, molybdenum and vanadium a fifth each, nickel and copper only a fifteenth.

Read it as a screening number that sends you to a preheat table, never as a verdict. And note who usually wins: on a modern low-carbon structural plate, the manganese term is LARGER than the carbon term. The formula is not really about carbon at all.