Welding math
Heat Input
Heat input packages volts, amps, and travel speed into one number that predicts how hot the joint gets and how slowly it will cool, which is why procedures control it rather than the three parameters separately.
The formula
HI = (V x I x 60) / (1000 x v)
Heat input in kilojoules per inch equals arc volts times amperes times sixty, divided by one thousand times the travel speed in inches per minute.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| HI | Heat input, the arc energy delivered per unit length of weld | kJ/in |
| V | Arc voltage measured as close to the arc as the machine allows | volts |
| I | Welding current flowing through the arc | amperes |
| v | Travel speed of the arc along the joint | in/min |
Why it works
Volts times amps is watts, and watts is joules per second. A weld does not care about joules per second on its own, though. It cares about joules delivered into each inch of steel, because that is what sets the peak temperature the surrounding metal reaches and how long it stays hot. Dividing power by travel speed converts a rate of energy into energy per length, and that is the whole idea behind heat input.
The arithmetic constants are just unit bookkeeping. Travel speed comes in inches per minute while power is per second, so the sixty converts minutes to seconds. Joules are inconveniently small for welding, so the thousand converts them to kilojoules. Strip both constants away and the formula is simply power divided by speed, which is how it is written in metric shops as kilojoules per millimetre.
Because travel speed sits in the denominator, it is the strongest lever an operator has. Doubling the travel speed halves the heat input at the same volts and amps. Nudging the amperage up ten percent only lifts heat input ten percent. That asymmetry is why welders who are told to reduce heat input are usually told to move faster rather than to turn the machine down.
Worked examples
A flat fillet on carbon steel
- Arc voltage
- 24 V
- Welding current
- 200 A
- Travel speed
- 10 in/min
- Multiply volts by amps to get arc power: 24 x 200 = 4,800 watts.
- Multiply by 60 to convert per-second energy into per-minute energy: 4,800 x 60 = 288,000 joules per minute.
- Divide by 1,000 x 10 to convert joules to kilojoules and spread the energy over the inches travelled in that minute: 288,000 / 10,000.
Result: 28.8 kJ/in
Just under 29 kilojoules goes into every inch of this joint. That is an ordinary mid-range figure for structural carbon steel and would leave a heat affected zone of moderate width with an unremarkable cooling rate.
The same joint run faster and colder
- Arc voltage
- 22 V
- Welding current
- 180 A
- Travel speed
- 12 in/min
- Arc power is 22 x 180 = 3,960 watts.
- Energy per minute is 3,960 x 60 = 237,600 joules.
- Divide by 1,000 x 12 = 12,000 to land in kilojoules per inch.
Result: 19.8 kJ/in
Trimming both the voltage and the current while adding travel speed drops heat input by nearly a third. On a steel prone to softening in the heat affected zone, that is the direction to move; on a thick section that needs slow cooling, it is the wrong direction.
In practice
- Read voltage at the arc, not at the machine's panel meter. Long leads and poor connections drop voltage between the two, and a panel reading can flatter the calculated heat input by several percent.
- A heat input limit in a procedure is nearly always a ceiling and a floor at once. Too much heat coarsens the grain and softens the heat affected zone; too little cools the joint fast enough to make it hard and crack-prone.
- Timing travel speed over a short distance exaggerates errors. Time the arc over at least a foot, or over a complete pass, and divide, rather than trusting a stopwatch over three inches.
- Weave beads and stringer beads at identical machine settings produce very different heat inputs, because weaving slows the net forward travel. If a procedure limits heat input, it is effectively limiting weave width too.
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.