Welding heat input calculation: the formula, the limits, and a worked example.
Heat input is the single number a welding engineer reaches for when a weld cracks, when toughness fails the Charpy test, or when an auditor asks why a procedure ran hot. Here is how to calculate it correctly in kJ/mm, which efficiency factor to apply, and where the real limits come from.
Welding heat input is the amount of energy the arc delivers to the joint per unit length of weld, expressed in kilojoules per millimetre (kJ/mm). It controls the cooling rate, and the cooling rate controls the microstructure in the weld metal and the heat-affected zone. Get it wrong on the high side and you soften the HAZ; get it wrong on the low side and you risk hard, hydrogen-cracking-prone structures. Most procedure qualification failures I have seen on the shop floor trace back to heat input that drifted outside the qualified band.
What heat input actually measures
Heat input is not the same as machine power. A 250 A weld run fast delivers far less energy per millimetre than the same 250 A run slowly. That is the whole point of the metric: it ties current, voltage and travel speed together into one figure that predicts how fast the joint will cool through the critical 800-500°C range. Two welds at identical amperage can have heat inputs that differ by a factor of three purely because of travel speed.
The heat input formula
The base equation, as used in ASME Section IX and AWS D1.1, is:
This raw figure is called arc energy. To convert arc energy into true heat input, you multiply by the process thermal efficiency, η:
Arc efficiency by process
AWS D1.1 Annex and most welding metallurgy texts use these thermal efficiency factors. ASME IX historically reports arc energy with η = 1, so always state which convention you are using.
| Process | Abbrev. | Thermal efficiency η |
|---|---|---|
| Submerged arc | SAW | 0.90 - 1.00 |
| Shielded metal arc (stick) | SMAW | 0.75 - 0.85 |
| Gas metal arc (MIG/MAG) | GMAW | 0.75 - 0.85 |
| Flux-cored arc | FCAW | 0.75 - 0.85 |
| Gas tungsten arc (TIG) | GTAW | 0.60 - 0.70 |
A worked SAW example
Take a structural butt weld on 20 mm S355 plate, welded by submerged arc at the following parameters: 30 V, 500 A, travel speed 400 mm/min, η = 1.0 for SAW.
- Arc energy = (30 × 500 × 60) / (400 × 1000) = 900,000 / 400,000 = 2.25 kJ/mm.
- Heat input = 1.0 × 2.25 = 2.25 kJ/mm.
Now run the same joint at 600 mm/min travel speed to chase productivity. Arc energy drops to (30 × 500 × 60) / (600 × 1000) = 1.50 kJ/mm. That single change in travel speed moved the cooling rate enough to shift the HAZ hardness by a measurable amount — which is exactly why travel speed is a recorded, controlled variable on every welding procedure.
Typical heat input limits
There is no universal number. The qualified Welding Procedure Specification (WPS) sets the band, and the band depends on the steel, the thickness and the toughness requirement. As a rough guide for carbon and low-alloy structural steels:
| Situation | Typical heat input | Why |
|---|---|---|
| Thin sheet, root runs | 0.5 - 1.0 kJ/mm | Avoid burn-through, limit distortion |
| General structural fill | 1.0 - 2.5 kJ/mm | Balance of productivity and toughness |
| Heavy section, multi-pass | 2.5 - 4.0 kJ/mm | Higher deposition, controlled cooling |
| Quenched & tempered steels | Tight upper cap | Excess heat softens the HAZ |
For toughness-critical work, the WPS will fix a maximum heat input to preserve HAZ notch toughness, verified by Charpy V-notch testing during qualification. For hardness-sensitive applications such as sour service per NACE MR0175, a minimum heat input is often imposed to keep HAZ hardness below 248 HV.
Why it changes the HAZ
Heat input governs the t8/5 cooling time — the seconds the weld spends cooling from 800°C to 500°C. Higher heat input means a longer t8/5, a slower cool, a softer and coarser-grained HAZ with lower strength but usually better toughness up to a point. Lower heat input means a short t8/5, a fast cool, and a risk of hard martensite that is brittle and prone to hydrogen cracking. The engineering job is to keep t8/5 inside the window the steel maker specifies.
Common mistakes
- Forgetting travel speed. Heat input is meaningless without it; amps and volts alone tell you nothing about energy per millimetre.
- Mixing conventions. Comparing an ASME arc-energy figure (η = 1) against an AWS efficiency-corrected figure makes a TIG weld look hotter than it is.
- Using nominal instead of measured parameters. The WPS may say 28 V, but the weld ran at 32 V. Heat input must be computed from recorded actuals.
- Ignoring run-out length on stick. For SMAW, travel speed is often back-calculated from electrode run-out length; getting that wrong skews everything.
Frequently asked questions
Heat input in kJ/mm equals voltage times current times 60, divided by travel speed in mm/min times 1000, multiplied by the process arc efficiency. It expresses the arc energy delivered per millimetre of weld.
AWS D1.1 does not give a single number — the limit comes from your qualified WPS. Structural welds commonly sit between roughly 0.5 and 2.5 kJ/mm, with the cap set during procedure qualification and toughness testing.
It sets the cooling rate. High heat input widens and softens the heat-affected zone; low heat input cools fast and can form brittle, crack-prone microstructures. The WPS keeps it inside a safe window.
It depends on the code. ASME IX reports arc energy with efficiency of 1.0; AWS D1.1 applies a thermal efficiency factor. State which one you used so reviewers compare like with like.
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