A welder lays down two beads on the same steel plate with the same electrode. One bead cools fast and turns hard and brittle; the other cools slowly and stays tough. Nothing about the steel changed. What changed was how much energy the arc poured into each millimetre of weld — and that single quantity, welding heat input, quietly governs almost everything that happens in the joint afterward.
This article explains what heat input is, how to calculate it from the parameters a welder actually controls, works a full numerical example, and points out the mistakes that cause heat input to be misread on a procedure sheet.
Why this calculation matters
Heat input sets the thermal history of a weld. A high heat input produces a large molten pool and a slow cooling rate. A low heat input does the opposite. Because the mechanical properties of a welded joint depend far more on cooling rate than on the filler alloy alone, heat input ends up controlling hardness, toughness, grain size in the heat-affected zone (HAZ), and the residual stress and distortion left behind.
This is not an academic concern. Welding procedure specifications (WPS) for structural steel, pressure vessels, and pipelines almost always state a heat input range, not just a current and voltage. Stay below the lower limit and the HAZ can cool fast enough to form brittle, crack-prone martensite. Run above the upper limit and the weld metal grows coarse grains and loses toughness, while distortion increases. The whole point of qualifying a procedure is to land inside a window — and heat input is the coordinate that defines that window.
The core formula
Heat input H is the arc energy delivered per unit length of weld. The arc supplies electrical power equal to voltage times current; the travel speed determines how that power is spread along the joint:
H = (eta * V * I) / v
where eta is the arc (thermal) efficiency, V is the arc voltage in volts, I is the welding current in amperes, and v is the travel speed. With current in A, voltage in V, and speed in mm/s, H comes out in joules per millimetre (J/mm). Multiply by 1000 to read kJ/mm, the unit most procedure sheets use.
The efficiency eta accounts for the fact that not all electrical energy enters the workpiece — some is lost as radiation, spatter, and convection from the arc. It depends on the process:
SAW (submerged arc) eta ~ 0.90 - 0.99
SMAW (stick) eta ~ 0.70 - 0.80
GMAW / MIG eta ~ 0.75 - 0.85
GTAW / TIG eta ~ 0.55 - 0.70
Laser eta ~ 0.40 - 0.50
Two relationships are worth internalizing. Heat input rises with voltage and current — more arc power — and falls as travel speed rises, because the same power is smeared over a longer bead. A welder who speeds up to "finish faster" is also, whether they intend to or not, reducing heat input and accelerating the cooling rate.
A useful companion concept is the cooling rate. A higher heat input slows cooling through the critical temperature range (often quantified as the time to cool from 800 to 500 C, the t8/5 time). Slow cooling favours softer, tougher microstructures; fast cooling favours hard, brittle ones. Heat input is the lever the welder has over that rate.
A worked example
Consider an arc weld run with the following parameters: arc efficiency eta = 0.8, arc voltage V = 25 V, welding current I = 200 A, and travel speed v = 5 mm/s.
Step 1 — assemble the arc power term. The electrical power delivered to the arc is V times I:
V * I = 25 * 200 = 5000 W
Step 2 — apply the efficiency. Only a fraction eta of that power enters the workpiece:
eta * V * I = 0.8 * 5000 = 4000 W
Step 3 — divide by travel speed. Spreading 4000 W of effective power over a bead advancing at 5 mm/s gives the energy per millimetre:
H = 4000 / 5 = 800 J/mm
So this weld receives a heat input of 800 J/mm, or 0.8 kJ/mm. That is a moderate value — typical for structural fillet welding on medium-thickness steel.
The practical reading is the part that matters. A higher heat input means a larger weld pool and a slower cooling rate, which shifts the microstructure and the residual stress of the joint. If a procedure called for 0.8 to 1.2 kJ/mm, this weld sits at the lower edge of the window. Slowing the travel speed to 3.3 mm/s would push H to about 1.2 kJ/mm — the upper edge — without touching the current or voltage at all. That is the kind of trade a welding engineer makes routinely.
Common mistakes
Forgetting the efficiency factor. Some references quote "heat input" as simply V times I divided by v, with no eta. That is the arc energy, not the heat delivered to the plate. Mixing the two overstates the real input — by 25 % for stick welding, by more than half for laser. Always check whether a stated value includes eta.
Mismatched speed units. Travel speed appears on equipment in mm/s, mm/min, or in/min. Use mm/s with current in A and voltage in V to get J/mm directly. Plugging mm/min into the same formula inflates the answer by a factor of 60.
Treating voltage and current as independent of the process. Efficiency is tied to the process, not chosen freely. A TIG weld and a submerged-arc weld at the same V and I do not deliver the same heat. Pick eta from the process before computing anything.
Assuming more heat input is always safer. It is not. High heat input lowers hardness and cracking risk in many steels, but it also coarsens grains, lowers HAZ toughness, and increases distortion. The goal is a qualified range, not a maximum.
Ignoring plate thickness and joint geometry. The same heat input cools far faster in thick plate than in thin sheet, because thick sections conduct heat away in three dimensions. Heat input is one input to cooling rate, not the whole story.
Try the interactive NovaSolver calculator
Running the arithmetic once is straightforward; seeing how current, voltage, travel speed, and process efficiency trade off against cooling rate is where a tool earns its place. The Welding Heat Input & Cooling Rate Calculator (Rosenthal Solution) on NovaSolver lets you pick the welding process — GMAW, GTAW, SMAW, SAW, or laser — and adjust current, voltage, travel speed, thermal efficiency, plate thickness, material, and preheat temperature, then returns the heat input along with the peak temperature distribution, HAZ width, and cooling rate from the Rosenthal analytical solution.
Related calculators
- Fillet weld calculator — to size the throat and leg of a fillet weld once you know the process and load.
- Weld joint strength calculator — to check whether a welded joint carries its design load with adequate margin.
- Welding residual stress calculator — to estimate the locked-in stress that heat input leaves behind after the weld cools.
You can browse the full set in the manufacturing tools hub.
Closing note
Welding heat input is a compact calculation with outsized consequences. It is just effective arc power divided by travel speed, but that ratio fixes the size of the weld pool, the speed of cooling, the microstructure of the HAZ, and the distortion of the finished part. Compute it with the right efficiency, keep the speed units consistent, and treat it as a qualified range rather than a single target. Get the heat input right and most of the metallurgy that follows takes care of itself.
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