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Welding distortion estimator
Enter a joint, a deposited area, an arc energy and a pass count, and read the three distortions the classic empirical relations give: how far the joint closes across the seam, how far the member shortens along it, and how many degrees the two sides fold through. Butt and fillet, in your browser, nothing sent anywhere.
Every coefficient in every equation is an editable field, and the equations themselves are printed below with their constants. That is deliberate. These are fitted relations, and a fitted relation is worth what its calibration is worth, so the calibration belongs where you can see it and change it.
The three relations, and which parts of them are real
Transverse shrinkage Δt = Ct · Aw / t + Cg · g (Ct = 0.2, Cg = 0.05)
Longitudinal, heat-input form ΔL = kL · α · Qnet / (c · ρ · Ap) · L (kL = 0.335)
Longitudinal, area form ΔL = CL · Aw · L / Ap (CL = 0.025)
Angular distortion θ = ka · β · Nm · α · Qpass / (c · ρ · t²) (ka = 1.0, β = 1, m = 1)
Out-of-plane offset y = b · tan(θ / 2)
t thickness · Aw deposited weld area · g root gap · Ap member cross-section · L weld length · b distance from the weld centreline · Qpass net heat input per unit length for one pass · Qnet = N · Qpass the total for the joint · N passes · α expansion coefficient · c specific heat · ρ density. Every constant in brackets is a default sitting in an editable field.
Where the coefficients come from. The transverse relation is the one carried in the Spraragen-Ettinger and Blodgett family of textbook treatments, and it is dimensionally consistent as written: Aw / t is a length, so Ct and Cg are pure numbers. The longitudinal shrinkage-volume form and the angular scaling are Okerblom-type results, and kL = 0.335 is the coefficient carried in that family. The area form of longitudinal shrinkage is the Blodgett-family cross-check that ignores heat input entirely. None of these is a table, a limit or an acceptance value, and none is reproduced from a standard.
ka is not a published constant, and pretending otherwise would be the one dishonest thing on this page. The verifiable part of the angular relation is its scaling: the angle rises with net heat input and falls with the square of the thickness, which follows from a shrinkage force acting off the mid-thickness plane against a section that stiffens as the cube of thickness. The number in front of that scaling is a calibration, and the default is a scale-setting choice rather than a measurement: ka = 1.0 puts an unrestrained single-sided butt in 12 mm carbon steel, filled with four passes at 0.8 kJ/mm of net heat input each, at about 3.9 degrees. That arithmetic is the entire content of the default, and because m = 1 the angle is linear in total net heat input, so the same coefficient scales straight to any other energy. Weld an article, measure the angle, scale ka by measured over calculated, and the field starts carrying your restraint and your sequence instead of a number chosen to set a scale.
Why the shrinkage-volume form can be checked by hand. Qnet divided by c · ρ is the volume of metal that one unit length of weld could raise by one kelvin. Multiplying by α turns that into a contraction, dividing by Ap turns it into a strain of the member, and kL is the share of the heated metal that yields in compression on heating and therefore genuinely shortens the member on cooling. Every step is dimensional bookkeeping except the last one, which is the fitted part.
How to estimate welding distortion
From a preparation and a set of welding parameters to a shrinkage and an angle you can put a tolerance against.
- Enter the joint and the deposited area. Thickness the shrinkage acts across, total weld cross-section area for all passes together, and the root gap you actually measure. The joint volume calculator returns the area from a preparation if you do not have a macro-section.
- Enter the arc energy per pass and the pass count. Arc energy per pass, not the total for the joint, and the thermal efficiency your welding procedure uses. The tool multiplies up to the total net heat input and shows it as a result so you can check it.
- Set the material properties. Expansion coefficient, specific heat and density. The defaults are ordinary carbon steel; austenitic stainless expands about half as much again and distorts correspondingly more for the same energy.
- Decide the balance factor before you read the angle. Leave it at 1 for a single-sided preparation. Move it towards zero only as far as your sequence really alternates about the neutral axis, because zero reports zero degrees and no real joint achieves that.
- Calibrate the angular coefficient against a measured joint. The default of 1.0 is a scale-setting choice, not a measurement. Weld one article, measure the angular change, and scale the coefficient by the ratio of measured to calculated. That single number then carries your restraint and your sequence, and the physical scaling around it stays valid when the energy or the thickness changes.
- Type your own tolerance and read the margin. The tolerance field is empty because nothing is built in. Enter the angular tolerance your drawing invokes and the tool reports how much is in hand before the plus or minus 30 % band is applied.
- Plus or minus 30 %, and that is the good case. The relations were fitted to unrestrained plates with uniform preparation. Restraint, clamping, tack spacing, fit-up scatter and welding sequence are not inputs to any of the three, and every one of them moves the answer. Use the tool to compare options and to fit its own coefficients to a measured article; do not use an uncalibrated absolute number to set pre-setting angles.
- Transverse shrinkage does not contain heat input, and that is not a bug. It is written against the deposited area and the root gap, because transverse closure is set by how much metal solidifies in the joint and by how far apart the plates were. Two procedures that deposit the same area into the same gap close the seam by roughly the same amount even at different energies. The angle and the longitudinal term are where the energy shows up.
- The balance factor is a modelling decision, not a checkbox. Setting it to zero cancels the first-order angular term and the tool reports zero degrees. No real double-sided sequence achieves that, because the two sides are never welded at the same instant on the same section. Choose a value that represents how finely your sequence actually alternates, and note in the record which value you used.
- The fillet reading is an assumption applied to a butt relation. On a T-joint the tool takes the thickness as that of the member being pulled and the gap as the fillet root gap. It is a defensible reading and it is not a published extension. If your fillet work matters, calibrate the coefficients on a fillet article rather than on a butt one.
- Tolerances come from your drawing, never from here. The comparison field is empty on purpose. General angular tolerances for welded structures live in the ISO 13920 clause family, and which class applies is a specification decision rather than a calculation — see the guide to ISO 13920 tolerance classes for how the class gets chosen and what it costs.
- The estimate assumes the heat input you typed. A procedure sheet records intent; the arc delivers whatever the travel speed and the machine actually did. Measuring it pass by pass is what makes the difference between calibrating this model and re-guessing it — see welding parameter monitoring and weld distortion monitoring with thermal cameras.
For how distortion is caught while the seam is still hot rather than at the marking-out table, read weld distortion monitoring with thermal cameras.
Questions engineers ask about this calculation
How close does a distortion formula get to what the shop actually measures?
Treat every figure on this page as plus or minus 30 %, and treat that band as optimistic until you have calibrated the coefficients against your own joint. These relations were fitted to unrestrained test plates with uniform preparation, and a real fabrication adds restraint, clamping, tack spacing, fit-up scatter and a welding sequence, none of which appears in any of the three equations. What the arithmetic is genuinely good at is comparison: which of two preparations shrinks more, what happens when the arc energy halves, whether a thickness change moves the angle enough to matter. Absolute numbers for pre-setting come from a measured first article, and the honest use of this tool is to fit its coefficients to that measurement so the next joint is predicted rather than guessed.
Which kind of weld distortion does heat input actually control?
The angular and the longitudinal terms, not the transverse one. Angular distortion scales with net heat input divided by the square of the thickness in the classic Okerblom-type result, so halving the energy roughly halves the angle while doubling the plate cuts it to about a quarter. Longitudinal shrinkage scales with heat input divided by the cross-section of the member resisting it. Transverse shrinkage is different: the textbook relation makes it a function of the deposited area and the root gap, and it does not contain heat input at all. That is not an oversight. Transverse closure is set by how much metal solidifies and contracts in the joint, which is the area, and by how far apart the plates were, which is the gap.
Why does angular distortion fall so quickly as the plate gets thicker?
Because the thickness enters as a square while the heat enters linearly. The bending that folds a joint comes from a shrinkage force acting off the mid-thickness plane; the resistance to that folding rises with the second moment of area, which goes as the cube of the thickness. Combine the two and the angle goes as heat input over thickness squared. A joint that folds three degrees in 8 mm plate at a given energy folds well under one degree in 16 mm at the same energy, which is why thick-plate distortion problems are usually about bowing and shrinkage rather than about the fold, and why thin-plate work is where the angle bites.
Does a double-sided preparation really cancel angular distortion?
It cancels the first-order term, which is not the same as cancelling the distortion. The balance factor in this calculator goes to zero for a sequence balanced about the neutral axis, and the equation then reports zero degrees, which is the model being honest about its own limit rather than a claim about the shop. In practice the two sides are never welded at the same instant on the same cross-section: the first side folds the joint, the second side has to pull it back, and what is left is the difference between two large numbers. That is why a balanced sequence is specified as an alternating pattern rather than as side one then side two, and why the residual is small but real. Set the balance factor between zero and one to represent how well your sequence actually alternates.
What weld cross-section area do I enter for a multi-pass joint?
The total deposited area of the finished joint, every pass added together, including the cap. The transverse relation is written against the metal that ends up in the joint, so splitting it per pass and adding the answers would count the same contraction several times. The pass count enters separately, through the arc energy per pass which drives the angular and longitudinal terms. If you do not have a macro-section, the joint volume calculator on this site returns the area from the preparation on the drawing, and that is the number to bring here.
How do I calibrate the angular coefficient against my own fabrication?
Weld one joint of the preparation you care about with the parameters you intend to use, unrestrained or restrained exactly as production will be, and measure the angular change. Then run this calculator with your real thickness, area, arc energy and pass count, and scale the angular coefficient by the ratio of the measured angle to the calculated one. That single number now carries your restraint, your sequence and your preparation, and it stays valid across changes of energy and thickness because the scaling around it is physical rather than fitted. Redo it when the joint family changes. This is the whole reason the coefficients are input fields on this page instead of constants inside the code.
Is longitudinal shrinkage worth calculating on a short weld?
Rarely on its own, and almost always as part of something longer. The magnitude is small, of the order of a fraction of a millimetre per metre for ordinary steel fabrication, so a single short seam disappears inside the cutting tolerance. It matters when it accumulates along a built-up beam or a stiffened panel where dozens of seams pull the same member, when it is resisted eccentrically and turns into camber rather than shortening, and when a machined datum has to survive it. The two routes reported here disagree when the arc energy and the deposited area tell different stories about how much metal was melted, and that disagreement is usually the more useful output than either number by itself.
Does clamping the work down reduce distortion or just postpone it?
It reduces the movement and raises the residual stress, and the split between the two depends on the joint rather than on the clamp. Restraint stops the plate taking the shape the contraction wants, so the strain that would have become movement stays in the metal as stress, and some of it reappears when the fixture is released or when the part is later machined. None of the three relations here has a restraint term, which means every figure this tool reports is the unrestrained case and therefore an upper bound on the movement and a lower bound on the stress. Heavy restraint on a crack-sensitive material is its own risk, which is a hydrogen and preheat question rather than a distortion one.
The estimate assumes the heat input you typed. WeldTrace records the one the arc delivered.
Every term on this page except the transverse one is driven by net heat input, and a procedure sheet is not a measurement of it. WeldTrace records current, voltage and wire feed speed at 25 kHz on every pass, with shielding gas flow alongside, so the energy that actually went into the joint is a record from the seam rather than a number carried forward from a calculation.
