Weld Shrinkage Calculator

Weld shrinkage calculator for butt and fillet joints that finds transverse closure, tack root gap, seam shortening, plate fold, flange tilt against AWS D1.1 and filler wire to buy.

What a Weld Shrinkage Calculator Predicts

A weld shrinkage calculator predicts how far parts move as the weld cools, so you can tack the root gap wide, cut stock long, or preset a plate before the arc starts. Measuring after the fact only tells you what went wrong.

Weld metal contracts in every direction as it cools, and the cold metal around it resists. TWI lists six forms of movement that result. Three of them can be estimated from the joint drawing and welding settings, which is the job of a weld shrinkage calculator. The others depend mostly on restraint and sequence.

Most online formulas start from a single weld size and a joint factor. This weld shrinkage calculator starts from the real groove instead: plate thickness, root gap, groove angle, root face and cap. That is why a square groove and a 60° V on the same plate give very different closures.

Transverse Weld Shrinkage Formula

Transverse shrinkage equals 0.2 times the weld cross-section area divided by plate thickness, plus 0.05 times the root opening. This is the Blodgett equation from Lincoln Electric's Design of Welded Structures, the weld shrinkage formula most often used for transverse shrinkage in welding.

$${\Delta }_t=0.2\times \frac{A_w}{t}+0.05\times g$$

Here Δ_t is transverse shrinkage, A_w is the total weld area including the cap, t is plate thickness and g is the root gap. Every term is a length or an area, so the formula works the same in inches or millimeters.

The weld area for a single-V groove is the gap strip plus the two bevel triangles. The cap is treated as a parabolic segment, two-thirds of its width times its height.

$$A_g=g\times t+(t-f{)}^2\times \tan (\theta /2)$$

In that formula f is the root face (land) and θ is the included groove angle. For a single-bevel groove, θ is the bevel angle and the triangle term is halved, using tan θ instead of tan(θ/2).

Worked example: 1/2 in single-V butt weld

Take a 1/2 in carbon steel plate with a 60° included angle, a 1/8 in root gap, a 1/16 in land and a 1/8 in cap that overlaps each toe by 1/16 in. The groove area is 0.1730 in² and the cap adds 0.0629 in², for 0.2359 in² of weld.

The first term gives 0.2 × 0.2359 / 0.5 = 0.0944 in. The gap term adds 0.05 × 0.125 = 0.0063 in. Total transverse shrinkage is 0.1006 in, or 2.56 mm, which is close to 3/32 in. A weld shrinkage calculator gives the same figure from these six joint dimensions.

How do you set the tack gap for weld shrinkage?

Add the predicted closure to the finished gap you want. To end at a 1/8 in root opening on the joint above, tack the root at 0.2256 in and let the weld pull it closed.

Closure adds across parallel seams. Four identical joints across one assembly pull it in by about 0.40 in, which is why a weld shrinkage calculator matters most on wide fabrications with many splices.

Weld Shrinkage Chart for Butt Joints

Thicker plate closes more because it takes far more weld metal, even though that area is divided by the thickness. These values come from the weld shrinkage calculator math with a 60° single-V, 1/8 in gap, 1/16 in land and 1/8 in cap on carbon steel.

Joint type changes the answer as much as thickness does. The table below holds the plate at 1/2 in with a 1/8 in gap and compares the common groove shapes.

Root gap and groove angle are the two settings a fitter controls. On the 1/2 in single-V, each extra 1/16 in of gap adds about 0.018 in (0.45 mm) of closure. Opening the angle from 45° to 75° raises closure from 0.083 in to 0.121 in. Check both in a weld shrinkage calculator before the joint prep is cut.

Shrinkage Allowance in Welding for Steel

TWI gives a rule of thumb for steel assemblies in its FAQ on how much to allow for weld shrinkage. The table sets that shrinkage allowance in welding beside results from the formulas above.

What is a good shrinkage rate for a weld?

For a steel 60° V butt joint, 1.5 to 3 mm of transverse closure per weld is normal, and the low end applies to fewer runs. A fillet with a leg up to three-quarters of plate thickness should close about 0.8 mm.

Results far outside that band usually mean an oversized groove, an open root gap or an oversized fillet. TWI notes that larger fillet legs in particular increase shrinkage, so check the leg size before blaming the welder. Use a weld shrinkage calculator for the joint in front of you and the TWI figures as a sanity check.

Longitudinal Shrinkage and Pre-Weld Cut Length

A seam shortens in proportion to the net heat put into it and its length, divided by the cross-section that resists the pull. This is longitudinal distortion in welding at its simplest, and the heat-input form below carries the 0.335 coefficient from Okerblom's work on it.

$$\Delta L=0.335\times \frac{\alpha \times Q\times N}{c\times \rho \times A_p}\times L$$

In that formula α is the thermal expansion coefficient, Q is net heat input per pass in J/mm, N is the pass count, cρ is volumetric heat capacity, A_p is the plate cross-section and L is weld length. Blodgett's simpler area form serves as a cross-check.

$$\Delta L=0.025\times \frac{A_w\times L}{A_p}$$

On a 36 in seam joining plates 24 in wide by 1/2 in thick, five passes at 25 kJ/in net shorten the run by 0.0235 in. The Blodgett form gives 0.0177 in. Cutting the blanks to 36.024 in brings the welded part back to 36 in.

The heat-input form adds every pass, so it reads higher than Blodgett's area form on multipass joints. Use the larger value for cut length when the part has a tight length tolerance, since a weld shrinkage calculator can only bracket this movement.

How much does a fillet-welded beam bow?

A beam bows when its welds sit off the neutral axis, because the longitudinal shrinkage pulls one side of the section shorter. Blodgett's camber equation gives the bow over the welded length, with every dimension in inches.

$$\Delta =\frac{0.005\times A_w\times d\times L^2}{I}$$

A_w is the total weld area, d is the distance from the weld to the neutral axis of the section, L is the welded length and I is the moment of inertia of the flange-and-web section. Bow grows with the square of length, so short parts barely move.

Take a 24 in by 1/2 in flange on a 24 in by 3/8 in web, joined by two 5/16 in fillets. The welds sit 4.90 in from the neutral axis and I is 1,204 in⁴. The bow is 0.0035 in over 36 in but 0.63 in over a 40 ft run.

Web depth changes the answer in both directions, because it moves the neutral axis away from the welds while adding stiffness. The table holds the same flange, fillets and 40 ft length and changes only the web height.

Matching welds on the opposite flange of an I-section pull the other way and cancel most of that camber. A weld shrinkage calculator that includes camber matters most on single T-sections, stiffeners and long one-sided brackets.

What is the formula for welding heat input?

Heat input equals arc voltage times current times 60, divided by travel speed in inches per minute. That gives joules per inch, and multiplying by the process thermal efficiency gives the net heat that reaches the plate.

$$Q=\eta \times \frac{60\times V\times I}{S}$$

The efficiency values below are the ones used in ISO/TR 17671-1 (formerly EN 1011-1). The table runs the same 250 A, 25 V and 12 in/min settings through each process on the 36 in seam above.

How many inches of weld per minute?

Inches per minute is the travel speed, and it is set by the heat input you want. Rearranged, S = 60 × V × I × η / Q, so 250 A at 25 V on GMAW needs 12 in/min to hold 25 kJ/in net.

Arc-on time follows from the same number. Five passes along a 36 in seam at 12 in/min take 15 minutes of arc time, before cleaning, grinding and handling are added.

What is CC and CV in welding?

CC is a constant-current power source, used for stick (SMAW) and TIG (GTAW). CV is constant voltage, used for MIG (GMAW) and flux-cored (FCAW), while submerged arc runs on either type.

On a CV machine the current follows wire feed speed, not a dial setting. Read the actual amps from the meter during a test run before putting them into any heat input or weld shrinkage calculator.

Angular Distortion and Weld Backside Shrinkage

Angular distortion happens because the weld is wider at the face than at the root, so the face side shrinks more and folds the plates toward it. TWI explains in its guide to distortion types and causes that each later run rotates the plates using the earlier deposit as a fulcrum.

A single-V butt weld folds the most because all the face width sits on one side. A double-V with a square groove on the far side spreads weld metal across both faces, and a fully penetrated square groove folds very little.

A weld shrinkage calculator that reports only closure misses this fold, which is why a weld distortion calculator needs the groove shape too.

What is weld backside shrinkage?

Weld backside shrinkage is the pull from the second side of a two-sided joint. Welding the back face of a double-V shrinks that side and folds the plates back the other way, which is how the fold from the first side gets cancelled.

A double-V balances when the two sides are split unequally, about 60/40 of the plate depth. On 1/2 in plate with a 1/16 in land, that puts about 0.27 in on one side and 0.17 in on the other. Confirm which side to run first on a test joint before production.

How do you calculate angular distortion of a fillet weld?

For a T-joint with fillets on both sides of the web, Blodgett's equation gives the drop at each flange tip in inches. Flange width, fillet leg and flange thickness are all in inches.

$$\Delta =\frac{0.02\times W\times w^{1.3}}{t^2}$$

W is the full flange width, w is the fillet leg and t is the flange thickness. A single fillet on one side of the web is taken as half that value.

AWS D1.1 limits combined flange warpage and tilt to 1/100 of the flange width or 1/4 in, whichever is greater. For a 24 in flange that limit is 0.25 in, and the table shows which double-fillet combinations pass.

A 1/2 in flange with 5/16 in fillets drops 0.424 in at each tip, a tilt of 2.03°. It needs a flange at least 0.652 in thick to stay inside the limit, or a pre-bend of 0.424 in in the opposite direction before fit-up.

Running flange width, leg and thickness through a weld shrinkage calculator before ordering plate catches this early, while a thicker flange still costs only material.

How does plate thickness affect weld distortion?

Flange tilt falls with the square of thickness. Going from a 3/8 in to a 3/4 in flange with 5/16 in fillets cuts the drop from 0.755 in to 0.189 in, exactly one quarter.

Transverse closure moves the other way on butt joints, because thicker plate needs a bigger groove. A 60° V closes 2.00 mm on 1/4 in plate and 5.37 mm on 1-1/2 in plate.

Weld Shrinkage in Stainless Steel and Aluminum

The Blodgett and TWI figures were built for steel. A weld shrinkage calculator can extend them to other metals by scaling with thermal expansion, since a metal that expands more also contracts more on cooling.

The weld shrinkage calculator results below run the same 1/2 in single-V joint and the same 25 kJ/in, five-pass procedure on three base metals. Expansion coefficients are near room temperature, in millionths per °F.

Aluminum's seam shortening jumps the most because the heat-input form also divides by heat capacity, and aluminum stores far less heat per unit volume than steel. Treat both non-steel rows as starting estimates and confirm them on a test piece.

Weld Size, Filler Metal and Arc Time

Every number above starts from the weld area, and the same area sets how much wire or rod to buy. Getting the weld size right is the first step in controlling shrinkage, because a weld shrinkage calculator carries that one area into closure, fold and filler weight alike.

How do you calculate a weld size?

A fillet weld is sized by its leg, and its strength comes from the effective throat, which is 0.707 times the leg. A 5/16 in fillet has a 0.221 in throat and a cross-section of 0.049 in² before convexity.

Sizing a fillet for load is a strength check rather than a shrinkage check. The Welding Calculator handles weld size and weld metal for a joint, then the shrinkage math shows what that size costs in movement.

What is a standard weld size?

AWS D1.1 sets a minimum fillet size by the thicker part joined, so the weld cools slowly enough to avoid cracking. Going above the minimum adds strength only if the design needs it, and always adds shrinkage.

Deposited weld metal is the weld volume times density, which is 0.2836 lb/in³ for carbon steel. The 1/2 in single-V over 36 in holds 8.49 in³, or 2.41 lb of weld metal.

Filler to buy is that weight divided by deposition efficiency. At 95% for solid GMAW wire you need 2.54 lb, while stick electrodes at 65%, after stub and spatter loss, need 3.71 lb for the same joint.

Higher-carbon steels may need preheat before welding, and the Carbon Equivalent Calculator shows when. Preheat also helps distortion, since a warmed part expands and contracts more evenly.

Weld Shrinkage Calculator Formulas for Excel

A spreadsheet copy of the transverse check in a weld shrinkage calculator takes six input cells. Put thickness in B2, root gap in B3, included angle in B4, root face in B5, cap height in B6 and cap overlap in B7, all in the same unit.

With 0.5, 0.125, 60, 0.0625, 0.125 and 0.0625 in B2 to B7, the sheet returns 0.1006 in of shrinkage and a 0.2256 in tack gap. That matches the online weld shrinkage calculator for single-V joints.

The sheet suits a batch of identical joints on a cut list. Longitudinal shortening, flange tilt and the metal scaling need more inputs, so keep those in the online weld shrinkage calculator rather than a free download.

How to Reduce Weld Shrinkage and Distortion

Put less weld metal in the joint, and put it where it balances. Every weld shrinkage calculator result above scales with weld area, so most fixes come down to a smaller groove, a tighter gap, a smaller fillet or a two-sided joint.

On the 1/2 in single-V, a 45° groove instead of 60° cuts closure from 0.101 in to 0.083 in. On a 1/2 in flange, a 1/4 in fillet instead of 5/16 in cuts tip drop from 0.424 in to 0.318 in.

When the weld metal cannot shrink further, work with the movement. Preset plates in the opposite direction, clamp parts back to back, weld a large assembly from the center outward, and weld the joints that contract most first.

Drill bolt holes after welding where you can. If a hole pattern has to go in first, lay it out with the Bolt Circle Calculator and check where it ends up with the True Position Calculator, or size the holes looser using the Clearance Hole Calculator.

What is the golden rule in welding?

For distortion, the rule fabricators repeat most is don't overweld. AISC's Steelwise review of Blodgett's Design of Welded Structures lists smaller fillet welds first, because less weld metal means a smaller shrinkage force.

Duane Miller and Omer Blodgett expand that idea in their 18 principles to minimize distortion, including presetting and preheat. Each principle reduces weld metal, balances it, or lets the part move freely.

How accurate are empirical shrinkage formulas?

Expect a weld shrinkage calculator to land in the right range rather than on an exact figure. TWI itself states that weld shrinkage is almost impossible to predict accurately, and studies of MAG-welded T-joints show heavy scatter between welders on the same procedure.

A shop calibration factor closes the gap. Weld one test joint, measure the closure, and divide by the prediction: a measured 3.1 mm against a predicted 2.56 mm gives a factor of 1.21 for that procedure.

What factors are not included in basic shrinkage calculations?

Restraint from clamps and fixtures, tack size and spacing, weld sequence, preheat and interpass temperature are not in any of these formulas. Neither is back-gouging, which adds weld metal to the second side.

Buckling of thin plate and twisting of open sections also fall outside any single-joint weld shrinkage calculator. Built-up girders with several weld lines need their camber summed weld by weld, and thin panels need a separate buckling check.

When should you use different joint factors?

Formulas built on weld size alone multiply by a joint factor, such as 1.0 for butt, 0.7 for fillet and 0.8 for T-joints. An area-based weld shrinkage calculator does not need one, because the groove shape is already in the area.

The difference shows on 1/2 in plate, where a square groove closes 1.01 mm and a 60° single-V closes 2.56 mm. Keep the calibration factor for your own shop data, not for joint type.