Weld Shrinkage Calculator helps estimate transverse contraction from weld area, plate thickness, and root gap, using S=(0.20×A/t)+(0.05×g) with weld volume and consumable mass now.
How Weld Shrinkage Is Calculated
A single-V butt weld shrinks because the deposited weld metal contracts as it cools, pulling the two plates toward each other across the joint (transverse shrinkage) and pulling the ends of the weld toward its center along its length (longitudinal shrinkage). Both effects trace back to how much weld metal fills the joint, which comes from the joint’s geometry: plate thickness, root gap, root face, included bevel angle, and cap height.
Joint geometry and cross-sectional area
Start with plate thickness $t$, weld length $L$, root gap $g$, included groove angle $\theta$, root face height $f$, and cap height $h$. The bevel depth is the portion of the thickness cut away by the V, which is everything above the root face:
$$d = t – f$$
The open groove area splits into a rectangular strip from the root gap and two triangular bevel faces. The gap rectangle runs across the full plate thickness, and the bevel triangles use the half-angle:
$$A_{gap} = g \cdot t \qquad A_{bevel} = d^2 \tan\left(\frac{\theta}{2}\right) \qquad A_{open} = A_{gap} + A_{bevel}$$
The width of the groove opening at the plate surface follows from the same bevel geometry:
$$w = g + 2d\tan\left(\frac{\theta}{2}\right)$$
The cap is modeled as a triangle sitting on top of the groove, with a base equal to that opening width and a height equal to the entered cap height:
$$A_{cap} = \frac{w \cdot h}{2} \qquad A_{total} = A_{open} + A_{cap}$$
Weld volume and consumable weight
Multiplying the total cross-sectional area by weld length gives the volume of metal the joint needs. That volume, multiplied by material density, gives the deposited mass sitting in the joint. Multiplying again by a process factor gives the gross filler metal to buy or feed, since not all of it ends up in the weld:
$$V = A_{total} \cdot L \qquad m_{deposited} = V \cdot \rho \qquad m_{gross} = m_{deposited} \cdot k$$
Density $\rho$ is 0.283 lb/in³ for carbon steel, 0.289 lb/in³ for stainless steel, and 0.098 lb/in³ for aluminum. The process factor $k$ is 1.10 for GTAW, 1.05 for GMAW, 1.02 for SAW, 1.20 for FCAW, and 1.50 for SMAW.
Transverse and longitudinal shrinkage
For carbon steel only, the calculator estimates how much the joint pulls together. Transverse shrinkage scales with total weld area relative to thickness, plus a small direct contribution from the root gap:
$$\Delta_{transverse} = 0.20 \cdot \frac{A_{total}}{t} + 0.05 \cdot g$$
Longitudinal shrinkage is modeled as a flat 0.1% of the weld’s length, and the calculator also reports transverse shrinkage as a percentage of thickness:
$$\Delta_{longitudinal} = 0.001 \cdot L \qquad \text{Shrink Ratio} = \frac{\Delta_{transverse}}{t} \times 100\%$$
Worked Example: Single-V Butt Weld in 1/2 Inch Carbon Steel
Take a 0.5 in thick carbon steel plate, welded GTAW along a 36 in joint, with a 0.125 in root gap, a 60° included angle, a 0.0625 in root face, and a 0.125 in cap. Bevel depth comes first: $d = 0.5 – 0.0625 = 0.4375$ in.
The gap area is $0.125 \times 0.5 = 0.0625$ in². The bevel area uses $\tan(30°) = 0.5774$: $0.4375^2 \times 0.5774 = 0.1105$ in². Open groove area is $0.0625 + 0.1105 = 0.1730$ in². The groove opening width is $0.125 + 2(0.4375)(0.5774) = 0.6301$ in, so cap area is $(0.6301 \times 0.125)/2 = 0.0394$ in². Total weld cross-section: $0.1730 + 0.0394 = 0.2124$ in².
Volume is $0.2124 \times 36 = 7.65$ in³. At 0.283 lb/in³ for carbon steel, deposited mass is $7.65 \times 0.283 = 2.16$ lb. GTAW’s 1.10 factor brings gross consumable to $2.16 \times 1.10 = 2.38$ lb, or about 0.066 lb of filler per inch of joint.
Transverse shrinkage is $0.20 \times (0.2124/0.5) + 0.05 \times 0.125 = 0.0850 + 0.0063 = 0.0912$ in. Longitudinal shrinkage is $0.001 \times 36 = 0.036$ in, shortening the finished weld to $35.964$ in. The shrink ratio is $(0.0912/0.5) \times 100 = 18.24\%$ of plate thickness.
| Quantity | Result |
|---|---|
| Total weld cross-section | 0.2124 sq in |
| Total weld volume | 7.65 cu in |
| Deposited weld metal | 2.16 lbs |
| Gross consumable (GTAW) | 2.38 lbs |
| Transverse shrinkage | 0.0912 in |
| Longitudinal shrinkage | 0.0360 in |
| Final length after welding | 35.9640 in |
| Shrink ratio (of thickness) | 18.24% |
What the Result Means
Transverse shrinkage is the amount the plates are expected to pull toward each other, measured perpendicular to the weld. It’s the number to build into a fit-up allowance: if you need a finished gap of a certain width after welding, open the joint that much wider before you strike an arc.
The shrink ratio expresses transverse shrinkage as a percentage of plate thickness so joints of different sizes can be compared on equal footing. The calculator doesn’t assign a good/bad label to any particular ratio; it’s a relative measure, and a higher ratio simply means the weld’s cross-section is large compared to the plate it’s joining, which pulls harder as it cools.
Longitudinal shrinkage is much smaller in practice, since it’s fixed at 0.1% of the joint length rather than tied to the cross-section. The final length figure is just the original length minus that amount, useful for predicting the finished part size before cutting stock to length.
If the material is set to stainless steel or aluminum, the shrinkage fields show “Not available.” The empirical shrinkage formula only applies to carbon steel; joint geometry, weld volume, and consumable mass are still calculated normally for any material.
What Changes the Result
Included angle has an outsized effect because bevel area grows with the square of bevel depth and scales directly with $\tan(\theta/2)$. Widening the angle from 60° to 75° increases the tangent term by roughly 50%, which pushes up cross-sectional area, weld volume, consumable weight, and transverse shrinkage together.
Root face works against bevel depth: a larger face leaves less of the plate to bevel out, shrinking the groove area. The calculator enforces root face less than plate thickness; setting them equal or larger halts the calculation, since there’d be no bevel left to weld.
Root gap enters the shrinkage formula twice: once indirectly through the cross-sectional area, and once directly as a flat $0.05 \times g$ addition. It’s a comparatively small effect on volume but a real one on the transverse figure.
Cap height feeds into total area through the cap triangle, so a heavier cap reads out as more consumable weight and slightly more transverse shrinkage, since the shrinkage formula uses total area, not just the open groove.
Weld length only affects longitudinal shrinkage and total volume; it does not change transverse shrinkage or the shrink ratio, since those depend on cross-section and thickness alone.
Welding process changes consumable weight through the multiplier (1.02 to 1.50) but has no effect on shrinkage, since the shrinkage model isn’t process-aware.
Any input that produces a non-positive or non-finite cross-section or groove width halts the calculation entirely, since that combination doesn’t describe a physically buildable single-V joint.
FAQs
What is transverse shrinkage in welding?
Transverse shrinkage is how much a joint pulls together perpendicular to the weld as the deposited metal cools and contracts. It’s driven mainly by how much weld metal fills the groove relative to plate thickness, which is why wider bevel angles and larger cross-sections produce more of it.
Why doesn’t the calculator estimate shrinkage for stainless steel or aluminum?
The shrinkage formula used here is an empirical one built around carbon steel’s thermal behavior. Stainless and aluminum have different thermal expansion and conductivity properties, so the calculator still returns joint geometry, volume, and consumable weight for those materials but withholds a shrinkage number rather than apply a formula that isn’t calibrated for them.
How much should I open the root gap to compensate for weld shrinkage?
Add the predicted transverse shrinkage to your target finished gap before fit-up. For example, if you need a 0.125 in gap after welding and the tool predicts 0.0912 in of shrinkage, set the pre-weld gap to roughly 0.216 in.
Does the welding process affect shrinkage?
No. The welding process (GTAW, GMAW, SAW, FCAW, SMAW) only changes the consumable multiplier used to estimate gross filler metal weight. Transverse and longitudinal shrinkage are calculated the same way regardless of which process is selected.
Why does my calculation say “Calculation Halted”?
This appears when an input is missing, non-numeric, or outside its allowed range: thickness and length below their minimums, a negative gap or cap, an angle outside 1° to 90°, or a root face equal to or greater than plate thickness. Fixing the flagged field lets the calculation run.
How is longitudinal shrinkage different from transverse shrinkage?
Transverse shrinkage pulls the plates together across the joint and depends on cross-sectional area relative to thickness. Longitudinal shrinkage shortens the weld along its length and is modeled as a flat 0.1% of the joint’s length, independent of joint geometry.
Does plate thickness or joint angle have a bigger effect on shrinkage?
Angle usually matters more per unit change, since bevel area scales with the tangent of the half-angle and with the square of bevel depth. Thickness affects both the numerator and denominator of the shrinkage formula, so its net effect is smaller than the angle’s.
What’s the minimum root face allowed?
Root face itself has no fixed minimum other than zero, but it must stay strictly less than plate thickness. A root face equal to or greater than thickness leaves no bevel to weld and the calculation will not run.