Weld Shrinkage & Distortion Calculator: Transverse, Longitudinal, Angular and Camber
Estimate weld shrinkage and distortion for butt and fillet welds: transverse shrinkage (0.2 Aw/t + 0.05 d), longitudinal shrinkage, angular distortion and edge lift, fillet flange warpage against the AWS D1.1 limit, beam camber, groove-area from bevel geometry, cut-length allowances and presetting angles.
How it works
Transverse shrinkage S = 0.2 × Aw ÷ t + 0.05 × d · longitudinal ΔL = 0.025 × Aw × L ÷ A_member · single-V angle θ ≈ 0.1 × (top width − d) ÷ t (radians) · fillet flange warpage Δ = 0.02 × W × ω^1.3 ÷ t² (inches; half for one fillet) · camber = 0.005 × Aw × e × L² ÷ I
Weld metal goes down molten and contracts as it cools, pulling the plate with it in three ways. Transverse shrinkage closes the joint across the seam; the classic Spraragen–Ettinger relation used in Lincoln Electric and Blodgett references gives about two tenths of the weld area divided by the plate thickness, plus 5% of the root opening. Longitudinal shrinkage shortens the seam in proportion to the weld area relative to the whole member cross-section (0.025 × Aw × L ÷ A). If you enter a heat input per pass, the calculator adds the Okerblom / White heat-input estimate (0.335 × α × Q ÷ cρ) as a second opinion. Angular distortion comes from uneven shrinkage through the thickness: a single-V groove is wide at the top and narrow at the root, so it closes more at the top and the plates fold up. Here the angle is estimated as one tenth of the difference between the groove top width and the root opening divided by the thickness. That gives about 5–7° for a free multi-pass single-V in 20 mm plate, in line with published measurements. A double-V welded alternately from both sides largely cancels it. For T-joints the flange warpage uses Blodgett’s fillet formula Δ = 0.02 W ω^1.3 ÷ t² (in inches) and is compared with the AWS D1.1 limit for welded girder flanges: flange width ÷ 100 or ¼ in (6.4 mm), whichever is greater. Give a web height and thickness and it also estimates beam camber from the welds sitting off the neutral axis (0.005 × Aw × e × L² ÷ I). Under More options you can work out the butt weld area from the bevel angle, root face, root opening and cap height, and enter several parallel seams. All of these are empirical estimates for carbon steel: use them to set cut-length allowances, presetting angles and the welding sequence, then confirm on the first part.
Worked example
A single-V butt weld with 250 mm² of weld metal in 20 mm plate, 2 mm root opening, 6 m long, six passes, with 500 mm of plate each side. Transverse shrinkage = 0.2 × 250 ÷ 20 + 0.05 × 2 = 2.60 mm, so add 2.6 mm to the overall width (1.30 mm to each plate). Longitudinal shrinkage = 0.025 × 250 × 6,000 ÷ (2 × 500 × 20) = 1.88 mm over 6 m (0.31 mm per metre). The groove top width is about 2 × 250 ÷ 20 − 2 = 23 mm, so the angle ≈ 0.1 × (23 − 2) ÷ 20 = 0.105 rad = 6.0°. The plates fold symmetrically, so each free edge 500 mm from the seam rises about 500 × tan 3.0° = 26.3 mm (52.7 mm if the other plate is held flat). Preset each plate 3.0° the other way, or weld a double-V from both sides. The weld holds about 11.8 kg of steel (41.7 mm² per pass).
Sources: TWI — Distortion: types and causes (Job Knowledge 33) · Prediction and Characteristics of Angular Distortion in Multi-Layer Butt Welding (Materials, 2019) · AISC Modern Steel — Blodgett on distortion and weld size · Kozak et al., angular distortion of T fillet joints in ship hulls (Polish Maritime Research)
Frequently asked questions
How much does a butt weld shrink across the joint?
Roughly 0.2 × weld area ÷ plate thickness, plus 5% of the root opening. A 250 mm² single-V in 20 mm plate with a 2 mm gap shrinks about 2.6 mm. TWI’s shop allowance for a 60° V butt is 1.5–3 mm per weld, depending on the number of runs.
How much does a fillet weld shrink?
Much less than a butt weld: TWI suggests about 0.8 mm across each fillet when the leg is no more than ¾ of the plate thickness, and about 0.8 mm along every 3 m of weld. Shrinkage grows with the square of the leg size, so an oversize fillet distorts far more.
Is angular distortion worse with more passes?
Slightly, for one-sided welds: many small passes give a larger final angle than fewer, larger ones. Published tests on 20–28 mm V-groove butt welds ended near 7° with 11–22 passes. Welding alternately from both sides (double-V) or presetting the plates is far more effective than changing the pass count.
What is the AWS D1.1 limit for flange warpage?
For welded beams and girders, the combined warpage and tilt of a flange may not exceed 1/100 of the flange width or ¼ in (6.4 mm), whichever is greater. Thin, wide flanges with large fillets are the ones that exceed it.
How do I preset a joint to counter distortion?
Tilt or bend the parts by the expected angle in the opposite direction before welding, so the weld pulls them flat. For a single-V butt, set each plate up by half the calculated angle; for a T-joint, pre-bend the flange. Check the first part and adjust the preset.
Can I straighten it afterwards?
Flame or induction straightening applies local heat to shrink the long side; mechanical pressing works on thinner sections. Both cost far more than presetting, and flame straightening has temperature limits for quenched and tempered steels, so plan the sequence first.
Related calculators
Guidance values from published welding references (AWS D1.1 / EN 1011 style preheat bands, typical deposition efficiencies). Always follow the qualified welding procedure specification (WPS), the consumable data sheet and the machine nameplate; verify preheat and interpass temperatures with a contact thermometer or temperature crayon.