Fillet weld calculation formulas
Let a and b be the two leg lengths, t the theoretical throat, L the effective length you enter for one weld line, N the number of identical lines, and ρ the selected density. All dimensions must use the same length unit.
- Equal-leg, 90° flat fillet: t = a / √2 ≈ 0.707 × a. Reverse: a = t × √2. Calculations use the exact √2 relation.
- Unequal legs at 90°: t = a × b / √(a² + b²).
- Triangular cross-section: A = a × b / 2.
- Geometric effective area per line: Aₑ = t × L.
- Triangular deposited-metal volume per line: V = A × L. Row volume = N × V.
- Mass in kg: m = V(mm³) × ρ(kg/m³) / 1,000,000,000.
- Volume per metre = A(mm²) × 1,000; mass per metre = A(mm²) × ρ / 1,000,000 kg/m.
- Volume per foot = A(in²) × 12 in³/ft; mass per foot = mass(kg/m) × 0.3048 / 0.45359237 lb/ft.
The throat and triangle-area model follows TWI, Design, Part 2. Our unequal-leg derivation equates the triangle area a × b / 2 with t × √(a² + b²) / 2. Volume is area times length; mass is density times volume. Unit conversions use 1 in = 25.4 mm and 1 lb = 0.45359237 kg.
Convexity, concavity and actual throat
TWI distinguishes the shortest root-to-face distance from the straight-face theoretical throat. A curved face needs its measured profile; maximum bulge alone does not locate the shortest distance.
This tool accepts a user-measured change Δ in that minimum distance: adjusted actual throat = t + Δ for convexity, or t − Δ for concavity. Adjusted actual-throat area = adjusted throat × L. The toes remain on the face, so the adjusted throat cannot exceed the shorter leg. No penetration is assumed.
For example, if a 6 mm equal-leg weld has an independently measured minimum throat 0.2 mm below its flat-face value, select concave and enter 0.2 mm. The estimate is 4.2426 − 0.2 = 4.0426 mm. Entering a 0.2 mm maximum depression without establishing the minimum throat is not sufficient.
Profile adjustment does not change the geometric effective area or triangular volume in this calculator. Actual reinforcement or concavity volume needs a measured cross-section. Convexity is not credited as extra design strength. See TWI's discussion of fillet profiles.
Worked example: 6 mm fillet, 1 m long
For equal legs a = b = 6 mm, flat face, L = 1,000 mm and carbon-steel density 7,850 kg/m³:
- Theoretical throat = 6 / √2 = 4.2426 mm.
- Geometric effective area = 4.242640687… × 1,000 = 4,242.6407 mm².
- Cross-section = 6 × 6 / 2 = 18 mm².
- Volume = 18 × 1,000 = 18,000 mm³ (18 cm³).
- Weight (mass) = 18,000 × 7,850 / 1,000,000,000 = 0.1413 kg, also 0.1413 kg/m.
For two identical weld lines, use quantity 2: total volume is 36,000 mm³ and mass is 0.2826 kg. For unequal legs 6 mm and 8 mm, t = 48 / √100 = 4.8 mm and A = 24 mm². These are original geometry examples, not exam questions.
Density choices and quantity assumptions
- Carbon steel: 7,850 kg/m³. Source: SSAB, Structural hollow sections, precision tubes, line pipes, steel sections and piles: Environmental product declaration (2014), p. 4 (density).
- Stainless steel 304: 7,900 kg/m³. Source: Atlas Steels, Technical Handbook of Stainless Steels, Appendix 3, p. 53 (12 August 2021).
- Aluminium: 2,700 kg/m³. Source: Hydro, Hygroove aluminium tube matches performance – at lower cost (21 April 2010).
These are approximate bulk-material references, not certified weld-deposit densities. Use custom density for the actual filler alloy. The model assumes a uniform right-angle fillet, no root gap or penetration, and a flat triangular deposited cross-section. It excludes face-curvature volume, weld shrinkage, dilution, spatter, stubs and process deposition losses. It does not calculate the consumable purchase weight.
Enter the effective weld length from your approved method; this tool does not deduct ends or gaps for you. It does not determine AWS D1.1 or AISC minimum weld sizes, weld acceptance, capacity, fatigue or allowable shear. A calculated throat is not evidence that a joint meets a code or WPS.
Fillet weld calculator for Excel
Use “Download spreadsheet (CSV)” to open the current inputs, row results, totals, assumptions and citations in Excel or another spreadsheet application. This is a snapshot of values; it does not contain live Excel formulas. Change the inputs here and export again to recalculate.