Planning welds: fill volume, wire consumption, welding time and arc energy

How do groove angle, gap and weld reinforcement affect material requirements? Simple geometry and balance equations help prepare welds, estimate consumption and arc-on time, and check the plausibility of process values.

Two plates, each 20 mm thick, are to be joined over a length of one metre. The proposed preparation is a V groove with a 60° included angle, a 2 mm root gap and a 2 mm root face. Production planning raises several questions: How much filler metal is required? How does consumption change if the gap increases by one millimetre? What arc-on time can be expected at a known wire feed speed? And how should the additional filling after grinding out the root be accounted for?

This example represents recurring tasks in welding coordination. Many can be addressed through geometry, a material balance and an energy calculation. The quantities used must be clearly distinguished and the chosen assumptions recorded. The calculations below refer to idealised cross-sections that remain constant over the length considered. The practical examples concern welding position PA.

Start with the volume to be filled. The entire melted weld region also contains parent metal. To estimate filler metal requirements, the starting point is the void created by the joint preparation, with allowances for face and root reinforcement and additional areas to be filled after intermediate operations. Melted parent metal is not automatically counted as additional wire consumption. The geometric balance assumes that other material movements or losses are accounted for separately.

For a constant fill cross-section:

With $A$ in mm² and $L$ in mm, $V$ is obtained in mm³. A useful conversion is: For one metre of weld length, the numerical value of the cross-sectional area in mm² equals the volume in cm³. A cross-section of 80 mm² therefore requires 80 cm³ per metre. If the preparation varies, divide the weld into sections and add their volumes.

Mass follows from density. With $\rho$ in g/cm³:

A density of $\rho=7.85$ g/cm³ is assumed for the steel examples below. Use the appropriate density for other materials. TWI describes the calculation of weld volume and mass using simple component areas and several joint preparations. Gene Mathers: Calculating Weld Volume and Weight, TWI Job Knowledge 95

For fillet welds, small dimensional changes have a quadratic effect. For an equal-leg fillet weld with a straight face, no gap and no allowance for additional penetration, a 90° angle between the members gives:

Here, $a$ denotes the geometric throat thickness and $z$ the leg length. For an included angle $\gamma$ between the two surfaces adjoining the weld, the same triangular geometry can be generalised:

For equal leg lengths, it follows that:

This relationship is a geometric derivation for the idealised profile described. It specifies neither a required throat thickness nor an allowance for penetration. For unequal legs, calculate the triangular area directly as $A=z_1z_2\sin\gamma/2$.

If angle and length remain constant, increasing $a=5$ to $a=6$ mm increases the theoretical fill volume by:

A deliberately larger weld may be required by the design. Unintentional oversizing, however, substantially increases material and time requirements even in this simple example. Any additional convexity is not yet included.

For butt welds, the angles, gap and root face must be clearly defined. For a symmetrical V-groove preparation with straight faces, adding the gap rectangle and the two bevel triangles gives:

Here, $t$ is the plate thickness, $c$ the root face height, $b$ the continuous gap and $\alpha$ the total included groove angle. Reinforcement is accounted for separately. Equal plate thicknesses, no edge misalignment and a constant gap are assumptions of this model.

For the opening example:

This is 227.06 cm³, or approximately 1.78 kg per metre, initially excluding reinforcement and root removal.

If only one face is bevelled, as in an HV or HY preparation, the triangular contribution is $(t-c)^2\tan\beta/2$. Here, $\beta$ is measured from the direction of the unbevelled face, perpendicular to the plate surface. The actual preparation, with or without a root face, determines the dimensions to use; its abbreviated designation alone is insufficient for a calculation.

For a preparation on both sides, add the areas on the two sides. With bevel depths $h_1+h_2=t-c$, the bevel contribution can be written as:

For an X preparation with a symmetrical groove on each side, $k_i=\tan(\alpha_i/2)$. For a preparation bevelled on both sides of only one plate, such as a straight-sided DHY geometry, $k_i=\tfrac12\tan\beta_i$. Add the gap contribution and the separately determined additional areas.

At fixed angles, this area balance also gives the geometrically most favourable depth split:

For equal angles, the bevel volume is smallest at equal depths. Different angles can favour an asymmetrical split. This mathematical result applies to the bevel contribution. Access, root configuration, root removal and reinforcement can change the practical decision. A smaller volume alone does not establish suitability for welding.

Account for reinforcement as separate areas. A blanket percentage allowance often obscures its basis. If width $w$ and height $u$ are known, an additional area can be approximated using a defined profile:

In each case, $w$ is the full width and $u$ the maximum height above the reference surface. TWI uses a triangular approximation; manufacturer MIGAL.CO describes half ellipses for its calculator. Both are assumptions about the profile. For identical dimensions they produce different areas. TWI Job Knowledge 95, MIGAL.CO: explanation of the cross-section calculation

In the opening example, the groove width at the top surface is $w=b+2(t-c)\tan(\alpha/2)=22.78$ mm. If the face reinforcement is assumed, for illustration, to be a half ellipse of the same width with $u=2$ mm, it adds 35.79 mm². The total volume is then 262.85 cm³ per metre, equivalent to 2.063 kg of steel. A wider cap bead, root reinforcement or intermediate operation is not included in this subtotal.

Grinding out the root is an additional production stage. When material is removed between welding operations, the total amount of filler metal deposited cannot be inferred from the finished cross-section alone. Weld metal deposited and subsequently removed has already consumed wire and arc-on time.

A useful balance therefore adds the deposited volumes of the individual working stages:

For the geometric estimate, determine the newly created void still to be filled after each grinding operation. Distinguish three cases: previously deposited weld metal is removed and later replaced; previously present parent metal is removed and replaced by filler metal; an already open part of the groove remains open. The last area must not be counted again as additional removal relative to the original groove balance.

An example illustrates the scale: if an additional 4 mm² of previously deposited weld metal is ground out over one metre and then replaced, a further 4 cm³ must be deposited. At the assumed steel density this is 31.4 g. If parent metal is also removed, its newly created fill area must be included as well.

A tulip-shaped ground-out region can be described by a dimensioned equivalent profile comprising straight faces and circular arcs. For a circular sector, $A=r^2\theta/2$; for a circular segment, $A=r^2(\theta-\sin\theta)/2$, with $\theta$ in radians in both cases. The contour must be assembled correctly, accounting for overlaps. The mathematical precision of the component areas does not replace information on the actual ground profile.

Wire feed speed and welding travel speed serve different purposes. Together with the wire cross-section, feed speed determines the quantity supplied per unit time. Travel speed determines the weld length over which that quantity is distributed. Kevin Beardsley describes this relationship, including reverse calculations for practical procedure planning. Pre-Calculating Wire-Feed Speed, Travel Speed and Voltage, 2010

For solid wire:

With $d$ in mm, $v_D$ in m/min and wire density $\rho_D$ in g/cm³, the deposited mass rate $\dot m_\mathrm{ab}$ is obtained in kg/h. The equation therefore gives the deposition rate after the assumed losses. $\eta_m$ is the fraction of the supplied wire mass that is actually deposited. It is not a thermal efficiency.

For $d=1.2$ mm, $v_D=8$ m/min, $\rho_D=7.85$ g/cm³ and the explicitly assumed value $\eta_m=0.97$:

For the previously calculated 2.063 kg of deposited metal, the calculated wire mass supplied through the process is $2.063/0.97\approx2.127$ kg. Remaining stock, discarded wire lengths and other purchasing-related losses may need to be added. TWI treats these losses separately. Welding Costs, TWI Job Knowledge 96

For cored wire, the circular area multiplied by a solid-material density is not a generally valid description of mass. Appropriate manufacturer data on mass per unit length and deposition, or measured deposition rates, are required.

The arc-on time alone follows from:

For this example it is approximately 29.95 minutes. This assumes a constant deposition rate throughout deposition. If root, fill and cap passes use different parameters, calculate their individual times and add them. Grinding, turning, cleaning and cooling are not arc-on time.

TWI describes a simple test for determining the actual deposition rate: weigh a plate, weld at specified parameters for a known time, and weigh it again. From the mass increase of the cleaned test piece and the arc-on time, $\dot m_\mathrm{ab}=\Delta m/\tau_\mathrm{LB}$. Record such values together with wire, gas, parameters and test conditions. Welding Costs – Continued, TWI Job Knowledge 97

The volume balance also enables reverse calculations. Assuming equal densities for solid wire and deposited metal, a constant bead cross-section $A_R$ to be built up by filler metal gives:

Use $v_s$ in mm/min, $v_D$ in m/min and $A_R$ in mm². With the wire values above and $A_R=25$ mm², $v_s\approx351$ mm/min. This is the part of the individual bead to be filled, not the entire melted cross-sectional area including penetration.

For multi-pass welds, the total joint cross-section cannot simply be used as the cross-section of a single bead. A calculated number of beads does not establish their arrangement or adequate sidewall fusion either. The balance provides a starting value for planning; the process conditions still require professional judgement. Beardsley, 2010

Arc energy complements the material balance. For sufficiently constant current and voltage, the arc energy per unit weld length is:

Use $U$ in volts, $I$ in amperes and $v_s$ in mm/min. At 28 V, 250 A and 350 mm/min, $E=1.20$ kJ/mm. This value applies to the bead considered. For a multi-pass weld, determine the arc energy of each bead separately; adding the values for all beads does not replace this assessment. Heat input additionally accounts for thermal efficiency $\eta_\mathrm{th}$:

With an illustrative assumption of $\eta_\mathrm{th}=0.8$, the result is 0.96 kJ/mm. This thermal factor has a different meaning from the mass efficiency used earlier. TWI explains the distinction between arc energy and heat input. What Is the Difference Between Heat Input and Arc Energy?

For pulsed or other waveform-controlled processes, multiplying simple mean current and voltage values does not generally give the mean power. Use an appropriate determination of power from the corresponding instantaneous values or a suitable energy measurement. With the resulting mean power $\overline P$ in watts:

Alternatively, for a measured total energy $W$ in joules and the corresponding weld length $L$ in mm, $E=W/(1000L)$. Kemppi explains these measurement and calculation methods and the influence of the voltage measurement point. Jani Kumpulainen: calculating heat input in MIG/MAG welding, 2020

If a permissible arc-energy range has already been established by a competent assessment for a particular operation, the equation can be rearranged for travel speed:

At 28 V and 250 A, with a range of 1.0 to 1.5 kJ/mm assumed solely for this example, the result is 280 to 420 mm/min. The approximately 351 mm/min obtained from the volume balance falls within this range. Thus, two calculation conditions are compatible. This does not demonstrate adequate fusion or the required mechanical properties. Recalculate if process values change.

Practical assessment starts with sensitivity to deviations. If the gap in the opening example increases from 2 to 3 mm, its rectangular contribution alone increases by:

This corresponds to 157 g of steel. At the assumed deposition rate, arc-on time increases by approximately 2.28 minutes. Any increase in cap reinforcement width caused by the wider gap would need to be considered separately.

Such calculations help relate drawing dimensions, actual preparation and production effort. They show whether a change primarily affects bevel volume, additional areas or time requirements. A minimum always applies only to the chosen objective and within specified limits. The smallest fill volume may entail poorer access or more elaborate preparation; TWI explicitly addresses this relationship. Welding Costs – Continued

Clear, concise documentation is often sufficient for traceable planning: dimensioned joint preparation, separate additional areas, fill quantity per working stage, assumed density, deposition efficiency or measured deposition rate, and current, voltage or power and travel speed for each bead. This makes clear which results follow from an exact geometric relationship and which depend on assumptions about the profile or process.

The geometry and balance equations derived here support material and process planning. Required weld dimensions, permissible preparation and technical requirements must come from the relevant design and production specifications. A consumption calculation complements these requirements; it is not a strength calculation, welding procedure qualification or assessment of weld imperfections.

Sources and context. The linked technical articles provide the basis for volume, consumption, time and energy balances. The generalised fillet-weld geometry, the minimisation of the bevel contribution and the numerical examples were derived geometrically or algebraically for this article. Profile shapes and efficiencies are explicitly identified assumptions. No normative limits are reproduced. Editions of standards cited in older sources must not be taken as confirmation of the current standards position. Sources checked on 17 September 2026. This article uses no third-party illustrations.

Back to welding technology