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Welding Math (and Science)

For Welders, Welding Students, Welding Instructors and Others Involved in Managing Welding Operations.

Understanding the fundamentals of how welding, particularly MIG welding, works and will assist in producing higher quality depositis and assessing welding problems.  If you are using or planning to use MIG Robotics welding this information is essential.

See Below: Why MIG Wire Melts

Also See: 1) Gas Pressure Versus Volume: Below2) Weld Cooling Rates; 3) Effective Heat Input4) Calculate Weld Metal Volume5) Weight of Welding Wire / Foot; 6) How to Read a Ruler; 7) Charpy Impact Variations Explained8) Teacher Testimonials About Our Welding Math and Science Information: Below


Welding Math and Physics PDF

See "Why Gas Waste" Video

Video-Welding Math & Science-Gas Flow Control-Part 1

Video-Welding Math & Science-Gas Flow Control-Part 2

Video-Welding Math & Science-Deposition & Penetration-Part 1

Video-Welding Math & Science-Deposition & Penetration-Spread Sheet Part 2


Video- Science of

MIG Welding

Shielding Gas

Flow Control


Welder Rap- -

on Gas Video

Self Study Program,

"Welding Math and Science;" 88 Pages, Part # WMS NOW a FREE pdf Downlod GOTO Purchase Page

This program provides basic information to help welding students and welding supervisors understand welding process characteristics using math and science.  Includes and Appendix with subjects like Reading a Ruler and Basic Math Functions

CLICK to See Program Details       CLICK for Purchase Page  

Received an Excellent Question From A Recent Welding Student Who is Working as a Welding Engineer and Watched Our, "Suggested MIG Gas Flow Settings" Video.  He Wondered How and Orifice or Needle Valve Can Automatically Set and Adjust to the Proper Pressure to Maintain Consistent MIG Gas Flow?

The Answer is Much Longer than the Question so a PDF was Produced:




What Causes MIG Welding Wire to Melt? 

This is the question I ask when giving a technical talk on the subject.  Many answers are offered.  Here is what it is NOT;  the “hot arc”, radiation from the arc or the wire passing through the arc.  Two phenomena are primarily responsible for wire melting.  A simple test will explain one of them: 

  1. BE VERY CAREFUL, ONLY CONDUCT THIS TEST WITH INSTRUCTOR SUPERVISION--AND STAND BACK THE WIRE MAY "EXPLODE!!"   (Use a Stick welder.  With the machine turned off; clamp one end of a 3 foot length of 0.035 welding wire in a stick electrode holder and the other under a work ground clamp .  With the stick welder set for 150 amps, turn it on (be careful to stand back). The wire will quickly turn red, then white and then it will melt like a fuse. Note the short time that took.  That demonstrates one of the causes of wire melting during welding.  As the wire passes from the end of the torch contact tip to the arc, it is carrying all the welding current and becomes very hot.  It starts at room temperature and can exceed 500 degrees F before the arc forms at the end (depending on the "sickout," the distance between the tip and the workpiece.)

  2. The second reason it melts is that current leaving or entering a surface, be it wire or hot puddle, requires a given amount of energy for the electrons to enter or leave that surface.  This energy, generated at the surface, melts the already hot wire.  Therefore assuming Electrode Positive this is referred to as Anode Potential (also called Work Function and measures as voltage) and is equal to the Amps x Anode Voltage.

The following equation obtained from Reference (1) defines the relationship:

Wire Melting Rate (lbs/hr) = a x Amps + b x Wire Stickout x Amps 2

Where "a" and "b" are constants and "Wire Stickout" is the distance from the torch contact tip to the workpiece measured in inches.  (Note, constant b has been modified to compensate for the fact that this equation was based on "Electrode Extension" that is measured from the contact tip to the top of the arc.)

The values for "a" and "b" for 0.035 inch diameter carbon steel wire are:

a = 0.017;  b = 0.00014

These two energy sources cause the wire to melt.  The first term (a x Amps) is the anode voltage times current and the second term defines the energy input due to resistance heating.


One of the major implications of this relationship is that an increase in the stickout (at a fixed wire feed speed) amperage will decrease.  That has a significant effect on another parameter, weld penetration.

(Note, stickout is also called tip-to-work distance. The term "Electrode Extension" or ESO is a more accurate measure of the distance between the end of the contact tip to the top of the arc.  However for these calculations the stickout or contact tip-to-work can be used and is easier to measure.)

Point of Interest

The voltage you measure on a MIG welder is a combination of the:

  1. 1) Small voltage drop due to resistive heating of the wire (I2R)

  2. 2) The anode and cathode potentials (that needed to get electrons out of the wire and into the puddle; could be 1/2 the total measured)

  3. 3) The voltage drop across the resistive arc.


Weld penetration can be determined by a simple equation defined some years ago by C. E. Jackson in Reference (2)

Weld Penetration (distance into the base material when making a weld on plate measured in inches) =

K [Amps4 / (Weld Travel Speed; ipm x Volts 2)]0.333

For 0.035 inch diameter solid carbon steel wire, the constant K = 0.0019

Using these equations we find the following when we change wire stickout for 0.035 inch solid wire.  Assuming a fixed wire feed speed that produces 200 amps at 3/8 inch wire stickout:

Stickout, inches


Penetration inches

% Loss in Penetration























  1. With a fixed wire feed speed the amperage decreased from 200 amps with a 3/8 inch stickout to a low of 154 amps when the stickout was increased to 7/8 inches.  The resistance heating of the wire (the 2nd Amp2 term in the equation) is a very efficient heating process.  Therefore the current needed to finish melting the wire as it enters the arc, becomes less as the wire is hotter with longer stickout.

  1. However there is a reduction in weld penetration when varying stickout in a normal range from 3/8 to 3/4 inches is 24%!  If extended to 7/8 inches penetration decreases 29%.

Therefore it is very important to keep the torch stickout constant.  Also the shorter the distance from tip to work for a fixed wire feed speed the greater the penetration since current also increases.  When welding in the short circuiting mode it is often desirable to use a long contact tip which protrudes from the shielding gas cup.  This helps assure adequate penetration is maintained by keeping current higher.  It also helps visibility so the welder can stay on the leading edge of the weld puddle.

The picture right is from our recently published book and is one of several examples presented of the effects of MIG welding parameter changes on weld performance.  See Book Details on Current Speicals Offers Page


Weld Penetration Definition

For the purposes of this exercise, weld penetration is a measure of how deep the weld penetrates in a bead-on-plate deposit. Have a different wire than the 0.035 inch solid wire used in this example?  No problem.  In fact not only changes in wire type and size but also shielding gas and torch angle will alter the actual value.  You can generate your own constant K for what you are doing by making a bead-on-plate deposit, cutting a cross section and etching it.

Caution About the Use of This Approach

The above equations are designed to work within a practical range for normal MIG welding.  There are much more elaborate equations that take into account the variable resistively of material with temperature, other arc effects etc.  However within a range of normal operation the above approach will work adequately.  As mentioned, you may need to develop your own coefficients.  Make a weld, measure the depth of penetration and work backwards!  That is what Clarence Jackson did with thousands of data points!


Reference (1):  AWS Welding Handbook, Volume 1,  9th Addition; pp 79

Reference (2): “The Science of Arc Welding” by C. E. Jackson. 1960 Welding Journal 39(4) pp 129-s thru 230-s

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"Advanced Automotive Welding"

Author: Jerry Uttrachi

(President of WA Technology)

Great book for welding students to also learn some welding math and science.

CLICK for Book Details


Download PDF Overview of the Book with Contents Page and Several Pictures from Each Chapter.

Review by Editors of Hemmings Motor News; August 2012

"Advanced Automotive Welding" by Jerry Uttrachi

Welding is a hot topic in the hobby these days.  For less than $500 a do-it-yourselfer can purchase a good quality welder and start laying beads or zapping in spot welds.

This kind of accessibility to a once specialized skill is excellent for the hobby, and we encourage everyone with an interest to learn to weld.  Just as important as buying the gear, however, is getting versed in the many different processes, techniques and materials used in all types of welding.  A class at a local welding school or a community college is a good place to start, as is the purchase of a book like Advanced Automotive Welding, part of Car Tech’s SA Design series.

Despite the “Advanced” in the title, the book is a good resource for beginning and intermediate welders.  The author, Jerry Uttrachi, is a former American Welding Society President, with 40 years of welding experience, as well as a car enthusiast, and he writes in a clear, mostly jargon free style.

The book covers all welding processes, as well as cutting processes, and includes insight into some car related welding projects.  Advanced Automotive welding is a good addition to any budding or experienced metal worker’s shelf.

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Gas Pressure/Volume Calculations

Understanding the relationship between gas pressure and volume will help when setting gas flow and understanding MIG shielding gas use and waste.

In 1662 Robert Boyle defined the basic relationship between gas Pressure and Volume.  He stated the relationship in mathematic terms as:

P/ P2 = V1 / V2   (Where P, pressure, is measured as absolute pressure =

gauge pressure + 14.7 psi at sea level)

For example, in a MIG gas delivery hose if the initial absolute pressure is doubled the gas volume must be double.  That was until 140 years later when around 1800 both Charles and Dalton independently added temperature to the relationship!  They defined the following relationship:

V1 / V2  = T/ T2  (Where T, Temperature is measured as absolute Temperature in degrees Rankin = Degrees Fahrenheit gauge + 460)

Applying this equation we'll see in general we need not worry about temperature effecting volume in normal ranges:

i.e. V1 / V2 =T/ T2

If T1=75 F than T1Rankin = 75+460=535 R

Assume T2 = T1 + 20% =90 deg F; then T2 Rankin = 90+460=550 R

V1/V2 due to 20 % Temp Difference =

V1 / V2 =T/ T2= 535/550=0.97

Or at a constant pressure, an increase in Temperature of 20% measured in degrees Fahrenheit yields only 3% increase in volume.  For most welding purposes and over the range of production temperatures there is not enough change in Volume with gas Temperature to consider it significant.

The general Gas Laws can be written as:

(PX V1) / T1 = (P2 x V2 ) / T2

It can also be written as P x V = (nR) T

where the constants nR can defined based on the gas.  We'll let you find details about the nR by searching the Internet since for our purposes ratio comparisons are all we need.




  1. The pressure needed in the gas delivery hose from gas source to welder/feeder to flow 30 CFH is 3 psi. 

  2. A regulator/flowmeter is used that utilizes an 80 psi regulator.

Therefore when welding stops gas continues to flow through the needle valve flow control  until the pressure in the gas delivery hose equals 80 psi.

Then the volume of excess gas in the gas delivery hose compared to the volume when welding will be:

V stopped / V welding = P stopped / P welding =

(80 psi +15) / (3 psi + 15) = 5.3 times the physical hose volume


Hose Expansion Causes More Excess Volume: Tests of a standard 1/4 inch diameter gas delivery hose showed it had a 13% increased volume due to the hose expanding with 80 psi pressure.  Therefore 87% of the excess gas stored in the hose is due to the increased Pressure and 13% of the excess due to Hose Expansion.  SEE MORE DETAILS.


Excess Gas Blasts Out of the MIG Torch When Welding Starts: The high velocity creates  turbulence in the shielding gas stream which takes several seconds to stabilize to a desirable  smooth Laminar flow.  The turbulence pulls in air causing excess spatter and internal weld porosity.  For a typical 5/8 inch diameter MIG nozzle more than 50 CFH flow rate causes this turbulent flow.  For a smaller 1/2 inch diameter nozzle flow rates should not exceed about 40 CFH.


Was This Welding Math Information Useful?  What Other Math Would You Like To See?  


FREE Technical Paper Available Entitled; "MIG Shielding Gas Control and Optimization"  (or Everything You Didn't Know You Needed to Ask About MIG Shielding Gas Control!)  It Summarizes Key points in this Web Site and numerous Technical Presentations made in US and International Welding Conferences about the gas shielding problems and solutions. 



Testimonials from Teachers About Our Welding Math Information

Email 1:

Brad Weaver, Science Teacher

Belmont Career and Technical Education Center Sent This Email Requesting:

"..permission to use the wonderful materials you have produced on welding math and physics with the students here at our career and technical education center.  As the science teacher at the center, I am always looking for ways to instruct key science and math concepts and skills in the context of the technical programs.  When the lesson materials come from their field of study, it is more meaningful to the students for the direct application of science and math. In searching for materials on instruction regarding the use of the ruler, I came across your website, and shared it with our welding instructor, Mr. Greg Hutchison." We would like to incorporate your materials into our lessons."

We Thanked Brad and  Gave Permission

Email 2:

Mrs. Vicki S. Morrow, a Mathematics Teacher Asked:

“Would it be possible for me to print out and share your welding math information with a specific student? He attends my school part-time and a trade school the remainder of the time. I thought I could make math more relatable to him because he is studying welding and is very interested in the subject. I really appreciate the information available on your site."

After providing permission she emailed and said:

"Thank you so much. Your site is perfect for what I need for my student."

See YouTube Video Discussion of Our

Patented Shielding Gas Saver System

Also shows some  Bernoulli gas equations


See "Welding; Go Green" Video

CLICK Here or Picture Left

Shows Calculation of How Industrial MIG Welders Waste 8 TONS/YEAR of CO2 (or Argon) Shielding Gas



See YouTube Video Discussion of

"Welding Race Cars" with Video Clips of

Richard Petty Discussing Importance of Welding


Calculate Weld Metal Volume for Any Weld Joint. 

Also Calculate Amount of Rod or Wire Needed to Fill the Weld. Joint.  Click Here or ICON.


New Info-"Friction Stir Welding"


Some additional gas physics you might find interesting was learned from a scientist, Evangelista Torricelli, who explained the effects of a vacuum in 1643.  He solved a puzzle at the time of why irrigation and mine water pumps could only lift water 33 feet.  He also invented the Barometer (his apparatus right.)   CHECK IT OUT
Want to know how to calculate weld cooling rate?  The equations for calculating cooling rates in thick and thin material are presented under "Welding 4130."  Cooling rates are very important to understand for 4130.  However the equations can be used for any material.  CHECK IT OUT


Improve MIG Weld Starts and Have Shielding Gas Cylinder Last 2 to 3 Times Longer!  Click Here.

Ideal for Welding Schools CLICK FOR DETAILS

A small shop fabricator in Georgia with a Miller TM 175 amp welder purchased a 50 foot Gas Saver System so he could use a larger cylinder and mount it on the wall of his shop.  He wrote:

"The system works great.  Thanks for the professional

 service and a great product."  CHECK OUT HIS SHOP

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