CWI Part A formula sheet (printable)

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AWS lists welding-related calculations as its own content area (08) in the Part A information guide. Every example below uses invented numbers and was computed with the same functions that power our CWI math calculator. Work it by hand first, then check it there.

The sheet at a glance

Heat input

Arc energy is the electrical power divided by how fast the arc moves. Heat input multiplies that by an efficiency factor k for the process. If a question gives you no k, it is asking for arc energy, so don't invent one. TWI and the Australian Welding Institute publish the factors; the heat input calculator lists them and lets you use a stopwatch instead of a speed.

Worked example. A GMAW pass runs at 24 V and 210 A at a travel speed of 12 in./min.

1. Power: 24 × 210 = 5,040 W.
2. Arc energy: 5,040 × 60 ÷ 12 = 25,200 J/in., which is 25.2 kJ/in.
3. With k = 0.8 for GMAW, heat input is 0.8 × 25.2 = 20.16 kJ/in.

In metric the same pass is 0.99 kJ/mm of arc energy and 0.79 kJ/mm of heat input.

The slip: leaving out the 60, or reporting 25,200 J/in. as 25,200 kJ/in. One is 60 times off and the other is 1,000 times off, and both show up as wrong options.

Carbon equivalent (IIW)

Carbon equivalent turns a steel's chemistry into one number that tracks how hard the heat-affected zone gets and how likely hydrogen cracking is. Part A asks you to run the formula on a given analysis. Whether the number triggers preheat is decided by the governing code or the WPS, never by the formula, so read welding metallurgy for the CWI exam for how the two connect.

Worked example. A plate analysis reads 0.18 C, 1.20 Mn, 0.10 Cr, 0.05 Mo, 0.03 V, 0.12 Ni and 0.15 Cu.

1. Carbon: 0.18
2. Manganese: 1.20 ÷ 6 = 0.200
3. Cr + Mo + V: 0.18 ÷ 5 = 0.036
4. Ni + Cu: 0.27 ÷ 15 = 0.018
5. Add: CE = 0.434

The slip: dividing the wrong group by the wrong number. Say the groups out loud, "manganese over six, chrome moly vanadium over five, nickel copper over fifteen," until they stick. The carbon equivalent calculator shows every term and also gives Pcm.

Tensile strength from load and area

Engineering stress is the maximum load divided by the ORIGINAL cross-section area. For a round bar, find the area first.

Worked example, US units. A 0.500 in. diameter round bar breaks at 11,250 lbf.

1. Area: π × 0.500² ÷ 4 = 0.1963 in²
2. Stress: 11,250 ÷ 0.1963 = 57,296 psi, or 57.3 ksi

Worked example, SI units. A flat bar 19 mm wide and 12 mm thick breaks at 120,000 N.

1. Area: 19 × 12 = 228 mm²
2. Stress: 120,000 ÷ 228 = 526.3 N/mm², which is 526.3 MPa and about 76.3 ksi

The slip: using π × d² for the area (four times too large), or using the necked-down area at the break instead of the original.

Elongation

Percent elongation is the stretch over the original gauge length, times 100.

Worked example. A 50 mm gauge length measures 61 mm after the break.

1. Stretch: 61 − 50 = 11 mm
2. Elongation: 11 ÷ 50 × 100 = 22%

The slip: dividing by the final length. 11 ÷ 61 gives 18%, which is a tempting wrong option.

Reduction of area

Reduction of area compares the cross-section before and after the test. Area goes with the square of the diameter, so you can't subtract diameters.

Worked example. A 0.500 in. round bar necks down to 0.300 in. at the break.

1. Original area: 0.1963 in². Final area: 0.0707 in².
2. Reduction: (0.1963 − 0.0707) ÷ 0.1963 × 100 = 64%

The slip: (0.500 − 0.300) ÷ 0.500 gives 40%. That is a diameter change, not an area change, and it is the first wrong answer a rushed candidate finds. For the test method behind these numbers, see destructive weld tests: bend, tensile and Charpy.

Unit conversions

Problems can give numbers in inch or metric units, so convert before you calculate and check the unit on your answer.

The inch is defined as exactly 25.4 mm (NIST SP 811). The other factors come from it and from the pound-force, so keep four digits and round only at the end.

The slip: converting the load but not the area, or the area but not the load. Pick one system at the start and stay in it.

Weld size and throat geometry

A fillet weld with equal legs has a theoretical throat equal to the leg divided by the square root of 2, which is about 0.707 times the leg. The throat is the shortest distance from the root to the face of an ideal flat-faced weld, and the leg is the side of the right triangle.

Worked example. A 3/8 in. equal-leg fillet: 0.375 ÷ 1.4142 = 0.265 in. throat. A 10 mm equal-leg fillet has a 7.07 mm throat.

The slip: reading leg as throat, or throat as leg. A question that gives one and asks for the other is a one-line check. For unequal legs, the fillet weld calculator returns the throat and the cross-section area for any leg pair, and the weld gauge reading trainer shows how you read leg and throat on a real gauge. Required sizes and acceptance limits come from the governing code, so they are not on this sheet.

Print this sheet

Use the print view on this page and keep the formula table beside you while you drill. Cover the right-hand column and write each formula from memory, then check it. When all nine rows come without a pause, move to the CWI math calculator and run twenty variations of your own.

Take the free 10-question check for Part A

Formulas are one domain of Part A. The rest is processes, symbols, NDE, metallurgy and terms, all from memory. Take the free 10-question check for Part A. It's scored by domain and takes no signup. The Part A course then gives you a lesson for every exam subject, full-length timed practice exams and a worked explanation with every answer.

FAQ

Do I get a formula sheet at CWI Part A?

No. Part A is closed book, so you need the formulas from memory. You may bring an approved calculator, which is inspected at check-in.

Which calculations show up on Part A?

AWS lists welding-related calculations as content area 08 in the Part A information guide. The ones in this sheet are the ones candidates practice: heat input, carbon equivalent, stress, elongation, reduction of area, unit conversion and fillet geometry.

What is the most common calculation mistake?

Unit and base errors: leaving out the 60 in arc energy, using π × d² for area, dividing elongation by the final length, or subtracting diameters for reduction of area.

Sources

Show the list

• CWI Part A Fundamentals Examination Information, American Welding Society, Rev. 03.01.2024 (content area 08, Welding Related Calculations).
• Travel speed and heat input calculator, Australian Welding Institute (arc energy and efficiency factor k).
• What is the difference between heat input and arc energy?, TWI.
• Carbon equivalent formulae in relation to hydrogen cracking, TWI (IIW formula).
• Guide to the SI, Appendix B.8, NIST (conversion factors).

Not affiliated with or endorsed by AWS.