Cert III in Carpentry (CPC30220 and CPC30326): the maths, unit by unit

Checked on 1 November 2026 on training.gov.au. Unit codes and titles are from the CPC Construction, Plumbing and Services Training Package Release 11.0 © Commonwealth of Australia, licensed under CC BY 4.0 (PDF). This page explains the sums; it is not assessment material, and your RTO and trainer set what you are assessed on.

Which Cert III Carpentry units have maths in them?

Both qualifications have 34 units: 27 core and 7 electives. CPC30326 Certificate III in Carpentry (Release 1, 23 September 2026) superseded CPC30220 and is mapped as equivalent; the only core change is formwork, where CPCCCA3028 became CPCCCA3029 with the same title. If you started on CPC30220, the codes below still match your units.

The maths in the second column is our summary of what each unit’s elements and assessment requirements name. Of the app calculators named there, Stairs, Concrete and Check Square are free; Stud Counter, Running Measurements, Decking, Raked Walls, Pitch and Dumpy Level are paid ones in the same app. The linked web calculators are free.

CPCCOM1015: measurements and calculations

The unit asks for basic formulae for “weight, area, volume, perimeter, circumference, ratio and percentage”, on rectangles, squares, circles, triangles, trapeziums, cubes and cylinders, with readings to the nearest millimetre. Four sums that cover most of it:

• Volume of a slab: 4000 × 3000 × 100 mm = 4 × 3 × 0.1 = 1.2 m³, which is 1200 litres. Order 10 percent extra: 1.2 × 1.10 = 1.32 m³.
• Volume of a cylinder (a post hole 300 mm across and 800 mm deep): π × 0.15² × 0.8 = 0.0565 m³ a hole, so six holes take 0.3393 m³.
• Circumference: the same 300 mm hole is π × 300 = 942.5 mm round.
• Area of a triangle (a gable 6000 mm wide and 1500 mm high): 6 × 1.5 ÷ 2 = 4.5 m².

Convert to metres before you multiply, and back at the end: how to calculate cubic metres goes through it.

CPCCOM3001: material quantities

Here the sums turn into an order: areas of lining, wrap, cladding and roofing, framing timber, sheet counts and lineal lengths, laid out to waste as little as possible. A 3600 mm long, 2400 mm high stud wall at 450 mm centres:

• Studs: 3600 ÷ 450 = 8 bays + 1 = 9 studs of 2400 − 90 = 2310 mm, so 9 × 2.31 = 20.79 lineal metres.
• Plates: top and bottom, 2 × 3.6 = 7.2 m (double the top plate if the plans say so).
• Noggins: one row, 8 × 405 mm = 3.24 m (noggin spacing shows why one row).
• Plasterboard on one face, 1200 × 2400 sheets stood up: 3600 ÷ 1200 = 3 sheets.

For decking the answer is lineal metres, not boards: a 6000 × 4000 mm deck in 90 mm boards with 5 mm gaps takes 4000 ÷ 95 = 42.1, so 43 boards of 6 m, 258 m, and 283.8 m with 10 percent waste. More in how many decking boards.

CPCCCA3002: setting out

The unit’s assessment asks for setting out to a 3 mm tolerance over a diagonal of at least 10 metres. Pythagoras gives the diagonal a square rectangle should have: for 8000 × 6000 mm, √(8000² + 6000²) = 10,000 mm. Pull both diagonals; if each reads 10,000 mm within 3 mm, the set-out is square to the unit’s standard. The 3-4-5 method is the same triangle at a smaller size: how to set out a building square.

CPCCCA3003 and CPCCCA3004: floors and wall frames

Floors: set out joists at the spacing the plans give, and keep bearers square and level. Walls: set out the plates and a pattern stud, then count and cut. The marks come off one tape hooked at the end of the plate: with the first stud’s centre 38 mm in and studs at 450 mm centres, the next marks are 38 + 450 = 488, 938 and 1388 mm (how to mark out studs). Spacing limits come from the plans and AS 1684: stud spacing in Australia and joist spacing in Australia say where to look.

A raked wall is the same set-out on a slope. With a 2400 mm low side, a 15° pitch and a 4000 mm plate: high side 2400 + 4000 × tan 15° = 3471.8 mm, and the raked top plate 4000 ÷ cos 15° = 4141.1 mm.

CPCCCA3007: pitched roofs

The unit asks you to calculate and set out a pattern rafter, cut ridges and common rafters to length, and work out hip and valley rafter lengths from the pitch. The base of all of it is the right triangle of rise, run and rafter line. With a 900 mm rise over a 3600 mm run: pitch = arctan(900 ÷ 3600) = 14.04°, and the line length √(900² + 3600²) = 3710.8 mm, before the overhang, birdsmouth and ridge deductions. Worked further in rafter length from pitch and how to calculate roof pitch. MeisterCalc’s Pitch calculator gives the angle and line length; it doesn’t do birdsmouths, hips or valleys.

CPCCCA3016: timber external stairs

“Calculate rise and going of stairs” is in the unit’s elements, and the stair has to meet the NCC. A deck 1050 mm above the path, with a 280 mm going: target riser (600 − 280) ÷ 2 = 160 mm; 1050 ÷ 160 = 6.56, so 7 risers of 1050 ÷ 7 = 150 mm and 6 treads. Check: 150 is inside 115 to 190 mm, 280 inside 240 to 355 mm, and 2R + G = 2 × 150 + 280 = 580 mm, inside 550 to 700. The free stair calculator does this check line by line, and stair requirements in Australia has every NCC rule with its clause.

CPCCCO2013 and formwork: concrete

Concreting to simple forms includes working out the volume of concrete. For a 3000 × 2400 mm shed slab, 100 mm thick: 3 × 2.4 × 0.1 = 0.72 m³, and 0.72 × 1.10 = 0.792 m³ to order. In 20 kg bags it depends on the product’s yield: bags of concrete per cubic metre compares the makers’ figures. The formwork unit for footings and slabs on ground is CPCCCA3029 in CPC30326 (CPCCCA3028 in CPC30220).

CPCCCM2006 and CPCCOM3006: levelling

The basic unit transfers heights, for formwork and slabs; the levelling operations unit adds reduced levels, “calculating rise and fall and height from collimation”. The height of collimation sum: benchmark RL 100.000 m, staff reading on the benchmark 1.500 m, so the instrument height is 100.000 + 1.500 = 101.500 m; a reading of 1.200 m on the next point puts it at 101.500 − 1.200 = 100.300 m. See how to calculate a reduced level and how to use a dumpy level. MeisterCalc’s Dumpy Level works the height of collimation method; rise and fall is done by hand.

Reading plans to scale

Scaling from drawings is part of the quantities unit, and the plans unit is CPCCCA3025 Read and interpret plans, specifications and drawings for carpentry work. At 1:100, 1 mm on the drawing is 100 mm on site: a wall that measures 36 mm on the plan is 36 × 100 = 3600 mm. Always use a written dimension over a scaled one when the plan has it.

For apprentices and teachers

The web calculators linked here are free, need no account, and show the formula with the numbers in, so they work as a check on hand working rather than a replacement for it. TAFE and RTO teachers are welcome to link this page or any of them from course material. In the app, the three calculators most Cert III work uses every week, Stairs, Concrete and Check Square, are free to use, with no trial and no card needed.

Try it

MeisterCalc has 16 construction calculators in millimetres, each with a live diagram. Stairs, Concrete and Check Square are free; the other 13 unlock with a weekly subscription that starts with a 3-day free trial, or with a one-time lifetime unlock, and Google Play shows the prices in your currency. It works offline on Android 7.0 or later.

Related

• What are the stair requirements in Australia?
• Which NCC applies in my state? NCC 2025 adoption dates
• What is the right noggin spacing for walls, floor joists and decks?
• How do I set out a building square?
• How do you calculate cubic metres?
• All free construction calculators
• Construction calculators for Australia