Maths for joinery

Real jobs, real numbers: sizing a frame, checking it’s square, reading the drawing, how much skirting, how many packs, what it costs. Pick a topic, read the worked example, then try five quick questions. Always write the unit, and ask yourself whether the answer makes sense.

Choose a topic

Frames and halving joints

A halving joint takes half the thickness out of each piece, so the two sit flush: set the marking gauge to thickness ÷ 2. A frame's sight size is the gap you can see through: the overall size minus one member on each side.

Worked example

Sight size of a practice frame

Frame: 600 mm wide overall, corner halvings
Stiles: 69 mm wide × 44 mm thick

How wide is the sight size (the gap between the stiles)?

1.There is a stile on each side, so take off two stile widths
2.2 × 69 mm = 138 mm
3.Sight width = 600 mm − 138 mm = 462 mm

Answer: 462 mm

Does it make sense?

462 mm + 69 mm + 69 mm = 600 mm, back to the overall width. ✔

Watch out

Halving depth comes from the thickness, not the width. These stiles are 44 mm thick, so each halving is 44 ÷ 2 = 22 mm deep — not 69 ÷ 2.

Your turn: question 1 of 5

Question 1 of 5. Type the number — the unit is shown for you.

Sight size of a frame

Frame: 830 mm wide overall
Stiles: 94 mm wide

Assumptions used on this page

Frame and joint questions use the finished (planed) timber sizes given in the question. Frames use corner halvings, so rails and stiles both run the full width or height of the frame.
Diagonal and 3-4-5 questions use numbers that work out exactly, so they can be done by hand. On the bench you compare the two diagonals with a tape.
Every measurement, price and waste percentage is supplied by the question. A waste percentage is set for that exercise only — it is not a recommended amount for real jobs.
Rooms and walls are treated as simple rectangles, and only the openings named in the question are taken off.
Total length from a cutting list is the least timber you could need. It does not prove the pieces fit into your stock lengths, because offcuts can be too short to use.
Saw cuts (kerf) are ignored in these exercises — the measuring and marking out topic covers them.
Prices are examples for practice, not real supplier prices.