Making Things Square In Three Dimensions

Measure twice, cut once is excellent advice when building anything, from carpentry to metalworking. While this adage will certainly save a lot of headache, mistakes, and wasted material, it will only get you part of the way to constructing something that is true and square, whether that’s building a shelf, a piece of furniture, or an entire house. [PliskinAJ] demonstrates a few techniques to making things like this as square as possible, in all three dimensions.

The first method for squaring a workpiece is one most of us are familiar with, which is measuring the diagonals. This can be done with measuring tape or string and ensures that if the diagonals are equal lengths, the workpiece is square. That only gets it situated in two dimensions, though. To ensure it’s not saddle-shaped or twisted, a little more effort is required. [PliskinAJ] is focused more on welding so his solutions involve making sure the welding tables are perfectly flat and level. For larger workpieces it’s also not good enough to assume the floor is flat, either, and the solution here is to minimize the amount of contact it has with the surface by using something like jack stands or other adjustable supports.

There are a few other tips in this guide, including the use of strategic tack welds to act as pivot points and, of course, selecting good stock to build from in the first place, whether that’s lumber or metal. Good design is a factor as well. We’ve also featured a few other articles on accuracy and precision,

32 thoughts on “Making Things Square In Three Dimensions

  1. One of the two absolute requirements for graduation from the world-class engineering school I attended was the making of a 1-inch cube out of iron or steel. This requirement was, thankfully, dropped well before I arrived, and I have no idea as to the metrics of accuracy or precision imposed on one’s submission.
    The other requirement? Everyone, with few exceptions, had to have taken a course, or demonstrated competency via a comprehensive test, in “Drownproofing”–even the “jocks”, who were exempt from taking P.E. (“…Once they had mastered the Drownproofing technique, students learned to stay afloat with their wrists and ankles bound, swim 50 yards (46 m) underwater, and retrieve diving rings from the bottom of the pool using their teeth…
    “…Drownproofing has been for many years widely taught to recruits in the U.S. Navy, U.S. Marine Corps, and U.S. Coast Guard…”—Wkipedia)

    Engineering education and training has now gone to hell in a hand-basket.

    1. Yeah education is now reaching time-bomb levels and we are going to see the real cost of some of this experimentation. All I can say is that I hope our foreign policy people are extreme pacifists at this particular moment

    2. I fondly remember my first days in apprenticeship.

      We all (huge group of totally scared boys only, because, well, world of adults and they yelled at us!) got a piece of U-steel, hammer and chisel and with a lot of elbow grease we converted it into a pile of chips and something else I really can’t remember. But I remember we did it for multiple weeks and then threw the results away because they were very precise albeit of no practical use.

      Today I still use hammer and chisel to remove pesky rounded hex nuts on my boat.

        1. I know someone who worked for Macau casino operators, aka the Chinese Triads.

          They like to hire westerners, think the lack of Chinese language skills and fear will prevent them from stealing.

          He got sick, his bosses put him on an airplane and told him to GTF out.

  2. One off carpenter’s standard for ‘square’.

    Guage blocks? Not even a machinist’s square.

    Not so much as a jig. If he had built one he could hit the welder’s standard for square by beating the jig into shape after it cooled.

        1. Hi! I am your friend! Can you help me, please, Sir? After learning of ‘guage’ not being correct name but ‘gauge’, I need help with learning ‘kno’ and ’emagonation’. What does it mean, Sir?

  3. While it doesn’t approach string, the gold standard for measurement, I seem to recall you used to be able to buy right-angled pieces of metal. Maybe it was just a beautiful dream….

  4. IIRC, Hackaday had an article about Guage blocks that are so precisely ground that they stick too each other.
    So, I entered “Guage blocks” into the Sesrch function above and lanGUAGE and Beetleblocks were returned (smh)!

  5. I’m in an old house that doesn’t have a level surface of more than about a square foot, so these are good tips. It’s painful to have to pull apart a project that’s somehow shifted in 5 different dimensions at each joint because I was slack.

    Along the same lines, I’ve been amazed over the years how many people have no idea how to test for a right angle on a large project, like a deck, using 3-4-5 measurements. My wife and I have both had neighbors/friends stare at us like were the Wizard of Oz when we’ve done that, and then go find a square to check our work.

      1. you red it hear.

        Bob says: ‘slackness is number one bane of humanity’

        Praise Bob!

        Truf: The Church has been overrun by Bobbies for decades. GD due paying followers wouldn’t know slack if it jumped them. Actual Subgeni were done with that dumbass joke, 30 years ago.

        Can’t blame the people in charge though, current members might be pink, but their money is green.

  6. For basic things like aligning parts to be welded I have a few simple tricks. I found a few peices of very “square” (on the outside) angle iron for use as clamping jigs. I also had a machinist friend take a couple of
    “Speed Squares” and machine the surfaces as square as possible. The speed square is also somewhat less likely to get out of wack if dropped that a conventional square. While I use string or a tape to square up a wall or shed, for a welding project i usually use soft iron mechanics wire (less problem with stretch). The tack weld then hit method is great and if you have a few small turnbuckles you can use the mechanics wire to pull diagonals in line with pretty good accuracy. A few screw jacks (most hydraulic jacks have a screw on top as well) work well for a base to work from if the floor isn’t level or flat.

  7. If one is truly interested in square, level, or anything else, check out Moore’s “Foundations of Mechanical Accuracy.” In an easy to follow sequence it defines fundamentals such as the flat surface and more importantly, how to make one with no external references. Critical along the way are the ability for surfaces to be “self proving” and able to also be verified without external reference. From there it proceeds to build up right angles as well as dividing a circle and some others. It goes into the history of metrometry too. I read it nearly cover to cover- truly a masterwork. It is striking how with just hand tools, scrapers and laps someone can work to 5 millionth of an inch accuracy.

  8. “not good enough to assume the floor is flat” I assume that was humor – the floor is never ‘flat’ ie in plane, or level..
    One answer is to make a big table that really is flat and will mainly stay that way (it’s going to weight a lot) then some solid jigs (I use 100mmx100mmx10mm angle steel that’s been machined square). And even then you have to be careful what you heat up when you are welding.. But wood things are then easy.

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