Form angles with a combination square

If you have a combination square but didn't spring for the (often expensive) protractor head you can still use it to measure or set angles.

If you imagine a flat spanning from the end of the head to the end of the beam/scale, you've created a right triangle; the head and beam are always perpendicular.

The head length is fixed so it can be measured; the beam length is, of course adjustable. The math is simple...

H = head length
B = beam length
A = angle desired

tan (A) = H / B

so:

B = H / tan (A)

Knowing our desired angle, A, and measuring our head length, H, we can calculate the beam extension, B, to form A.

In this photo...

Attachment 48685

I measured H to be 3 & 7/16 in and calculated the beam length needed to form a 30 degree angle...

B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 3 & 15/16 in.

I set the beam to that length and then measured the angle formed with an electronic inclinometer...

Attachment 48686

OK, it's not perfect, but close enough for many applications, especially if the more accurate tools are not to hand.

Quote:

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Originally Posted by mklotz

edit ... B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 3 & 15/16 in.

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Love the concept, Marv. But you lost me at the end. What does ~=3-15/16 relate to? Isn't beam length 5.954?

Quote:

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Originally Posted by Saltfever

Love the concept, Marv. But you lost me at the end. What does ~=3-15/16 relate to? Isn't beam length 5.954?

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Obviously a finger fumble on my part. That '3' should be a '5'. Specifically, that line should read...

B = 3.438 / tan (30) = 3.438 / 0.577 = 5.954 in ~= 5 & 15/16 in

I would fix it in the original post but the time limit on editing has run out so I can't. Thanks for catching that and sorry for the confusion.

Many thanks, Marv. That is a very useful idea. I had never thought of the using the square's head as a side. I'm going to look at it with new eyes from now on! :hattip:

I know your thoughts on the imperial system so it was very nice of you to provide the fraction for those that still work with them. Although, now that everyone has a digital caliper now days, I suspect the use of fractions is diminishing. BTW, 61/64ths would be much closer to .954 for those that have a 64ths scale but you were just being kind using 15/16th for those of us with old eyes! :D

Quote:

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Originally Posted by Saltfever

Many thanks, Marv. That is a very useful idea. I had never thought of the using the square's head as a side. I'm going to look at it with new eyes from now on! :hattip:

I know your thoughts on the imperial system so it was very nice of you to provide the fraction for those that still work with them. Although, now that everyone has a digital caliper now days, I suspect the use of fractions is diminishing. BTW, 61/64ths would be much closer to .954 for those that have a 64ths scale but you were just being kind using 15/16th for those of us with old eyes! :D

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Yes, there are closer approximations to .954 than my 15/16. I wrote a program to find the closest rational fraction approximation to any decimal number. It tells me that 83/87 is good to 0.01 %. I really should use numbers like that just to confuse and infuriate the inferial system lovers.

I stuck with sixteenths because I figure that the old inferial eyesight isn't good enough to read anything smaller on the ruler. Besides, what I'm trying to get across here is the idea that the square can be used for approximate angle setting/measuring when better methods are not to hand. There are much more accurate tools for working with angles.

The Usonians will never adopt the metric system because, if they did, they would have two measurement systems they don't understand instead of just one. :-)

Marv, I'm thinking of drilling a precision hole 1" back from the end so I can center punch more precise angular locations. I think I can keep it within 477/500"! :D

I memorized the machinist decimal equivalent chart over 50 years ago and haven't used fractions since. I'm not a woodworker but even when I use a tape I automatically convert without thinking about it. Imperial or metric are seamless to me.

Congratulations mklotz - your angle forming method is the Tool Tip of the Month for January 2025!

This is a simple and easy angle measurement method using a tool that all of us have.

Some more nice tool tips from January:

Making Better Drill Press Mortises by Make Things
Small Stock Center Marking Method by mklotz
Why Nail Specifications Use "D" by Make Things
Plane Sole Adjustment by Make Things
Safe Fuel Tank Welding Method by tonyfoale
Sled Truing Method by Make Things
Making Tools Mobile by Make Things
One Rail Dado Router Track by Make Things

mklotz - we've added your Tool Tip to our All Tool Tips of the Month winners post.

And, you'll be receiving a $100 prize, in your choice of Amazon, PayPal, or bitcoin. Please PM me your current email address and prize choice and I'll get it sent over right away.

Congrats again :thumbsup: