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Miter Angles

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Forum topic by dpwalker posted 1046 days ago 1475 views 0 times favorited 6 replies Add to Favorites Watch
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dpwalker

265 posts in 1435 days


1046 days ago

I understand the formula for figuring out a miter angle (360/sides/2). Maybe I’m lazy but isn’t it easier & less complicated to just divide 180 by the number of sides? I get the same answer when I try both ways. Is there something I’m missing? Are there situations where this just won’t work?

-- You have not really lived until you do something for someone who can never repay you.


6 replies so far

View Murdock's profile

Murdock

107 posts in 1088 days


#1 posted 1046 days ago

360/sides/2 always = 180/sides

Since all the operations are all division you can change the order so:
360/sides/2 = 360/2/sides = 180/sides

I think the reason that people start from 360 is because the corner angle is 360/sides, if you need that you can always multiple the miter by 2.

-- "Anyone who has never made a mistake has never tried anything new." - Albert Einstein

View Tootles's profile

Tootles

681 posts in 1106 days


#2 posted 1046 days ago

Now how do I answer this? The last time this issue was raised, it caused some discussion.

Okay, first the simple answer: 360/sides/2 is exactly the same as 180/sides. Yes that is probably easier to remember. However …

The crux of the question might revolve around what you define as the mitre angle. I generally understand it in the context of a box in which it is the angle between the outside face and the end edge of the piece of wood that is the front, back or a side. Using that definition, the formula for the mitre is actually:
(sides – 2) * 90 / sides .

The angle calculated using the formula 180/sides is technically known as the complement of the mitre angle (as I have defined it). BUT, and here is the funny bit, knowing the complementary angle is generally more important than knowing the mitre angle, because for most saws, that is the angle that you will set your blade to in order to make the cut.

Does that confuse the matter further? I’ll watch this post and do a sketch if necessary

-- I may have lost my marbles, but I still have my love of woodworking

View Bill White's profile

Bill White

3353 posts in 2564 days


#3 posted 1045 days ago

Just buy longer boards. Keep cuttin’ ‘till it fits.
I know it is a smart a$$ed answer, but seems to me that any formula that will yield the end result will work.
Bill

-- bill@magraphics.us

View dpwalker's profile

dpwalker

265 posts in 1435 days


#4 posted 1045 days ago

Tootles & Murdock if I understand correctly 360/sides/2 = the outside angle. Or two 45 inside angles = a 90 corner angle. While 180/sides will give the actual angle to be cut on the saw? That being said I only need to be concerned with 360* if I want to know the actual corner angle? I was never any good at math so forgive my ignorance here :)

-- You have not really lived until you do something for someone who can never repay you.

View Tootles's profile

Tootles

681 posts in 1106 days


#5 posted 1045 days ago

I like using sketches to explain things such as these.

A quick reminder, the angle that I have refer to as the mitre angle is the way I understand it. Others may refer to a different angle as the mitre angle, and that is fine as long as it is clear which angle they mean.

The sketch below shows a hexagonal box with the mitre angle marked. I have also marked the interior angle between sides which Murdock mentioned. It is twice the mitre angle or, as a formula, (sides – 2) * 180 / sides

The following sketch shows how the mitre angle gets translated to a table saw by using the complementary angle of the mitre angle. I have shown the blade, the blade angle setting and one of the side pieces of the hexagonal box with the angles already cut both left and right.

And another close-up of the same view.

Hopefully that explains a bit better.

-- I may have lost my marbles, but I still have my love of woodworking

View dpwalker's profile

dpwalker

265 posts in 1435 days


#6 posted 1044 days ago

Tootles, Thank you for the clarification. You are right, the sketches do make the explanation easier. Thank you for sharing this.

-- You have not really lived until you do something for someone who can never repay you.

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