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Thread: Quilting Math Question

  1. #1
    Super Member ShowMama's Avatar
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    Does anyone know if there is a formula for figuring the diagonal measurement of a quilt block? Say, if I make an 8" square 9-patch block, is there a formula that I can use to figure the diagonal measurement from one corner to the opposite corner? Oh, I know I could just make a block and then measure it's diagonal, but was hoping there is some easy method to figure it out on paper. I'm wanting to make a quilt with sashed blocks on point and want it to end up a certain size, but don't exactly know how big to make my blocks and sashing. Any help would be appreciated.

  2. #2
    Super Member ghostrider's Avatar
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    The diagonal of a square is 1.414 times the length of one side. Best to round up and trim down.

  3. #3
    Senior Member lee_stitches's Avatar
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    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3

  4. #4
    Senior Member lee_stitches's Avatar
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    Quote Originally Posted by ghostrider
    The diagonal of a square is 1.414 times the length of one side. Best to round up and trim down.
    Your way is much easier.

  5. #5
    Power Poster QuiltE's Avatar
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    Quote Originally Posted by ShowMama
    Does anyone know if there is a formula for figuring the diagonal measurement of a quilt block? Say, if I make an 8" square 9-patch block, is there a formula that I can use to figure the diagonal measurement from one corner to the opposite corner? Oh, I know I could just make a block and then measure it's diagonal, but was hoping there is some easy method to figure it out on paper. I'm wanting to make a quilt with sashed blocks on point and want it to end up a certain size, but don't exactly know how big to make my blocks and sashing. Any help would be appreciated.
    .... or instead of "making" it, you could cut draw it on paper.
    Don't forget the seam allowances!

  6. #6
    Power Poster ckcowl's Avatar
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    the 1.414 number is used in both directions- if you have a square you need the diagonal of- times the size of the square by 1.414- if you want to figure out the size of setting triangles for said square- to make it on point you divide by 1.414 make a square that size- then cut in half diagonally for your setting triangles.
    also- if you have a square- which you multiply by 1.414- that gives you the size the square will be when put on point.

  7. #7
    Super Member ghostrider's Avatar
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    Quote Originally Posted by lee_stitches
    Quote Originally Posted by ghostrider
    The diagonal of a square is 1.414 times the length of one side. Best to round up and trim down.
    Your way is much easier.
    It's the same as yours, just more universal. If the sides are 1, the diagonal equals the square root of 2 which is 1.414. ;)

  8. #8
    Senior Member qbquilts's Avatar
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    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    You need to add in the seam allowance before doing the math. So the 8" finished block becomes 8.5". Plugged into the formula, you get 12.02. Just to demonstrate that you can use the formula OR the "Multiplying by 1.414" trick, multiplying gives you 12.019. Round UP to the nearest 1/8 for ease in cutting, so sashing strips would need to be cut at 12 1/8.

  9. #9
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    For quick no-math measurements I measure diagonals on my cutting mat. Quick and easy, no brain strain. Don't forget to add seam allowances.

  10. #10
    Super Member ghostrider's Avatar
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    Quote Originally Posted by qbquilts
    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    You need to add in the seam allowance before doing the math. So the 8" finished block becomes 8.5". Plugged into the formula, you get 12.02. Just to demonstrate that you can use the formula OR the "Multiplying by 1.414" trick, multiplying gives you 12.019. Round UP to the nearest 1/8 for ease in cutting, so sashing strips would need to be cut at 12 1/8.
    Sashing would be the length of the side of the block, just like straight set quilts. You sash the sides, not the diagonals, using the unfinished length.

    Diagonals are needed for setting and corner triangles and to compute that measurement, you use the finished block size plus the finished sashing width....not adding the seam allowances. Here's a chart for you to use.
    http://quiltville.com/onpointmath.shtml

    How big do you want your quilt to be?

  11. #11
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    Quote Originally Posted by scraphq
    For quick no-math measurements I measure diagonals on my cutting mat. Quick and easy, no brain strain. Don't forget to add seam allowances.
    This is exactly what I do!!!

  12. #12
    Junior Member Quilter Lois's Avatar
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    Take a quilt square ruler and measure from 8" to 0 diagonally across the ruler.

  13. #13
    MTS
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    Quote Originally Posted by qbquilts
    You need to add in the seam allowance before doing the math. So the 8" finished block becomes 8.5". Plugged into the formula, you get 12.02. Just to demonstrate that you can use the formula OR the "Multiplying by 1.414" trick, multiplying gives you 12.019. Round UP to the nearest 1/8 for ease in cutting, so sashing strips would need to be cut at 12 1/8.
    No, the formula is used on FINISHED sizes/measurements.

    The seam allowances are either added to or subtracted from the sizes, after or before the calculation, depending on what you're trying to figure out.

    If I've got an 8" square block and I want to know how wide it will be on point, it's 8" x 1.414 = 11.3" (then round up).
    The unfinished size will be ~12", but that has nothing to do with the calculation.

    Let's say I've got a design where I want six on-point blocks/squares that are ~10" across (because I want a 60" wide top).
    I take 10" divided by 1.414 = 7.07" (and round up or down).
    I would THEN add the seam allowance to cut my squares.
    For blocks, I'd want them to be the 7" (or 7.125" or 7.25", depending on your round) FINISHED.

    The seam allowance is always a constant .5".
    You wouldn't want to perform the calculation by including it.
    Actually, you'd pretty much exclude it for any calculation (not just this example).

  14. #14
    Junior Member KyKat's Avatar
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    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    correct.
    The theorem can be written as an equation relating the lengths of the sides a, b and c, called the Pythagorean equation: where c represents the length of the hypotenuse (the diagonal), and a and b represent the lengths of the other two sides.

  15. #15
    Power Poster MadQuilter's Avatar
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    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    Sorry, but that does not take the seam allowance into account. We just had that discussion on the German forum. It appears that Mrs. Pythagoras had it figured out, but her husband didn't listen. So the seam allowance is not part of the Pythagorean Theorem.

  16. #16
    Super Member quiltingfan's Avatar
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    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    :? math major???? Totally impressed. :thumbup:

  17. #17
    Senior Member SUZAG's Avatar
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    Quote Originally Posted by lee_stitches
    Pythagorean Theorem? A squared + B squared = C squared is the formula for a right triangle. 8 squared + 8 squared = C squared. 64 + 64 = C squared. 128 = C squared. The square root of 128 = 11.3
    Show off! LOL huh??

  18. #18
    Senior Member lee_stitches's Avatar
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    Middle School Math teacher, lol. You caught me!

  19. #19
    Super Member AliKat's Avatar
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    This works. Just have a calculator handy as it is much safer.

    ali

  20. #20
    Super Member sewingsuz's Avatar
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    Oh Boy, Do I have to understand all this. I'll wait until I need to know and ask or I'll bookmark this one!!!! EEEIKKEES

  21. #21
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    Half square triangles - If cut from a square - the theoretical amount to the add to the finished size is 7/8 inch. I actually add an inch and trim the HST units down after sewing them.

    (Example: Four inch finished size (two pieces make a square unit) - cut 4-7/8 inch squares

    Quarter square triangles - if cut from a square - the theoretical amount to add to the finished size is 1-1/4 inch

    (Example: Four inch finished size (four pieces in the square unit) - cut 5-1/4 inch squares.

  22. #22
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    I am so happy I have no plans to do this! LOL

  23. #23
    Super Member jitkaau's Avatar
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    You have to go back to Pythagoras' Theorem:

    http://www.mathguide.com/lessons/Pythagoras.html

  24. #24
    BMP
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    I am totally confused, MATH isnt a strong point for me !!!

  25. #25
    Super Member SandyinZ4's Avatar
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    Thanks everyone, this was really helful for those of us who like to do our own thing!

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