Crochet Sphere Calculator
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How to crochet spheres:
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To make a more perfect sphere, I think you have to figure out rows based on an approximate size, then make sure the circumference/rows are whole numbers
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Make a test swatch of single crochet and measure the height and width of 1 stitch. Also measure over multiple stitches and rows and divide for more accurate numbers. I use millimeters for easy conversion with the larger values for circumference and diameter.
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Stch Height(mm):
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Stch Width(mm):6
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To make a ball with a specific circumference and diameter:
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Circ = Diam * PI
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Diam = Circ / PI
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Diam = Rad * 2
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1. List measurements: Radius, Diameter, Circumference (when the circ is a whole number, divisible by the stitch height to produce another whole number of rows, the sphere will be most perfect)
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Circ(mm):100.00(100/2/5=10)
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Diameter(mm):31.83
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2. Divide the length of the circumference by 2 to get half,
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100/2=50
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then divide this length by the stitch height to get the number of rows.
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50/5=10
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3. Divide the number of degrees in half a circle (180) by the number of rows + 1 to get the interval of degrees for each row. (Add 1 because you are dividing an area with edges, so you need 1 more section than you do 'cuts'. Imagine cutting half a pie 11 times, you would end up with 10 pieces)
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180/(10+1)=16.364°
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4. List row numbers in a column and multiply each row number (in this case 1-10) by the degree interval (in this case 16.364°)
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Row number:
Row # * degree:
Angle of degree per row:
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11*16.364=16.36363636
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22*16.364=32.72727273
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33*16.364=49.09090909
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44*16.364=65.45454545
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55*16.364=81.81818182
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66*16.364=98.18181818
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77*16.364=114.5454545
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88*16.364=130.9090909
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99*16.364=147.2727273
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1010*16.364=163.6363636
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5. Now find the sine value for each degree. Use either an online sine calculator (rapidtables.com) or use a formula.
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Row number:Degree per row:
Formula for sine in °s:
Sine value:
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116.36363636
=SIN(16.364*PI()/180)
0.2817325568
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232.72727273
=SIN(32.728*PI()/180)
0.5406408175
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349.09090909
=SIN(49.092*PI()/180)
0.7557495744
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465.45454545
=SIN(65.456*PI()/180)
0.9096319954
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581.81818182=SIN(81.82*PI()/180)0.9898214419
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698.18181818
=SIN(98.184*PI()/180)
0.9898214419
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7114.5454545
=SIN(114.548*PI()/180)
0.9096319954
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8130.9090909
=SIN(130.912*PI()/180)
0.7557495744
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9147.2727273
=SIN(147.276*PI()/180)
0.5406408175
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10163.6363636
=SIN(163.64*PI()/180)
0.2817325568
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6. Multiply the sine value by the total circumference of the circle from step 1 to find the circumference of each row: (the sine value is a percentage of a whole based on a radius of 1, so multiplying it by the total circumference of the desired circle will give you proportional values for each smaller row. Essentially, 'what proportion is this row's circumference based on the whole circumference of my circle?')
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Row number:Degree per row:Sine value:Sine * total circ:Row Circumf:
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116.363636360.2817325568=0.2817386464*10028.17325568
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232.727272730.5406408175=0.5406514957*10054.06408175
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349.090909090.7557495744=0.7557620427*10075.57495744
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465.454545450.9096319954=0.909642541*10090.96319954
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581.818181820.9898214419=0.9898259575*10098.98214419
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698.181818180.9898214419=0.9898259575*10098.98214419
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7114.54545450.9096319954=0.909642541*10090.96319954
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8130.90909090.7557495744=0.7557620427*10075.57495744
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9147.27272730.5406408175=0.5406514957*10054.06408175
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10163.63636360.2817325568=0.2817386464*10028.17325568
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7. Finally, divide each row's circumference by the width of one stitch to find the number of stitches per row: (this will be a decimal so round to the nearest whole number)
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Row number:Degree per row:Sine value:Row Circumf:
Circ / stitch width:
Stiches per row:
Stitches Rounded:
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116.363636360.281732556828.17325568/64.6955426145
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232.727272730.540640817554.06408175/69.0106802919
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349.090909090.755749574475.57495744/612.5958262413
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465.454545450.909631995490.96319954/615.1605332615
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581.818181820.989821441998.98214419/616.4970240316
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698.181818180.989821441998.98214419/616.4970240316
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7114.54545450.909631995490.96319954/615.1605332615
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8130.90909090.755749574475.57495744/612.5958262413
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9147.27272730.540640817554.06408175/69.0106802919
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10163.63636360.281732556828.17325568/64.6955426145
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Now that you have the pattern worked out, you can set up a spreadsheet for easy duplication of any size sphere with any dimension of stitches. It might be necessary to list stitch height and width and number of rows multiple times in a column to make the formulas easy to drag down for duplication.
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To find circumference and diameter based on how many rows you want, multiply total rows by stitch height to get half the circumference * 2 = total circ
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my differences between khold's method: I used whole row numbers to find circumference, whereas he started with an integer in mm for the diameter and calculated circumference and row number, where row number would be a decimal and you would round that. doesn't make sense to me to do it that way because ultimately you would end up with 2 spheres with the same number of rows but slightly different stitches. obviously one of them would have to be wrong. so finding whole row numbers and basing the size off that to calculate diameter and circumference makes more sense to me. I think as the spheres get bigger, the difference in methods doesn't make a huge difference
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