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Square to Round Converson Table

As par of controlled hand forging there are times when you want to round out a square taper and need to know the resulting diameter. 
This is an approximate cross sectional conversion chart I am working on. 

DIAMETER OF CIRCLE SQUARE WIDTH SQUARE WIDTH IN 64/ths           AREA
1/ 8 0.111 7.088 0.012
3/16 0.166 10.632 0.028
1/ 4 0.222 14.176 0.049
3/ 8 0.332 21.264 0.110
1/ 2 0.443 28.352 0.196
5/ 8 0.554 35.440 0.307
3/ 4 0.665 42.528 0.442
7/ 8 0.775 49.616 0.601
1 0.886 56.704 0.785
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