Spreadsheet: 129719d1321837854-excel-2007-calculate-an-angle-between-2-3d-vectors-scratch
Sheet: 5-point practice Cal 02

 | Shoulder |  |  | Hip |  |  | Knee |  |  | Ankle |  |  | Toe |  |  | Shoulder-Hip-Knee
Frame | X | Y | Z | X | Y | Z | X | Y | Z | X | Y | Z | X | Y | Z
1 | 56.5536 | 1141.8 | 1417.38 | 87.4513 | 1093.62 | 863.25 | 144.279 | 961.507 | 505.299 | 53.9009 | 1227.68 | 197.849 | 28.0045 | 1145.58 | 82.3287 |  | << In one messy formula
2 | 60.7091 | 1139.26 | 1417.73 | 91.4098 | 1088.41 | 864.185 | 149.708 | 952.522 | 506.961 | 64.9521 | 1209.32 | 189.701 | 40.8525 | 1123.16 | 78.313
3 | 64.6619 | 1136.52 | 1418.05 | 94.985 | 1083.49 | 865.348 | 154.496 | 944.285 | 508.815 | 76.0216 | 1191.23 | 181.351 | 54.0247 | 1100.15 | 74.1763
4 | 68.5599 | 1133.8 | 1418.16 | 98.5797 | 1077.69 | 865.966 | 159.576 | 936.719 | 510.34 | 87.6089 | 1172.44 | 172.452 | 66.6031 | 1077.01 | 70.0211
5 | 72.3963 | 1131.16 | 1418.13 | 101.378 | 1072.75 | 867.151 | 164.009 | 929.795 | 511.346 | 98.8513 | 1152.82 | 163.593 | 78.9506 | 1052.85 | 65.4475
6 | 186.975 | -507.698 | 974.498 | 239.396 | -179.868 | 650.55 | 278.238 | -499.909 | 421.548 | 275.629 | -288.828 | 74.0655 | 229.889 | -405.699 | 24.4845
7 | 186.994 | -506.761 | 977.176 | 239.893 | -179.594 | 652.514 | 278.5 | -499.168 | 422.079 | 275.654 | -288.707 | 74.0312 | 229.917 | -405.766 | 24.3805
8 | 187.426 | -505.605 | 980.225 | 240.095 | -179.212 | 654.187 | 278.716 | -498.295 | 422.714 | 275.698 | -288.634 | 73.9903 | 229.916 | -405.775 | 24.3235
9 | 187.589 | -504.649 | 983.591 | 240.428 | -178.973 | 656.169 | 279.051 | -497.32 | 423.406 | 275.665 | -288.566 | 73.9834 | 229.853 | -405.789 | 24.3234
10 | 187.659 | -503.641 | 987.321 | 240.504 | -178.874 | 658.558 | 279.158 | -496.172 | 424.235 | 275.726 | -288.409 | 73.8376 | 229.757 | -405.813 | 24.2311
11 | 187.75 | -502.512 | 991.246 | 240.9 | -178.425 | 661.001 | 278.908 | -495.012 | 425.091 | 275.663 | -288.309 | 73.9203 | 229.738 | -405.872 | 24.1278
 |  |  |  | Shoulder - Hip |  |  | Knee - Hip |  |  | Angle
 |  |  |  |  | -0.08648697166956819 | -0.9947078790215393 |  | 0.3424730156306028 | 0.9279068556310881 |  | << In three simpler formulas
 |  |  |  |  | -0.09133808816224742 | -0.9942918783042545 |  | 0.351479029908021 | 0.9239722784930448
 |  |  |  |  | -0.09536610353649182 | -0.9939475043716034 |  | 0.3593833941885675 | 0.9204557284596997
 |  |  |  |  | -0.1009447425519951 | -0.9934250787516746 |  | 0.3639088731748506 | 0.9180289345445476
 |  |  |  |  | -0.1052766531443614 | -0.9930701091050682 |  | 0.3679376244936693 | 0.9157710222305617
 |  |  |  |  | 0.7067488710531316 | -0.6983799020221454 |  | 0.8093183294728673 | 0.5790992906719624
 |  |  |  |  | 0.7051897940310786 | -0.6997904095147679 |  | 0.8072564792249207 | 0.582087863187226
 |  |  |  |  | 0.7029253646621035 | -0.7021608307889657 |  | 0.8055871888356456 | 0.584398677965775
 |  |  |  |  | 0.7006426597607697 | -0.7043989147010856 |  | 0.8033965543660635 | 0.5874124530273822
 |  |  |  |  | 0.6982197521050326 | -0.7068107916177038 |  | 0.800585442788798 | 0.591228380609394
 |  |  |  |  | 0.6958453792654181 | -0.7090671865132141 |  | 0.7981666283674886 | 0.5947669654729165