This application is based on the Pythagorean principle, Pythagoras' theorem is applied to understand and calculate the pre and post-operative SIA magnitude consequently subtracting post-operative values from pre-operative values that yielded the final resultant SIA magnitude which is with the existing calculators. Pythagoras theorem states that the square of the hypotenuse side is equal to the sum of squares of the other two sides in a right-angled triangle and hence hypotenuse can be calculated with known measurements of the two sides. Manual keratometry measured the horizontal (Kh) and vertical (Kv) curvatures expressed in diopters.
Therefore, in the present study, the principal meridians are represented as the two sides of a triangle to calculate the hypotenuse that is considered as
the SIA magnitude.
Thus, preoperative and post-operative SIA magnitude is
calculated and their difference is considered the resultant
SIA magnitude

The law of cosine is applied for calculating angle theta when the angle opposite and the other two sides are known, thus the pre and post-operative SIA axes are calculated. Thus, we have
Cosine theta = adjacent side/hypotenuse
Sine theta = opposite side/hypotenuse

These formulae are for understanding the law of cosines however we want to find out the angle theta of the hypotenuse that is the SIA axis which is calculated from the tangent formula as shown below
Tan theta = opposite side (Kh)/adjacent side (Kv)
OR
Theta = tan-1 (Kh/Kv) according to the inverse tan
functions
Since the astigmatic axis doubles in direction, the
the formula is multiplied by 2.