NOTE: To find the Headstay angle, pick a point on your boat back from the tack about where the clew will be and measure the distance from there to the tack, from there to a point up the head stay, and from that point on the head stay down to the tack. Enter those numbers into the LP calculator as the foot, leech,and luff dimensions. The resulting angle at the tack will be the head stay angle. If the sail is near 100% or if the deck is flat, you can use I, J, and head stay length to calculate the head stay angle.

This page calculates the area of the triangle given the three sides then calculates the LP by solving the equation area = 1/2 * LP * luff. The initial area calculation uses Heron's formula that says the area of a triangle abc is SQRT ( s * (s - a) * (s - b) * (s - c) ) where s = 1/2 (a + b + c). The final calculation is the perenct of LP to J. NOTE: An actual measurement of a real sail will probably give a different result as this calculation does not try and predict luff hollow. If the luff hollow at the LP is known, it could be substracted from the calculated LP. This might change the result by a small amount.

The ratio of the chord to the arc is calculated by first calculating the radius of an arc segment with a unit chord length by solving the formula r^2 = (1/2) ^ 2 + ( r - h) ^ 2 where h is the depth fraction.
The arc lenght is given by 2 * r * atan ( (1/2) / (r - h)) and the shortening is 1/arc.

Headstay angle is the foot length times the sin of the difference between the headstay angle and the sail's clew angle.