We report here a new possible two formulas for obtaining the length of irregular arc
ℓ
in terms of their base
b
and height
h
. The first formula is obtained by applying the law of cosines and intersecting chord theory and
ℓ
is given by
)416228422321(1cos)242(31018.2
hhbbbhhhb

. While the other is obtained by applying Pythagorean theory and
ℓ
is given by
Khbh

224
with an error of
2)2(
bh K

, where K is a constant and equal 0.313165528 and can be used only in case of 2h
<
b. Finally, the earth circumference is calculated by using the two formulas and their values are 39910.0252 Km and 39999.5504 Km, which is consistent with the reported elsewhere (39992.1984 km).