These equations are from Inductance: Loop and Partial — Clayton R Paul.
Note that the inductance is fairly similar for either square or circular loops for a given length of wire (circumference/perimeter).
Inductance of a circular loop:
\(L_{circular} = \mu_0a(\ln{\frac{8a}{r_w}}-2)\)with:
a = radius of loop
r_w = radius of wire
(assumed a >> r_w)
For a 22 AWG wire:
1 cm = 45 nH (wire length 6.3 cm)
10 cm = 740 nH (wire length 63 cm)
100 cm = 10 uH (wire length 630 cm)
Inductance of a square loop:
\(L_{square} = 2\frac{\mu_0}{\pi}l(\ln{\frac{l}{r_w}}-0.774)\)with:
l = length of side
r_w = radius of wire
(assumed l >> r_w)
For a 22 AWG wire:
1 cm = 22 nH (wire length 4 cm)
10 cm = 400 nH (wire length 40 cm)
100 cm = 6 uH (wire length 400 cm)
Inductance of a rectangular loop:
\(L_{rectangle} = \frac{\mu_0}{\pi}[-l\ln(1+\sqrt{1+(\frac{w}{l})^2})-w\ln(1+\sqrt{1+(\frac{l}{w})^2})
+l\ln\frac{2w}{r_w}+w\ln\frac{2l}{2w}
+2\sqrt{l^2+w^2} -2w -2l]\)