

low frequency inductance

formula

example


long, thin wire (as segment of closed circuit)

(reference 1) 


conductor from parallel wires (currents in same direction) r << d

(reference 8) 


return circuit of parallel wires (currents in opposite directions) r << d

(reference 1) 
l 
= 
100 
cm 
w 
= 
2 
cm 
r 
= 
0.5 
mm 

L 
= 
1.478 
μH 


strip line (as segment of closed circuit)

(reference 1) 
l 
= 
100 
cm 
w 
= 
50 
cm 

L 
= 
1.185 
μH 


return circuit of parallel plates (current runs in opposite directions)

(reference 2) 


coaxial cable

(reference 2) 


loop

(reference 1) 


single layer solenoid
N: number of turns

"Ffactor" is computed automatically
(reference 7)
The displayed equation is valid for dimensions that are entered in inches, which is taken into account in the provided calculation. 

"Where great accuracy is required, a correction factor may be applied to the equation to take account of the fact that the coil is wound of spaced round wires rather than with a uniform current sheet. This correction rarely exceeds 0.5%, is greater for widely spaced turns, and increases with the number of turns." (see reference 7 for details)


single layer short solenoid
(l < 0.8 R)
N: number of turns

Nagaokafactor K is computed automatically
(reference 1) 


single layer long solenoid (l > 0.8 R)
N: number of turns

(reference 1) 


single layer very long (ideal) solenoid
(l >> 2R )
N: number of turns

(reference 3) 


multi layer solenoid
N: number of turns

"Ffactor" and correction factor B are computed automatically correction factor dL for insulation thickness:
D : distance between wire centers d : diameter of bare wire
(reference 9)



multi layer thin wall solenoid
N: number of turns

(reference 4) 
N 
= 
1000 

d 
= 
10 
mm 
l 
= 
5 
cm 
m_{r} 
= 
1 


L 
= 
1.645 
mH 


toroid
N: number of turns

(reference 4) 


spiral (flat coil)
N: number of turns

(Wheeler formula)
(reference 1) 
N 
= 
20 

R 
= 
5 
cm 
w 
= 
2 
cm 

L 
= 
63.501 
μH 

windings cover entire area

(Schieber formula)
(reference 1)

N 
= 
20 

R 
= 
5 
cm 
L 
= 
1.380 
nH 

Both formulas can also be used for printed flat coils. For the Wheeler formulas errors up to 20% have been reported. A more accurate calculation takes the ratio between coil radius, R, and windingthickness, w, into account (Grover method). See reference 1 for details.


conical coils

The inductance of conical coils is calculated from the geometric sum of the helical and the planar contribution. See reference 5 for details.
L_{H} : inductance of equivalent helical coil L_{P} : inductance of equivalent planar coil
(reference 5)


