Introduction

This web page uses formulae published in the ARRL Handbook For Radio Amateurs.

Inductance of a Straight, Non-magnetic Wire, In Free Space

Equation
L (uH) = K × b × { ln(2b/a) − 0.75 }
Where:
L = Inductance in uH
K = 0.00508 (inches), 0.0002 (mm)
a = Wire Radius (in or mm)
b = Wire Length (in or mm)
ln = Natural Log (2.303 × LN10)
Calculator
Wire Size (AWG/in/mm)
Wire Length (in/mm)
Inductance = 0.081 uH
Any length of wire has some inductance, however, at low frequencies, 1-30 MHz, the added effect of this inductance is usually minimum. At VHF and UHF frequencies the inductance of a wire may have a great effect on a circuit. Now, there is no diagram for this because it is simply a straight round wire in free space. By free space I mean, it is far enough from grounds or other wires so that they have minimum effect.

At VHF frequencies, and above, skin effect will reduce the inductance. The constant, 0.75 will approach infinity, however, skin effect will not reduce the inductance by more than a few percent.

Enter your data below. Internally, all input data is converted to inches for calculation purposes, however, for entry purposes, the dimensions can be mixed or matched.

Inductance of a Straight Wire, One End Grounded

This section is very similar to the section above, except that this wire is close to a ground plane and has one end grounded to that ground plane. The figure to the right details the dimensional requirements.

Equation
L (uH) = K1 × b ×   log10  
2 × h
a
×
b +     b2 + a2
b +    b2 + 4h2
+ K2 ×     b2 + 4h2 −    b2 + a2 + b/4 − 2h + a
Where:
L = Inductance in uH
K1 = 0.0177 (inches), 0.0004605 (mm)
K2 = 0.00508 (inches), 0.0002 (mm)
a = Wire Radius (AWG || in || mm)
b = Wire Length (in || mm)
h = Height above Ground Plane (in || mm)
Ground Plane
a
b
h
Calculator
Wire Size - a
Wire Length - b
Wire Height - h
Inductance = 0.084 uH

As you can see from the equation in the drawing, it's quite a messey job calculating the inductance. But you don't have to deal with the equation. Just enter your data in the spaces provided and let the web page do the calculation. All input data is converted to inches for calculation purposes, however, for entry purposes, the dimensions can be mixed or matched.

Inductance of a Flat Strip over a Ground Plane
Equation
L (uH) = K × b ×   ln  
2 × b
w + h
+ 0.5 + 0.2235 ×
w + h
b
Where:
L = Inductance in uH
K = 0.00508 (inches), 0.0002 (mm)
b = Strip Length (in || mm)
w = Strip Width (in || mm)
h = Insulator Thickness (in || mm)
ln = Natural Logarithm (2.303 × ln10)
w
b
h
Copper
Strip
Ground Plane
Calculator
Strip Width - w
Strip Length - b
Insulator Thickness - h
Inductance = 0.054 uH

The diagram on the right shows the dimensional requirements for calculating the inductance of a Flat Strip over a Ground Plane. The drawing shows a Copper Strip of width w and length b, separated from a Ground Plane of thickness h. The Flat Strip is often etched into a printed circuit board and the Ground Plane is usually a continuous layer of copper on the opposite side of a printed circuit board. In that case, the thickness h would be the printed circuit board thickness.

Just enter your data in the spaces provided and let the web page do the calculation. All input data is converted to inches for calculation purposes, however, for entry purposes, the dimensions can be mixed or matched.