# I want to calculate the inductance of a coil, I have found two different formulas, which is right?

#### ASH111

Joined Nov 6, 2018
3
I want to calculate the inductance of a coil with the following specs;

Number of Turns: 100
Loop Diameter: 25 mm
Wire Diameter: 0.5 mm
Relative Permeability: 1000

I have used the AAC online calculator at https://www.allaboutcircuits.com/tools/coil-inductance-calculator/ and got the answer of 0.627 H using the formula Lcoil≈N^2 μ0 μr (D/2) [ln(8D/d)−2]

I have also used the rimstar online calculator at https://rimstar.org/science_electronics_projects/coil_design_inductance.htm and got the answer of 0.124 H using the formula Could someone let me know which one of these is right?

Many thanks.

• robertstaley28

#### AlbertHall

Joined Jun 4, 2014
8,363
There is no 'correct' formua for the inductance of a coil. There is a variety of different approximate formulas available. Some work best for long thin coils while others work best for short fat coils, and still others go for the middle case. The only sure way is to wind it and measure it.

• robertstaley28

#### ASH111

Joined Nov 6, 2018
3
There is no 'correct' formua for the inductance of a coil. There is a variety of different approximate formulas available. Some work best for long thin coils while others work best for short fat coils, and still others go for the middle case. The only sure way is to wind it and measure it.
Thanks for your response. Are you able to explain how the two different formulas work? For instance, both have the same μ0 x μr x turns^2 but one formula uses area over length and the other formula uses (D/2) [ln(8D/d)−2].

If I understood the formulas a bit better I might be able to use one in preference to the other. I am trying to get reasonably close to the correct figure before I build the inductor.

• robertstaley28

#### Xavier Pacheco Paulino

Joined Oct 21, 2015
726
• robertstaley28

#### SLK001

Joined Nov 29, 2011
1,507
I want to calculate the inductance of a coil with the following specs;

Number of Turns: 100
Loop Diameter: 25 mm
Wire Diameter: 0.5 mm
Relative Permeability: 1000
A coil with these parameters isn't going to be anywhere near a precision device. What are you using the coil for? If you need an exact value (explain why), then this coil isn't the one you want. As for formulas, I've tried them all and none of them work. I usually ended up winding the coil and measuring the value.

• robertstaley28

#### FourierSeries

Joined Nov 7, 2018
2
Option 1:
Resonate your coil with a known capacitance. Once you know the resonant frequency you can easily calculate the inductance. You might also be able to operate the coil and its core at a known current (or approximate current) for better accuracy of L for the intended circuit (since the increased mu provided by the core isn't linear).

Option 2:
If you're using a ferrite core then it is likely you can find a datasheet showing how to calculate inductance. In the datasheet you might find a graph relating inductance to the number of turns.

Hope that helps.

I want to calculate the inductance of a coil with the following specs;

Number of Turns: 100
Loop Diameter: 25 mm
Wire Diameter: 0.5 mm
Relative Permeability: 1000

I have used the AAC online calculator at https://www.allaboutcircuits.com/tools/coil-inductance-calculator/ and got the answer of 0.627 H using the formula Lcoil≈N^2 μ0 μr (D/2) [ln(8D/d)−2]

I have also used the rimstar online calculator at https://rimstar.org/science_electronics_projects/coil_design_inductance.htm and got the answer of 0.124 H using the formula Could someone let me know which one of these is right?

Many thanks.

• BR-549 and robertstaley28

#### wayneh

Joined Sep 9, 2010
16,102
I want to calculate the inductance of a coil with the following specs;

Number of Turns: 100
Loop Diameter: 25 mm
Wire Diameter: 0.5 mm
Relative Permeability: 1000

I have used the AAC online calculator at https://www.allaboutcircuits.com/tools/coil-inductance-calculator/ and got the answer of 0.627 H using the formula Lcoil≈N^2 μ0 μr (D/2) [ln(8D/d)−2]

I have also used the rimstar online calculator at https://rimstar.org/science_electronics_projects/coil_design_inductance.htm and got the answer of 0.124 H using the formula Could someone let me know which one of these is right?

Many thanks.
Neither of those look familiar. Look up the Wheeler formula for a multilayer coil (solenoid). It should get you within a few percent of the actual value. But check to see what the length-to-diameter ratio is. I think the Wheeler multilayer formula is best when L > 0.4D. Maybe your coil requires a different formula based on its dimensions.

Maybe useful: http://www.rfcafe.com/references/electrical/inductance.htm

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