# Inductance Equations using SI Units

Started by June 6, 2012
```I've been planning to wind some coils.  I want to get an idea of what
sort of inductance I'd get for a given winding, coil diameter and
length, and so on.  These are all air-core, so I don't need to take
into account the effects of iron.

When I Google for information, I seem to get the same few formulas,
none of which are in SI units.  I can find equations and formulas that
use inches, or that (apparently) were based on the CGS system; but
nothing that uses SI units.

Can anyone point me to a source of equations that stick with SI units?
Either a link or a reference to a book would be great - or even the
proper search terms to use with Google.

--
Hoare's Law of Large Problems:
Inside every large problem is a small problem struggling to get
out.

```
```"chiron613" <chiron613@NOSPAM.gmail.com> wrote in message
news:20120606123653.18ef13fa@UL80JT...
> I've been planning to wind some coils.  I want to get an idea of what
> sort of inductance I'd get for a given winding, coil diameter and
> length, and so on.  These are all air-core, so I don't need to take
> into account the effects of iron.
>
> When I Google for information, I seem to get the same few formulas,
> none of which are in SI units.  I can find equations and formulas that
> use inches, or that (apparently) were based on the CGS system; but
> nothing that uses SI units.
>
> Can anyone point me to a source of equations that stick with SI units?
> Either a link or a reference to a book would be great - or even the
> proper search terms to use with Google.

When I googled "inductance calculator + si units", I eventually navigated to
this:

http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle

```
```On Wed, 6 Jun 2012 18:53:35 +0100
"Ian Field" <gangprobing.alien@ntlworld.com> wrote:

>
<snip>
>
>
> When I googled "inductance calculator + si units", I eventually
> navigated to this:
>
>
> http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle
>
>

Thanks, Ian.  What I was looking for, though, were some equations or
formulas.  I don't learn much from a calculator, and I don't really
have a good way to even know whether it's accurate.  But I appreciate
your response.

--
Cutler Webster's Law:
There are two sides to every argument, unless a person
is personally involved, in which case there is only one.

```
```On Wed, 6 Jun 2012 12:36:53 -0500, chiron613
<chiron613@NOSPAM.gmail.com> wrote:

>I've been planning to wind some coils.  I want to get an idea of what
>sort of inductance I'd get for a given winding, coil diameter and
>length, and so on.  These are all air-core, so I don't need to take
>into account the effects of iron.
>
>When I Google for information, I seem to get the same few formulas,
>none of which are in SI units.  I can find equations and formulas that
>use inches, or that (apparently) were based on the CGS system; but
>nothing that uses SI units.
>
>Can anyone point me to a source of equations that stick with SI units?
>Either a link or a reference to a book would be great - or even the
>proper search terms to use with Google.

googling    solenoid equation meters    seems pretty good.

--

John Larkin         Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser drivers and controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro   acquisition and simulation
```
```On Wed, 6 Jun 2012 13:57:26 -0500, chiron613
<chiron613@NOSPAM.gmail.com> wrote:

>On Wed, 6 Jun 2012 18:53:35 +0100
>"Ian Field" <gangprobing.alien@ntlworld.com> wrote:
>
>>
><snip>
>>
>>
>> When I googled "inductance calculator + si units", I eventually
>> navigated to this:
>>
>>
>> http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle
>>
>>
>
>Thanks, Ian.  What I was looking for, though, were some equations or
>formulas.  I don't learn much from a calculator, and I don't really
>have a good way to even know whether it's accurate.  But I appreciate
>your response.

This is also not the DIY equations that you're looking for but there's a
handy Windows calculator over at
<http://www.dl5swb.de/html/mini_ring_core_calculator.htm>

For the DIY question, the ARRL Handbook is a great resource but it's
very ... inchy. I can't reproduce all of the goodies, but for your basic
single layer air-core inductor, try
L = (d^2 * n^2) / (18 * d + 40 * l)
where L is in micro-henries, d is diameter of the winding circle (center
of wire to center of wire), l is inductor length, and n is the number of
turns, where length is >= 0.4 * d. And of course, it's all in inches.
Unit conversion left as an exercise, or something.   ;-)

--
Rich Webb     Norfolk, VA
```
```On Jun 6, 2:57=A0pm, chiron613 <chiron...@NOSPAM.gmail.com> wrote:
> On Wed, 6 Jun 2012 18:53:35 +0100
>
>
>
> "Ian Field" <gangprobing.al...@ntlworld.com> wrote:
>
> <snip>
>
> > When I googled "inductance calculator + si units", I eventually
> > navigated to this:
>
> >http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=3Dutil_induct.=
..
>
> Thanks, Ian. =A0What I was looking for, though, were some equations or
> formulas. =A0I don't learn much from a calculator, and I don't really
> have a good way to even know whether it's accurate. =A0But I appreciate
> your response.
>
> --
> Cutler Webster's Law:
> =A0 =A0 =A0 =A0 There are two sides to every argument, unless a person
> =A0 =A0 =A0 =A0 is personally involved, in which case there is only one.

If it's a long solenoid then you can get a guesstimate from physics.

L*i =3D N*flux.  (N=3D number of turns)  For a long solenoid the B field
is roughly constant.  B~ mu(sub zero)*i*N/L (where L is the coil
length) (MKS units)
So the flux is B*A (A is the area of the coil).  Putting it all
together,

L =3D mu(sub zero) * N^2 * A/L

For a single loop there should be another (simple) solution, but the
integral will be a lot harder.  (There's an equation in Terman that I
could quote.... It happens to be sitting on my desk.)  A page down on
here looks like the same equation.

www.thompsonrd.com/induct2.pdf

George H.
```
```On Wed, 06 Jun 2012 12:08:38 -0700
John Larkin <jlarkin@highlandtechnology.com> wrote:

<snip>

>
> googling    solenoid equation meters    seems pretty good.
>
>

Rich, George, and John, thanks for the ideas.  It looks like I'm going
to have to suck it up and do the conversions.  I hesitate to do that,
because I often multiply when I should divide (or vice versa), and wind
up with something like furlongs per fortnight as units.

--
One of the most striking differences between a cat and a lie is that a
cat has only nine lives.
-- Mark Twain, "Pudd'nhead Wilson's Calendar"

```
```chiron613 wrote:
> On Wed, 06 Jun 2012 12:08:38 -0700
> John Larkin <jlarkin@highlandtechnology.com> wrote:
>
>
> <snip>
>
>
>
>>googling    solenoid equation meters    seems pretty good.
>>
>>
>
>
> Rich, George, and John, thanks for the ideas.  It looks like I'm going
> to have to suck it up and do the conversions.  I hesitate to do that,
> because I often multiply when I should divide (or vice versa), and wind
> up with something like furlongs per fortnight as units.
>
I don't think many of us understand exactly what you're looking for? At
least I am a bit confused, if not for others here ;)

Doing induction calculations seems to be a black art it seems. For
years i've seen a variation of formula's to represent the value of a
coil once all the data is known.

For example..

In a long single coil, a formula of this type is used and there are
others, too.

u n^ A
L =---------
l

L = uH

u = permeability of air, some where around 1.26-05

A = cross section area of the coil in "m"^

l = Length of the coil in "m"

N = number of turns^

And now for the big HOWEVER>

If you were doing magnetic cores..
the math changes just a little.

0.012 n^ u A
L =-------------
Lc

In this case, the "u" permeability for air is 1.0

Note the constant 0.012? This was from a formula I got some where, it
was a note slide in one of my books that is so old it's turning yellow.

and "A" cross section area is now cm^ not "m"

and Lc is your magnetic size of the field, the physical length of it,
which can extend a bit depending on the form you're on.

I also have some math for inches.

Like I said, it's a black art. for the last few months I've been playing
around with a concept that involves using reluctance alterations to
monitor surface changes. This has forced me to dig out some older
references in my library.

It seems the internet is becoming a junk yard and is hard to find a
agreed method of doing certain things, like this for example.

Jamie

```
```On Wed, 06 Jun 2012 15:25:15 -0400, Rich Webb wrote:

> On Wed, 6 Jun 2012 13:57:26 -0500, chiron613
> <chiron613@NOSPAM.gmail.com> wrote:
>
>>On Wed, 6 Jun 2012 18:53:35 +0100
>>"Ian Field" <gangprobing.alien@ntlworld.com> wrote:
>>
>>
>><snip>
>>>
>>>
>>> When I googled "inductance calculator + si units", I eventually
>>> navigated to this:
>>>
>>>
>>> http://www.technick.net/public/code/cp_dpage.php?
aiocp_dp=util_inductance_circle
>>>
>>>
>>>
>>Thanks, Ian.  What I was looking for, though, were some equations or
>>formulas.  I don't learn much from a calculator, and I don't really have
>>a good way to even know whether it's accurate.  But I appreciate your
>>response.
>
> This is also not the DIY equations that you're looking for but there's a
> handy Windows calculator over at
> <http://www.dl5swb.de/html/mini_ring_core_calculator.htm>
>
> For the DIY question, the ARRL Handbook is a great resource but it's
> very ... inchy. I can't reproduce all of the goodies, but for your basic
> single layer air-core inductor, try
>   L = (d^2 * n^2) / (18 * d + 40 * l)
> where L is in micro-henries, d is diameter of the winding circle (center
> of wire to center of wire), l is inductor length, and n is the number of
> turns, where length is >= 0.4 * d. And of course, it's all in inches.
> Unit conversion left as an exercise, or something.   ;-)

Lessee.  18 / 25.4 = oh, this is too complicated.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
```On Wed, 06 Jun 2012 22:29:35 -0400
Jamie <jamie_ka1lpa_not_valid_after_ka1lpa_@charter.net> wrote:

<snip>
> >
> I don't think many of us understand exactly what you're looking for?
> At least I am a bit confused, if not for others here ;)
>
OK, it's pretty simple.  I can find all manner of equations, formulas,
calculators, etc., that calculate inductance but that use non-SI units
such as inches, feet, pounds (or whatever).

Of course I could just convert the various values into SI units, but...
it's a pain, and I tend to mix things up a bit and reverse the
calculations I should be doing (multiply when I should divide, etc.).

>   Doing induction calculations seems to be a black art it seems. For
> years i've seen a variation of formula's to represent the value of a
> coil once all the data is known.
>
Same here.  To my understanding, the actual calculations (accurate
ones) require diffeq's.  In order to simplify, accuracy is sacrificed
and they come up with various approximations that work under a certain
set of conditions (long solenoid; coil with thickness << than diameter;
single layer of turns, etc.).

Hmm... your math below came out kind of funny-looking in my reader. I
One equation looks like:

u n^ A
L=-----------
l

I assume the ^ should be indicating that n is squared?

>   For example..
>
>   In a long single coil, a formula of this type is used and there are
> others, too.
>
>      u n^ A
>   L =---------
>        l
>
>   L = uH
>
>   u = permeability of air, some where around 1.26-05
>
>   A = cross section area of the coil in "m"^
>
>   l = Length of the coil in "m"
>
>   N = number of turns^
>
> And now for the big HOWEVER>
>
>   If you were doing magnetic cores..

I don't know what you mean by magnetic cores.  Do you mean using cores
that contain iron, that would affect the inductance?

> the math changes just a little.
>
>     0.012 n^ u A
> L =-------------
>        Lc
>
>   In this case, the "u" permeability for air is 1.0
>
> Note the constant 0.012? This was from a formula I got some where, it
> was a note slide in one of my books that is so old it's turning
> yellow.
>
> and "A" cross section area is now cm^ not "m"
>
> and Lc is your magnetic size of the field, the physical length of it,
> which can extend a bit depending on the form you're on.
>
>    I also have some math for inches.
>
> Like I said, it's a black art. for the last few months I've been
> playing around with a concept that involves using reluctance
> alterations to monitor surface changes. This has forced me to dig out
> some older references in my library.
>
>    It seems the internet is becoming a junk yard and is hard to find a
>   agreed method of doing certain things, like this for example.
>

You're right about that.  Back in the olden days (when I was learning
this stuff) the problem was a lack of information.  You had to either
have it in books at home, or go to the library or school for it.

Now there is an endless amount of information, but so much of it is
crap that you've got to sort through lots of chaff to find the wheat.
Way too much information, often unreliable, and too much to process in
a reasonable time.

Ah, well.  Thanks for your ideas.  Maybe I'll eventually figure this
out somehow.  Or I *could* just wind the stupid coils and measure the
inductance, and try to figure out a relationship myself.

--
Happiness is good health and a bad memory.
-- Ingrid Bergman

```