Confusion about inductors in series vs. combined

I suddenly was getting confused while reading about inductors. The formula for inductance I was using was the one like in the answer to this question. However, I have also read that the inductance of inductors in series is the sum of the inductances (like with resistors in series), but that suggests to me that longer inductors would have larger inductances. The formula in the link has length on the bottom. I'm probably missing something simple here but I'm not sure what.

• Too many references outside the question. Please post the relevant information here. – Eugene Sh. Jun 25 '18 at 20:45
• " longer inductors would have larger inductances while the formula has inductance on the bottom." Please expand in much more detail. For a given core size and wire gauge (identical turns per unit length) longer inductors DO have more inductance. And what formula "has inductance on the bottom"? Certainly not the one in your link. – WhatRoughBeast Jun 25 '18 at 20:49
• Oops, I meant to say length on the bottom. – Tom Jun 25 '18 at 20:50
• I think you mean that the formula has length of winding on the bottom. Inductors do add in series just like resistors. – John D Jun 25 '18 at 20:51
• n (# of windings) is also related to length, and appears squared in the numerator. – The Photon Jun 25 '18 at 21:06

The answer you linked describes the effect of spacing out the windings on the total inductance. That is, length refers to the length of the solenoid, not the length of wire used to create the windings. Consider: 