The one-eighth rule tells you whether a source will colour your headphones. It does not tell you how. This does: it takes the shape of a headphone's impedance curve, puts your source's output impedance in series with it, and draws the frequency response you actually end up with.
Then it does the same for every source in the database that publishes an output impedance — the table below says how many that is — and ranks them, so you can see at a glance which ones leave your headphones alone.
Your source's output impedance sits in series with your headphones, and the two form a voltage divider. Because a headphone's impedance changes with frequency, the divider changes with frequency too — so the source stops being neutral and starts drawing its own tone control over your music:
attenuation(f) = 20 · log10 ( Z(f) / (Z(f) + Zsource) )
Everything on the chart is plotted relative to 1 kHz. That matters, because it is the reason two correct calculators can print different numbers for the same pair — some reference the lowest impedance, some the nominal figure. Referencing 1 kHz matches what you would hear after matching levels by ear, which is the comparison people actually make.
Where the headphone's impedance is high, less voltage is lost in the source and that region comes out louder. That is why a dynamic driver's bass resonance turns into a bass boost on a high-impedance output, and why a multi-driver armature IEM — whose impedance can swing by a factor of five across the band — can come out sounding like a different headphone entirely.
A planar is the opposite case and worth trying in the dropdown: its impedance is almost perfectly flat, so there is almost nothing for a source impedance to work against. Even a 120Ω tube output tilts a real planar by only a few tenths of a decibel, against more than 2 dB for a multi-driver in-ear. This is the part of the one-eighth rule that gets lost — the rule is about the spread between a headphone's lowest and highest impedance, not about its nominal figure.
First, these are archetypes, not measurements of specific models. The shapes are typical of each driver type and the numbers are yours to adjust; nothing here claims that your particular headphone measures this way. If you have a real impedance plot in front of you, read the lowest point, the highest point and where the peak sits, type those in, and the answer becomes specific to your pair.
Second, impedance has phase as well as magnitude, and this calculates with magnitude alone because phase is almost never published. Where a headphone's impedance is strongly reactive the true attenuation is slightly less than shown — for a 60Ω load at 45 degrees fed from a 90Ω source the difference is about 0.66 dB. That is smaller than the numbers above, but it is not nothing: the first verdict band here is only half a decibel wide, so on a borderline source the neglected term can be enough to move it between bands.
For the simple yes-or-no version, the one-eighth rule checker is quicker. For whether the source can also make enough power, the matcher does all three checks at once.