At which frequency is given a capacitor value

I am wondering what is the frequency ty value of a capacitor is given for.

For example if you look at the datasheet of the GRM32ER60J107ME20L if you look at the caracteristic on page 2 figure 1 you have Z = 0.2Ohm for f = 120kHz.

Then you have: Z = 1/(2 * PI * F * C)

=> C = 1 / ((2 * PI * F * Z) = 63µF.

The problem is this capacitor is a 100µF capacitor. I understand the value changes with the frequency but what is the frequency for which the value 100µF is right? Is it always the same frequency?

You assume that the capacitor is "only" a capacitor, unfortunately it is not :-(

Any physical capacitor (one that you can touch) also has series resistance and inductance. So the formula you use for Z is incomplete, Z consists of the sum of 3 impedances: Z = Zc + Zl + Zr

The capacitor value does not change, it is still 100 uF at 120 kHz BUT since the impedance of the capacitor is so low at 120 kHz, the parasitic components namely the series inductor and the series resistor also come into play. These make the impedance at 120 kHz appear higher than you would expect (from an ideal capacitor).

For a quick indication how "good" a capacitor is I look at the green |Z| curve, you see that at low frequencies it goes down in a straight line. This means it behaves like a capacitor at these frequencies. At around 0.1 MHz it starts to deviate from that straight line. Indicating that this particular capacitor is "good" up to around 0.1 MHz.

Up to what frequency a capacitor is "good" depends on many things, it's value, the way it is constructed. What type of capacitor it is. Find a datasheet for a 10 pF capacitor and you will notice that it will still be "good" at a much higher frequency.