The VIC-II's pixels are not actually square. The actual pixel aspect ratio (PAR) can be calculated as follows (PAL):
For a 1:1 really square pixel, a pixel clock of 14.75000 MHz is needed. Without interlacing, like the VIC-II does, half of it, i.e., 7.37500 MHz. The C64 is clocked at 0.98525 MHz, where 8 pixels are drawn each cycle, which makes a pixel clock of 0.98525 MHz * 8 = 7.88200 MHz. That makes 7.37500 / 7.88200 = 0.93568. This means that the pixels are a bit narrower than a 1:1 pixel.
The above calculation only considers the difference in width between a C64 pixel and a 1:1 pixel. However, with a CRT-based display the height differs too if the raster line timing of the C64 doesn't match the standard line timing. The reason for this is that the vertical speed of the raster beam is constant during the active display area. This makes the vertical distance travelled by the raster beam between lines directly related to the time it takes for it to move from one line to the next.
The PAL standard line frequency is 15.62500 kHz. The C64 is clocked at 0.98525 MHz and one line is 63 cycles which results in a line frequency of 0.98525 * 1000 / 63 = 15.63889 kHz. That makes 15.625 / 15.63889 = 0.99911. This means that the pixels are slightly shorter than a 1:1 pixel.
Together this results in a total PAR (X:Y) of 0.93568:0.99911 which is equivalent to PAR (X/Y) 0.9365. This means that the pixels are taller than they are wide.
The following table contains the above calculations for all C64 variants:
|1:1 pixel clock||1:1 line freq||CPU clock||cycles/line||PAR X:Y||PAR X/Y|