The standard calculation takes the pivot as the average of the previous session's high, low and close, then derives support and resistance levels by reflecting the prior range around it. Everything is arithmetic; nothing is drawn by hand.
That objectivity is the appeal. Every trader using the same formula gets the same lines, which removes the argument about where a level is and makes the levels genuinely common reference points. They are most used in futures and index trading where sessions are well defined.
Pivots are not forecasts and carry no volume information. They are best treated as a grid of plausible reaction points to be combined with something else, and they lose meaning in markets without clean session-breaks such as continuously traded crypto.
Related: central-pivot-range, prior-day-high-low, support, resistance, session-breaks