formular to calculate width/height (relative to parent) of container with translateZ inside of parent container with perspective

Question

What is the formular to calculate the widths/heights of child elements with translateZ inside of parent container with set perspective (keyword: &

Answer 1

The formular to calculate the widths/heights of child elements with translateZ inside of parent container with set perspective is:
$scale = 1 + (translateZ * -1) / perspective.

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Where to throw this formular at transform: scale( $scale ).
perspective is parents perspective value and translateZ is elements translateZ value as well. See snippet at the bottom or SASS mockup as you like.

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So actually the answer was given in the question!
While this is the correct answer to the asked question this didn't solve my specific problem at all so here is a follow-up-question.

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Credits: @Trolleymusic who at least opened my eyes somehow with his answer.

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CSS example:

/* formular: 1 + (translateZ * -1) / perspective */

#parent {
  perspective: 10px;
}

.child--1 { /* 1 + (-100 * -1) / 10 */
  transform: translateZ(-100px) scale( 11 );
}

.child--2 { /* 1 + (-200 * -1) / 10 */
  transform: translateZ(-200px) scale( 21 );
}

.child--3 { /* 1 + (1 * -1) / 10 */
  transform: translateZ(1px) scale( 0.9 );
}