# What is the formula for proportions of elements using perspective and translateZ?

I would like to do the following: Given a container with perspective and an inner element with a translateZ value I’d like to “pull it up” with translateY in order to visually touch the top of the surrounding container: http://jsfiddle.net/8R4ym/129/

Is there some kind of formula that, given the perspective value of a container, the width and height of an element and it’s Z-translation I can get to that kind of “top” calculation? I have been playing around with it but I can’t seem to find some rules for it, as it seems that those are all variables.

Thanks for any help.

Problem courtesy of: Seka

## Solution

Yes!

There’s actually quite a simple formula for finding the offset – the 3d Projection article
on Wikipedia has a diagram and the formula.

The formula is `bx = ax * bz / az`
where:

• `ax`
is the original distance from the transform origin point
• `az`
is the perspective + the negative `translateZ`
• `bz`
is the perspective

and this will give you:

• `bx`
– the new distance from the transform origin point

So, you need to know:

• `bz`
: the `perspective`
(eg: `1000px`
)
• `ax`
: the offset from the transform origin point, eg: if the origin point is 50% then this needs to be the element’s `top`
relative to the center of the parent element ( `parent.height/2 + element.top`
) — let’s say `-500px`
• `z`
: the element’s `translateZ`
(eg: `-600px`
)
• `az`
is then `bz + z * -1`
, in this case: `1000 + (-600 * -1) = 1600`

so the formula is: `-500 * 1000 / 1600 = -312.5`

The element is offset vertically `-312.5px`
from the origin, whereas originally it was offset `-500px`
, the difference between the two number is what you’ll need to add to the old `top`
value to get the equivalent new value.

This formula also works for the Y axis.

I put together a quick example here: http://jsfiddle.net/trolleymusic/xYRgx/

Solution courtesy of: Trolleymusic

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