How do we calculate bounding box for AI/PDF image

Perhaps look at the work of the master:

https://raw.githubusercontent.com/Paul-Riggott/PS-Scripts/master/PDF%20ProcessorII.jsx

As for the PDF, this metadata is in the native PostScript Points unit of measure. You can get this from the PDF, you may possibly need to use BridgeTalk?

The following Acrobat Reader/Acrobat Pro script shows the common page boxes:

function ThePageSize(){
var aRect = this.getPageBox("Crop",this.pageNum);
var aWidth = aRect[2] - aRect[0];
var aHeight = aRect[1] - aRect[3];
var bRect = this.getPageBox("Art",this.pageNum);
var bWidth = bRect[2] - bRect[0];
var bHeight = bRect[1] - bRect[3];
var cRect = this.getPageBox("Trim",this.pageNum);
var cWidth = cRect[2] - cRect[0];
var cHeight = cRect[1] - cRect[3];
var dRect = this.getPageBox("Bleed",this.pageNum);
var dWidth = dRect[2] - dRect[0];
var dHeight = dRect[1] - dRect[3];
var eRect = this.getPageBox("Media",this.pageNum);
var eWidth = eRect[2] - eRect[0];
var eHeight = eRect[1] - eRect[3];
var pageLabel = this.pageNum + 1;
var totalPages = this.numPages;
app.alert("Page: " + pageLabel + " of " + totalPages + " pages" + "\n\n" + ("Crop: " + Math.round(aWidth*0.3528*100)/100 + " mm x " + Math.round(aHeight*0.3528*100)/100 + " mm" + "\n\n" + ("Art: " + Math.round(bWidth*0.3528*100)/100 + " mm x " + Math.round(bHeight*0.3528*100)/100 + " mm") + "\n\n" + ("Trim: " + Math.round(cWidth*0.3528*100)/100 + " mm x " + Math.round(cHeight*0.3528*100)/100 + " mm") + "\n\n" + ("Bleed: " + Math.round(dWidth*0.3528*100)/100 + " mm x " + Math.round(dHeight*0.3528*100)/100 + " mm") + "\n\n" + ("Media: " + Math.round(eWidth*0.3528*100)/100 + " mm x " + Math.round(eHeight*0.3528*100)/100 + " mm")));
}
app.addMenuItem ({cName: "Show PageBox Sizes", cParent: "View", cExec: "ThePageSize()" });

P.S.: The other box is the bounding box or BBox, however, I have had inconsistent results with this data:

https://www.pdfscripting.com/public/PDF-Page-Coordinates.cfm

This link may shed some light on the topic:

https://community.adobe.com/t5/acrobat/need-help-with-adding-bounding-box-trim-box-to-multiple-pdf-files/td-p/10089795

"The .ai image actual width and height are 612 and 792 respectively."

Hi

I am not a scripter, but I do have a question for you on the numbers you are looking for. Do you want the width and height for the vector paths or the paths with their appearances? I copied this next paragraph from Help for you. If you get a script that works, you'll need to determine which set of values you are seeking.

"When an object is selected and a selection tool is active, the Info panel displays the object’s x and y coordinates, width (W), and height (H). The values for width and height are affected by the Use Preview Bounds option in the General preferences. When Use Preview Bounds is selected, Illustrator includes the stroke width (and other attributes such as drop shadows) in the object’s dimensions. When Use Preview Bounds is cleared, Illustrator measures only the dimensions defined by the object’s vector path."

~ Jane