The easiest way is to use Kurt's suggestion of the Documdent info panel.
Another way is to use the Dimension tool and Transform panel.
Select the oval with the selection tool
Open the Transform panel. The Transform panel will show the width and height of the ellipse's bounding box.
If the oval is rotated: The width and height in the Transform panel represent the bounding box dimensions. If the oval is rotated, its true length is not directly displayed.
Calculate using trigonometry: If the oval is rotated, you can use the following formula to estimate the perimeter, where 'w' is the width, 'h' is the height, and 'θ' is the rotation angle in radians:
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