How do I get only the image URL from the_post_thumbnail()?

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You might also try:

If you only have one size thumbnail: 

$thumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ) );

Or…if you have multiple sizes:

$thumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), "size" );

Note that wp_get_attachment_image_src() returns an array: url, width, height, is_intermediate.

So if you just want only the image url:

echo $thumbnail[0];

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