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Making a product in-stock & out of stock filter
WooCommerce product stock filter tutorial
Product stock status in WooCommerce is stored in the _stock_status private custom field, which can have two values: instock and outofstock
On the search instance Frontend Search Settings -> Custom field filters panel you can easily make a filter on this field:

..this will result in:

- To the Custom Field input enter: _stock_status
- In this example I use the Radio type, but Checkboxes or Drop-down is just as good
- To the values textarea enter:||Any value**instock||In stockoutofstock||Out of stock
For more information about custom field filters please visit the Custom Field Filters documentation.