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If your cookware isn't stainless steel, try scouring the rust off with fine steel wool. Use a little bit of dish soap when scrubbing. This can prevent major scratching to your pan. If steel wool is unavailable or your cookware is stainless steel, try scouring the rust off with Bar Keepers Friend and a plastic scrubby. If you need a more natural or earth-conscious solution, try the following scouring options that our ancestors used to scour off rust:  Horsetail Rush- plants in genus Equisetum. A paste made from equal parts lemon juice and cream of tartar. Fine-grained sand (not on stainless steel though).
Use steel wool to remove thin layers of rust from most pans. Use gentle scrubs, like Bar Keeper's Friend, for stainless steel. Use all-natural scrubs for any pan, rubbing hard to remove the rust.