I hope you have found a solution for your problem. If not, can you please elaborate what you mean by an app for Basic shopify plan that can calculate shipping fee by distance. Are you referring in relation to local delivery or carrier specified shipping rates?
If you are looking for a carrier to calculate shipping rates based on the distance, I would like to suggest you Multi carrier shipping label app which can solve your problem by allowing you to calculate real time shipping rates for widely used carriers like FedEx, DHL, USPS and UPS etc. Even you can try the app with 14 days free trial.
Different courier has different shipping rates to different locations, all you need to do is to input correct weight and volume for each product then apply the courier shipping rates would be okay.
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