Uber ride requests and price estimation.
Uber API is a free Transportation API that requires OAuth authentication, is served over HTTPS and supports CORS, so it can be called from the browser.
Details from developer.uber.com.

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The Uber API is provided by Uber Developers (developer.uber.com).
Yes. The Uber API is listed in the Transportation category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Uber API uses OAuth authentication, so you need to register for credentials before making requests.
Yes. The Uber API supports CORS, so front-end JavaScript can call it directly.
Yes. The Uber API is served over HTTPS, so it's safe to use in production.