Wolfram|Alpha is a "computational knowledge engine" whose long-term goal is "to make all systematic knowledge immediately computable and accessible to everyone. We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything." It contains 10+ trillion of pieces of data, 50,000+ types of algorithms and models, and linguistic capabilities for 1000+ domains.
The API provides two general classes of queries. At the highest level, you can submit free-form queries like users might enter at the Wolfram|Alpha site itself, and get back full Wolfram|Alpha output in a variety of formats. The second type of query is a lower-level request for a single well-defined result, or range of results, from their entity/property-based data API, such as a caloric value for a food item, or a tide table for a requested location
The ProgrammableWeb directory's Search category contains more than 2000 APIs for adding search technology and functions to websites and applications. Here we filter through popular user favorites and highlight those that developers may find useful for enhancing applications.