The Altmetric Explorer is a powerful web app that allows you to track the conversations around scientific articles online. Altmetric collects and analyzes hundreds of thousands of postings about tens of thousands of articles and datasets each month. It makes this data available to end users through an intuitive user interface and to developers through an API.
The Altmetric score is their quantitative measure of the attention that a scholarly article has received and is derived from volume (the frequency of mentions, but only from an individual source), sources (the category of mentions are ranked: tweets, newspaper mentions, etc. and are given weights), and authors.
A browser button is available for download for free and can be used on any article to determine the piece's score.