Get out your sliderule app (yes, there is such a thing) in commemoration of Foursquare Day, April 16 – 4/4^2 for the mathematically challenged. The check-in service itself is celebrating by announcing it now has 20 million users who collectively have checked in more than 2 billion times.

It’s also rewarding its users. Anyone who checks in today will receive a souvenir badge (pictured). There are festivities as well, some organized by cities and civic organizations who understandably love anything that might increase business.

The day’s page has a message to its users that reads as follows:

In 2010, foursquare fans declared April 16 4sqDay (– nerds after our own heart!). Two years and two billion check-ins later, you’re still why we get out of bed each day. Thanks to all 20 million of you for making us part of your lives. Happy 4sqDay!

This is the second annual Foursquare Day, an event that originated as a grassroots movement created by fans of the service. The 20 million is about double the number Foursquare had a year ago, when it reported 9.3 million users and 600 million check-ins. So although new users are joining at a slower pace, each person is checking in more frequently than previously.

Related links:

Foursquare blog – Happy 4sqDay from team @foursquare to you!

Foursquare Day – check-in page

Foursquare Day – founders’ blog

Foursquare Day – civic proclamations

Mashable – Foursquare Tops 20 Million Users

VentureBeat – Foursquare confirms 20M users, 2 billion check-ins, on 4sqDay 2012

The Next Web – Foursquare hits 20 million users and 2 billion checkins, seeing a million new signups per month

Business Insider – Foursquare May Not Be Toast Yet, But It’s Browning At The Edges

Tampa Bay Times – Foursquare scavenger hunt to boost Mayor Bob Buckhorn’s plan for downtown Tampa