Is there any online tool for converting coordinates between different EPSG?

This one's pretty handy: http://cs2cs.mygeodata.eu/

Also useful for batch conversions.

To do a one-off projection, I usually use the geometry service on our ArcGIS Server's REST endpoint.

You could also use ArcGIS Online's Rest Endpoint, which is available here.

Here is a sample which shows how you can project from 4326 to 3857.

Please note that you need to comply with their Terms & Conditions.

Two other handy tools for future reference:

• twcc.fr (the world woordinate converter)
• epsg.io, very useful for both transformation, retrieving available coordinate systems, ...

And to find which coordinate system might be suitable for your needs : georepository.com