As a gif fanatic, I am glad that more people are starting to use WebM more often.
You can probably use GUI based converters to convert your format of choice to WebM. But chances are high that almost all of this software use a wrapper around FFmpeg to accomplish this anyways. So why not get rid of the middleman?
First make sure that your FFmpeg is compiled with support for
libvorbis or if you are compiling from source, use this flags:
--with-fdk-aac --with-ffplay --with-freetype --with-frei0r --with-libass --with-libvo-aacenc --with-libvorbis --with-libvpx --with-opencore-amr --with-openjpeg --with-opus --with-rtmpdump --with-speex --with-theora --with-tools
Now you should be able to compile your mp4/fig file using ffmpeg like this:
ffmpeg -i 1.mp4 -vcodec libvpx -acodec libvorbis "1.webm".
On my 10+ tests, I have found WebM format to have 1/3th the size of mp4.