The standard grips this chord is usually shown with.
Fmaj13 is F, A, C, E, G and D, a major thirteenth. The shape this page opens on is written 100010, lowest string first.

Also written FM13, FΔ13 or F major 13. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Fmaj13 on the guitar, and 57 derived voicings in 5 families.
In which keys. Every note of Fmaj13 belongs to C major (the IV), D minor (the ♭III), F major (the I) and A minor (the ♭VI).
The common shapes, written lowest string first: 100010, 112231, xx3230, x53355, x87755, x85755, x-8-8-9-10-10, 13-12-12-12-13-12.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. Fmaj13 has 1x223x, x-8-x-9-10-10, 13-x-14-14-15-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Fmaj13 has xx2231, x7776x, x-x-12-10-10-12, 12-12-12-10-x-x, x-x-14-14-15-13, 1522xx, x5325x, 5737xx.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Fmaj13 has x5x251, 1x223x, 5x375x, x7x765, 10-x-7-9-6-x, x-8-x-9-10-10, 12-x-12-10-10-x, 13-x-14-14-15-x.
Rootless. The root left to the bass player. Frees a finger for a tension. Fmaj13 has xx0210, xx2233, x0203x, x3223x, xx5755, x5755x, x7778x, x-x-10-9-10-10.
Open string. An open string left ringing against a fretted grip. Because it costs no finger, it sounds a note the closed shape has none left for -- a tension on top, or a pedal root underneath. Either a familiar grip with open strings added, or a shape so sparse the open strings carry the chord. These belong to their key rather than to a shape, so D, A, G and E have many and Eb a handful. Fmaj13 has 000503, 530000, 000067, x00500, 03020x, 57000x.
Tensions. A shell of Fmaj13, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (B).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.