The standard grips this chord is usually shown with.
Cmaj13 is C, E, G, B, D and A, a major thirteenth. The shape this page opens on is written x32201, lowest string first.
Note by note. C is the root, E is the major third, G is the fifth, B is the major seventh, D is the ninth and A is the thirteenth.

Also written CM13, CΔ13 or C major 13. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 7 common shapes for Cmaj13 on the guitar, and 55 derived voicings in 5 families.
One note away. Change a single note of Cmaj13 and you have Cmaj9 (with one note taken away), Cmaj11 (with one note moved), C69 (with one note taken away) or C13 (with one note moved).
In which keys. Every note of Cmaj13 belongs to C major (the I), E minor (the ♭VI), G major (the IV) and A minor (the ♭III).
The common shapes, written lowest string first: x32201, x33455, 877787, 8-8-9-9-10-8, x-12-10-10-12-12, x-15-12-14-12-12, x-15-14-14-12-12.
Under the hand. 1 of the 7 shapes here sits in open position, and the first uses 1 open string with 1 left unplayed. 4 of the 7 need a barre. Together they cover the neck from the 1st fret to the 15th.
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. Cmaj13 has x3x455, 8-x-9-9-10-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Cmaj13 has x2221x, xx7557, 7775xx, x-x-9-9-10-8, x-14-14-14-13-x, xx2415, 5324xx, x3745x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Cmaj13 has 5x241x, x2x210, x3x455, 7x755x, x-12-x-9-12-8, 8-x-9-9-10-x, 12-x-10-14-12-x, x-14-x-14-13-12.
Rootless. The root left to the bass player. Frees a finger for a tension. Cmaj13 has x2223x, xx0200, x0200x, xx2203, xx5455, xx7757, xx7987, x-x-9-9-10-10.
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. Cmaj13 has 030455, x20253, 530000, 00400x, x04000, 57000x.
Tensions. A shell of Cmaj13, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (F#).
What kind of chord this is. Cmaj13 is a major chord — root, major third, fifth. major chords on every root, and what they are for.
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.