The 13th Chord adds another tone to the 11th chord and, hence the name, the tone is 13 steps from the root. If you are playing the piano, you could play this chord with seven tones while the guitar is limited to six tones. Therefore, at least one tone are always excluded which can vary depending on the chord shape. If you don't feel confortable with the stretch, see more shapes below.
None for the moment in this category
Chord constructionC13 x - C - E - Bb - D - A
D13 x - D - F# - C - E - B
E13 x - E - G# - D - F# - C#
F13 x - F - A - Eb - G - D
G13 x - G - B - F - A - E
A13 x - A - C# - G - B - F#
B13 x - B - D# - A - C# - G#
Guitar versions of the chord
Notes in chordC13 C - E - G - Bb - D - F - A
D13 D - F# - A - C - E - G - B
E13 E - G# - B - D - F# - A - C#
F13 F - A - C - Eb - G - Bb - D
G13 G - B - D - F - A - C - E
A13 A - C# - E - G - B - D - F#
B13 B - D# - F# - A - C# - E - G#
The intervals are 1 - 3 - 5 - b7 - 9 - 11 - 13
Alternative chord shapes
Besides the chord pictures above there are different ways to play the 13th chord. On the picture below you can see an alternative and which, like the already given example, also is movable.
With the root on 6th string:
Since the root is on the sixth string, you use 3X345X to play G13 with the shape above. In this chord shape you will mute the second string with an adjacent finger. This chord can sound great with a single stroke as an outro, for example in a 12 bar blues (as a last stroke, in the last bar). (The similar shape 3X3455 is sometimes also referred to as G13, bur are more correctly a G13 6/9.)
These are two common voicings:
On the diagram to the left, the root is on the 2nd string and on the diagram to the right the root is on the 1st strings. Two examples with short notations are E13: X5665X and F13: XX1231.