Incorrect spelling, explanation:
13rd is a mistake, because full-word form thirteenth ends with th, so the number form should also have suffix th. Therefore 13th is the correct form. rd is the suffix only for numbers with third at the end, for example twenty-third – 23rd.
Correct spelling, explanation: this is the correct way to write this number down, because full-word form ends with th (thirteenth; 13th). Only numbers ending with rd (so with third) have this suffix, for example 33rd, 963rd etc.). Therefore
13rd is incorrect and 13th is the correct form.
Definition of 13th:
numeral, ordinal number between 12th and 14th
It’s her 13th birthday today, so she is very excited.
The meeting is on April 13th.
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