First, calculate the minimum edit distance from the recognized string to the reference transcription.
Then, the WER is definied as:
$Word Error Rate = 100 \times \frac{Insertions+Substitutions+Deletions}{Total \, Words \, in \, Correct \, Transcript}$

University of Michigan - Ann Arbor

It's the standard evaluation metric for speech recognition systems. The word error rate is based on how much the word string returned by the recognizer (the hypothesized word string) differs from a reference transcription.

Word Error Rate

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Computation Steps of Word Error Rate

It's available from the National Institute of Standards and Technologies (NIST). It's a free script serving as the standard method for computing word error rates.  

SCLITE

The percentage of sentences with at least one-word error.

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