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Each read gives us read_length - kmer_size + 1 kmers. Therefore kmer coverage is calculated by:
read_length - kmer_size + 1
kmer_coverage = coverage * (read_length - kmer_size + 1) / read_length
kmer_coverage is the expected number of times each kmer is seen.
kmer_coverage
If we take per base sequencing error rate (err_rate) into account, kmer coverage is:
err_rate
kmer_coverage = coverage * (read_length - kmer_size + 1) / read_length * (1-err_rate*kmer_size)