Measures of RNA abundance are important for many areas of biology and often 
obtained from high-throughput RNA sequencing methods such as Illumina sequence 
data. These measures need to be normalized to remove technical biases inherent 
in the sequencing approach, most notably the length of the RNA species and the 
sequencing depth of a sample. These biases are corrected in the widely used 
reads per kilobase per million reads (RPKM) measure. Here, we argue that the 
intended meaning of RPKM is a measure of relative molar RNA concentration (rmc) 
and show that for each set of transcripts the average rmc is a constant, namely 
the inverse of the number of transcripts mapped. Further, we show that RPKM does 
not respect this invariance property and thus cannot be an accurate measure of 
rmc. We propose a slight modification of RPKM that eliminates this inconsistency 
and call it TPM for transcripts per million. TPM respects the average invariance 
and eliminates statistical biases inherent in the RPKM measure.