Comparison of RPKM (reads per kilobase per million) and TPM (transcripts per million).

rpkm_versus_tpm.R

# RPKM versus TPM
# 
# RPKM and TPM are both normalized for library size and gene length.
#
# RPKM is not comparable across different samples.
#
# For more details, see: http://blog.nextgenetics.net/?e=51

rpkm <- function(counts, lengths) {
  rate <- counts / lengths 
  rate / sum(counts) * 1e6
}

tpm <- function(counts, lengths) {
  rate <- counts / lengths
  rate / sum(rate) * 1e6
}

genes <- data.frame(
  Gene = c("A","B","C","D","E"),
  Length = c(100, 50, 25, 5, 1)
)

counts <- data.frame(
  S1 = c(80, 10,  6,  3,   1),
  S2 = c(20, 20, 10, 50, 400)
)

rpkms <- apply(counts, 2, function(x) rpkm(x, genes$Length))

tpms <- apply(counts, 2, function(x) tpm(x, genes$Length))

genes
#   Gene Length
# 1    A    100
# 2    B     50
# 3    C     25
# 4    D      5
# 5    E      1

counts
#   S1  S2
# 1 80  20
# 2 10  20
# 3  6  10
# 4  3  50
# 5  1 400

rpkms
#         S1    S2
# [1,]  8000 4e+02
# [2,]  2000 8e+02
# [3,]  2400 8e+02
# [4,]  6000 2e+04
# [5,] 10000 8e+05

tpms
#             S1         S2
# [1,] 281690.14    486.618
# [2,]  70422.54    973.236
# [3,]  84507.04    973.236
# [4,] 211267.61  24330.900
# [5,] 352112.68 973236.010

# Sample means should be equal.

colSums(rpkms)
#    S1     S2 
# 28400 822000
colSums(tpms)
#    S1    S2 
# 1e+06 1e+06

colMeans(rpkms)
#   S1     S2 
# 5680 164400
colMeans(tpms)
#    S1    S2 
# 2e+05 2e+05

Consider using the length estimates produced by your read counter (HTSeq, STAR, Subread, Kallisto, Salmon, etc.).

Here are some tutorials I found useful:

• RNA-seq analysis is easy as 1-2-3 with limma, Glimma and edgeR
• Bioconductor workflow for single-cell RNA sequencing: Normalization, dimensionality reduction, clustering, and lineage inference

Thank you so much!

hi @slowkow , gene length is in base pairs, correct?

I don't understand why the the formula for calculating TPM is different in the article "Measurement of mRNA abundance using RNA-seq data: RPKM measure is inconsistent among samples" Wagner 2012 and in the article "Misuse of RPKM or TPM normalization when comparing across samples and sequencing protocols" Zhao 2020.
Is it possible to use TPM to normalize dna-sequenced samples?

rate <- counts reads mapped to contig / contig length
rate / sum(rate) * 1e6