The space \(\mathcal{ML}(\Sigma)\) of measured laminations of a surface \(\Sigma\) of genus \(g\) with \(n\) punctures is an integral piecewise linear manifold of dimension \(6g-6+2n\). H. Masur showed [Proc. Am. Math. Soc. 94, 455–459 (1985; Zbl 0579.32035)] that there exists a measure on \(\mathcal{ML}(\Sigma)\), unique up to scaling, which is invariant under the action of the mapping class group. The authors consider two different ways to normalize this measure: the first normalization \(\mu_\omega\) (“the symplectic Thurston measure”) comes from the symplectic form on \(\mathcal{ML}(\Sigma)\) as defined by Thurston, the second normalization \(\mu_{\mathbb{Z}}\) (“the integer Thurston measure”) from the integral affine structure on \(\mathcal{ML}(\Sigma)\) (which is natural for the counting of hyperbolic geodesics and counting problems on the space of quadratic differentials). In the present paper, answering a question of K. Rafi and J. Souto [Geom. Funct. Anal. 29, No. 3, 871–889 (2019; Zbl 1420.30012)], the authors determine the ratio between these two measures (explicitly, \(\mu_\omega/\mu_\mathbb{Z} = 2^{2g+n-3}\)). As the authors note, this result was obtained independently, by different methods, also by F. Arana-Herrera [“Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani’s asymptotics for simple closed hyperbolic geodesics”, Preprint, arXiv:1902.05626] and by V. Delecroix et al., [“Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves”, Preprint, arXiv:1908.08611].