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We consider first-passage percolation (FPP) on the triangular lattice withvertex weights $(t_v)$ whose common distribution function $F$ satisfies$F(0)=1/2$. This is known as the critical case of FPP because large (critical)zero-weight clusters allow travel between distant points in time which issublinear in the distance. Denoting by $T(0,\partial B(n))$ the first-passagetime from $0$ to $\{x : \|x\|_\infty = n\}$, we show existence of the "timeconstant'' and find its exact value to be  \[  \lim_{n \to \infty} \frac{T(0,\partial B(n))}{\log n} =\frac{I}{2\sqrt{3}\pi} \text{ almost surely},  \]  where $I = \inf\{x > 0 : F(x) > 1/2\}$ and $F$ is any critical distributionfor $t_v$. This result shows that the time constant is universal and dependsonly on the value of $I$. Furthermore, we find the exact value of the limitingnormalized variance, which is also only a function of $I$, under the optimalmoment condition on $F$. The proof method also shows an analogous universalityon other two-dimensional lattices, assuming the time constant exists.

Universality of the time constant for $2D$ critical first-passage percolation