Based upon an over-one-month frequency comparison of two ${}^{40}{\mathrm{Ca}}^{+}$ optical clocks, the frequency difference between the two clocks is measured to be $3.2\times {10}^{-17}$ with a measurement uncertainty of $5.5\times {10}^{-17}$, considering both the statistic ($1.9\times {10}^{-17}$) and the systematic ($5.1\times {10}^{-17}$) uncertainties. This is the first performance of a ${}^{40}{\mathrm{Ca}}^{+}$ clock better than that of Cs fountains. A fractional stability of $7\times {10}^{-17}$ in 20 000 s of averaging time is achieved. The evaluation of the two clocks shows that the shift caused by the micromotion in one of the two clocks limits the uncertainty of the comparison. By carefully compensating the micromotion, the absolute frequency of the clock transition is measured to be 411 042 129 776 401.7(1.1) Hz.

• Received 13 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.013001