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In this paper, we present the physics performance of the ESSnuSB experiment in the standard three flavor scenario using the updated neutrino flux calculated specifically for the ESSnuSB configuration and updated migration matrices for the far detector. Taking conservative systematic uncertainties corresponding to a normalization error of $5\%$ for signal and $10\%$ for background, we find that there is $10\sigma$ $(13\sigma)$ CP violation discovery sensitivity for the baseline option of 540 km (360 km) at $\delta_{\rm CP} = \pm 90^\circ$. The corresponding fraction of $\delta_{\rm CP}$ for which CP violation can be discovered at more than $5 \sigma$ is $70\%$. Regarding CP precision measurements, the $1\sigma$ error associated with $\delta_{\rm CP} = 0^\circ$ is around $5^\circ$ and with $\delta_{\rm CP} = -90^\circ$ is around $14^\circ$ $(7^\circ)$ for the baseline option of 540 km (360 km). For hierarchy sensitivity, one can have $3\sigma$ sensitivity for 540 km baseline except $\delta_{\rm CP} = \pm 90^\circ$ and $5\sigma$ sensitivity for 360 km baseline for all values of $\delta_{\rm CP}$. The octant of $\theta_{23}$ can be determined at $3 \sigma$ for the values of: $\theta_{23} > 51^\circ$ ($\theta_{23} < 42^\circ$ and $\theta_{23} > 49^\circ$) for baseline of 540 km (360 km). Regarding measurement precision of the atmospheric mixing parameters, the allowed values at $3 \sigma$ are: $40^\circ < \theta_{23} < 52^\circ$ ($42^\circ < \theta_{23} < 51.5^\circ$) and $2.485 \times 10^{-3}$ eV$^2 < \Delta m^2_{31} < 2.545 \times 10^{-3}$ eV$^2$ ($2.49 \times 10^{-3}$ eV$^2 < \Delta m^2_{31} < 2.54 \times 10^{-3}$ eV$^2$) for the baseline of 540 km (360 km)., Comment: 13 pages, 8 figures, 3 tables. Changes: Text updated, this is a published version