We derive new approximations for quintessence solutions that are simpler and an order of magnitude more accurate than anything available in the literature, which from an observational perspective makes numerical calculations superfluous. For example, our tracking quintessence approximation yields ∼0.1% maximum relative errors of H(z)/H0 and ωm(z) for the observationally viable inverse power law scalar field potentials, and similarly for viable thawing quintessence models using two slow-roll parameters. The approximations are trivially computed from the scalar field potential and as an application we give analytic expressions for the Chevallier-Polarski-Linder parameters calculated from an arbitrary scalar field potential for thawing and tracking quintessence models.