 where "λ" is the longitude relative to the central meridian of the projection, "φ" is the latitude, "φ" is the standard parallel for the equirectangular projection, sinc is the unnormalized cardinal sine function (with the discontinuity removed), and

In his proposal, Winkel set

A closed-form inverse mapping does not exist, and computing the inverse numerically is somewhat complicated.David M. Goldberg and J. Richard Gott III show that the Winkel tripel fares well against several other projections analyzed against their measures of distortion, producing small distance errors, small combinations of Tissot indicatrix ellipticity and area errors, and the smallest skewness of any of the projections they studied.By a different metric, Capek's "Q", the Winkel tripel ranked ninth among a hundred map projections of the world, behind the common Eckert IV projection and Robinson projections.