CoordinateChartData

CoordinateChartData[chart, property] gives the value of the specified property for chart.

CoordinateChartData[chart, property, {x1, x2, ..., xn}] gives the value of the specified property for chart evaluated at the point {x1, x2, ..., xn}.

Examples

Get properties of polar coordinates:

CoordinateChartData["Polar", "StandardName"]

Metric tensor for spherical coordinates:

CoordinateChartData["Spherical", "Metric", {r, θ, φ}]

Please visit the official Wolfram Language Reference for more details.