Miller cylindrical projection calculator for latitude and longitude

It modifies the Mercator latitude formula so the north and south poles remain at a finite height instead of stretching toward infinity. Choose a radius to control the output scale, or keep the unit-sphere default for normalized coordinates. Results are deterministic, rounded only at the requested final precision, and available in the browser or through the API from $0.002 per item.

How the Miller cylindrical projection works

The Miller cylindrical projection starts with the familiar geometry of a normal cylindrical map: longitude controls horizontal position, the central meridian is x equals zero, and the equator is y equals zero. Its distinguishing change is in the vertical formula. The calculator first converts latitude and longitude from degrees to radians. It then computes x as the sphere radius multiplied by longitude, while y is one and one-quarter times the radius multiplied by the natural logarithm of the tangent of pi over four plus two-fifths of latitude. Scaling latitude before applying the Mercator-like logarithm reduces the extreme vertical expansion. At a geographic pole, the tangent receives an angle of eighty-one degrees rather than ninety degrees, so the result stays finite. The projection remains cylindrical and neither conformal nor equal-area. That tradeoff makes it useful for world-map layouts where a recognizable shape and bounded map height matter more than preserving an exact geometric property everywhere.

Choose inputs, scale, and precision

Supply latitude between minus ninety and ninety degrees and longitude between minus one hundred eighty and one hundred eighty degrees. Both must be finite numeric values; numeric-looking strings are deliberately rejected so an upstream formatting mistake cannot silently change a calculation. Radius is optional and defaults to one. With that default, x and y are normalized spherical coordinates. Set radius to Earth’s mean radius in meters when you need projected values measured in meters, or use another positive radius when working with a different sphere or a custom drawing scale. The calculator does not infer a datum, ellipsoid, false easting, false northing, or central-meridian offset. Longitude zero is always the central meridian. The decimals option controls only how the returned x and y values are rounded, from zero through twelve places. The formulas operate at JavaScript floating-point precision before that final rounding step, while the original input values and selected radius are echoed for traceability.

Interpret the result and know the limits

Read x as the horizontal displacement from the prime meridian and y as the vertical displacement from the equator. Their unit is exactly the radius unit: a radius in kilometers yields kilometers, a radius in meters yields meters, and radius one yields dimensionless normalized values. Positive x lies east and negative x west; positive y lies north and negative y south. The origin therefore represents latitude zero and longitude zero. A finite y at ninety degrees is expected and is a key difference from ordinary spherical Mercator, not evidence that the coordinate was clipped. Even so, finite does not mean distortion-free. Scale and area distortion still increase toward high latitudes, and the output is not suitable as a direct substitute for a locally accurate engineering or cadastral coordinate reference system. Use it for Miller world maps, educational comparisons, visualization pipelines, and reproducible formula checks. If a workflow requires inverse conversion, ellipsoidal parameters, antimeridian wrapping, or an EPSG-defined transformation, pair this result with a geospatial library designed for those requirements.