Custom Mercator Projection with a Movable Equator
Every Mercator map is honest along one line and stretched everywhere else. This lab lets you choose that line: drag the red handle across the globe, and the map recalculates with new poles ninety degrees away. Antarctica, normally smeared along the bottom edge, snaps into a compact continent the moment the equator runs through it.
10⁸ m · 40,075 km (the equator) · D3 · TopoJSON · SVG
Keep exploring the scale
Every toy changes one assumption. Try another and see what moves.
Same maths, new centre
What moving the equator does to a Mercator map
Mercator’s scale factor at latitude φ is 1/cos φ in every direction, so area grows by 1/cos²φ. That is 1 on the equator, about 1.6 at 38°, 4 at 60°, and infinite at the poles, which is why the poles never fit on the sheet. Tilting the equator does not change any of those numbers. It changes which places sit at which latitude, and the map redistributes its stretching accordingly.
Three experiments to run
- Leave Antarctica selected and drag the equator through it. The continent that usually fills the bottom edge collapses into a compact shape, and the Arctic Ocean takes its place along the top.
- Drop one of the new poles on your own city by reading the pole readout as you drag. Your neighbourhood swells to fill the map edge; the equator now passes through countries a quarter of the world away.
- Line the equator up with a meridian. That is a transverse Mercator, the family behind the UTM grid that surveyors and hikers use, and it keeps a narrow north–south strip almost free of distortion.
Reading the workspace
The readouts give the equator handle and the new north pole in latitude and longitude, so a setting can be written down and repeated. Highlight countries in the draggable set to move them across the tilted map, and export either the map alone or the map with the globe beside it as a PNG.
Why this is not a new projection
Cartographers have rotated Mercator’s axis for centuries. Transverse and oblique Mercator variants exist precisely because a country or a route can be placed along the line of least distortion. The lab makes that choice interactive and shows the consequence at the same time: whatever you move toward the equator sharpens toward its measured area, and whatever you push toward the new poles inflates, exactly as Greenland and Antarctica do on the ordinary version.
Related scale tools
Questions about the projection lab
What does a custom Mercator projection change?
Only where the line of zero stretching sits. Standard Mercator centres on the geographic equator; this lab lets you tilt that line anywhere, which moves the projection's poles too. Everything else about the projection, including its straight compass bearings, stays the same.
What happens to a country when the equator moves next to it?
It contracts toward its measured size, because Mercator's scale factor is 1 on the equator and grows with distance from it. A country that ends up near one of the new poles does the opposite and can stretch to several times its true area.
Why can't a flat map show every country at true size?
A sphere cannot be unrolled onto a plane without tearing or stretching. Every projection chooses what to keep: Mercator keeps angles, equal-area maps keep area, and no map keeps shape, area, distance, and direction all at once.
Where do the new poles end up when I tilt the equator?
Ninety degrees away from the tilted equator, on the axis you have rotated. The workspace reports the equator handle and the new north pole in latitude and longitude, so you can place a pole on a city and watch that city's map neighbourhood balloon.
Why is Antarctica selected by default?
Because it is the most extreme case. On a standard Mercator map Antarctica is stretched into a band along the bottom edge; tilt the equator through it and it collapses into a compact continent while some other place takes over as the ragged edge.
Same projection, different centre. Nothing here changes measured area; only where the stretching lands.