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Map Projection Distortion Calculator

Every flat map of a round world distorts something, and Mercator distorts area — by the square of the secant of the latitude, which reaches a factor of four at sixty degrees and thirty at eighty. That is why Greenland looks the size of Africa when it is about a fourteenth of it. This computes the stretch at a series of latitudes and checks each figure against the projection's own formula.

What this generator does

Computes the linear and area scale factor at a series of latitudes for the chosen projection, and checks each against the secant of the latitude computed separately — including the conformality condition that Mercator's area scale is the square of its linear one.

How to use this tool

  1. Choose a projection.
  2. Read the linear and area scale at each latitude.
  3. Look at sixty degrees: four times the area it should be.
  4. Compare Mercator against equirectangular in the same table.

Understanding the controls

Projection
Mercator preserves angles and pays for it in area. Equirectangular keeps the vertical scale true and distorts shape instead, which is why it looks stretched near the poles.

Common use cases

  • Explaining why Mercator exaggerates high-latitude countries
  • Quantifying map distortion for a geography lesson
  • Choosing a projection with the trade-off made explicit
  • Checking a projection implementation's scale factors
  • Producing distortion figures for a cartography exercise

How this generator works

A cylindrical projection wraps the globe onto a tube, so a line of latitude that is genuinely shorter than the equator gets drawn the same width — stretched east-west by the secant of the latitude. Mercator then stretches north-south by the same factor to keep angles correct, which squares the area distortion; equirectangular does not, which keeps the vertical scale true and distorts shape. Before display every figure is recomputed from the latitude, the equator is confirmed undistorted, distortion is confirmed to increase with latitude, and Mercator's conformality is checked directly.

Randomness and fairness

Nothing here is random. A projection and a latitude give exactly one scale factor.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • Only two cylindrical projections are covered; conic and azimuthal projections distort along quite different patterns.
  • Distortion is given at points rather than as a Tissot indicatrix, so the direction of stretching is described rather than drawn.
  • The sphere is assumed, so ellipsoidal refinements to the scale factors are not applied.
  • Above eighty degrees Mercator's distortion grows without limit, which is why the table stops there.

Privacy and your data

Every scale factor is computed in your browser. Nothing you choose is transmitted, stored or included in analytics.