Gnomonic Projection

Azimuthal perspectiveCreator: Known since antiquity; mathematically associated with ThalesYear: VI w. p.n.e.

A gnomonic map does one thing uniquely well: it turns every great circle into a straight line. The cost appears immediately — the farther from the center, the faster the world races toward infinity.

Projection guide

The shortest route gets a ruler

Imagine a lamp at Earth's center and a plane touching the globe. Point shadows land on the plane, and the planes of all great circles intersect it in straight lines.

That is why this is not a whole-world atlas but a precise window aimed at a particular problem: a route, ocean, or hemisphere. Change the route and the map center must change too.

Global Cartographic Grid

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Distortion Properties

PropertyCharacteristic
Area
✅PreservedNot preserved; grows rapidly toward the visible boundary
Shape
❌DistortedReasonable only near the center; heavily stretched near the edge
Distances
❌DistortedOnly locally true at the center
Angles & Directions
✅PreservedNot preserved
Continuity
❌DistortedShows less than a hemisphere in a finite view

History & Origin

One of the oldest perspective projections. Points on the sphere are projected from Earth's center onto a tangent plane. Its unique property is that every great-circle arc becomes a straight line.

Applications

Planning shortest long-distance routes, aviation and marine navigation, and teaching the contrast between great circles and rhumb lines. A route planned on a gnomonic chart was traditionally transferred in segments to a Mercator chart.

How to read this map

A lamp at the globe's center casts a shadow onto a tangent sheet.

  • A straight line means a great circle, not a constant bearing.
  • The center is the most reliable part of the map.
  • The edge is a mathematical limit, not the end of the world.

What you gain and lose

It preserves straight great-circle routes at the cost of area, shape, and full-globe coverage.

Best for

Planning shortest routes and explaining great-circle geometry.

Avoid for

Whole-world maps, area comparison, and regions near the view boundary.

TEST THIS PROJECTIONCompare countries in Gnomonic Projection →GREAT CIRCLE VS RHUMB LINESee routes in Gnomonic Projection →
Take the challenge

Can you recognize this projection without the label?

The projection quiz uses graticules and world outlines, so it is a natural next step from this page.

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Daily challenge

One attempt, the same set for everyone

Size Illusion · Build a streak and come back tomorrow for another map.

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✦ How do different countries look in this projection?

Analyze shape distortions of 5 countries in this cartographic projection and test them in the sandbox.

Poland
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A useful starting point for European route demonstrations.

Test on map →
United States
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Transatlantic routes reveal the contrast with Mercator.

Test on map →
Greenland
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Greenland looks calm near the center and explodes in scale near the edge.

Test on map →

Facts worth remembering

  • The hemisphere boundary lies at infinity.
  • Navigators transferred points from a straight gnomonic route onto a Mercator chart.
  • It is the only standard projection that straightens every great circle.

Compare with other projections

The best internal links are the ones that help you think. These projections show different answers to the same problem: how to flatten a sphere.

Conformal CylindricalMercator ProjectionCompare with this conformal cylindrical projection and see how shapes, area, and readability change.Perspective AzimuthalGlobe (Orthographic)Compare with this perspective azimuthal projection and see how shapes, area, and readability change.Azimuthal equidistantAzimuthal Equidistant ProjectionCompare with this azimuthal equidistant projection and see how shapes, area, and readability change.

Keep reading about maps that reshape intuition

Gnomonic vs Mercator — which straight line is shortest?Two maps, two straight lines, and two different questions: shortest route versus constant compass bearing.Great circle vs rhumb line — why the shortest route looks longerThe great circle is the shortest path on the globe; the rhumb line keeps a constant bearing. On the Mercator map their roles swap. We explain why planes fly along a curve and how to test it.Why Airlines Fly in Arcs? Great circle vs rhumb lineExplaining why flights from Europe to the USA travel in arcs near the Arctic Circle. Discover geodesics and the shortest paths on a globe.

Frequently Asked Questions

Every great circle lies in a plane through Earth's center. Projecting from that same center makes its intersection with the map plane a straight line.

Points 90° away from the center project to infinity, so a practical map must be clipped before the hemisphere boundary.

No. It is the shortest great-circle route, but its bearing usually changes. A constant-bearing route is straight on Mercator.