Minecraft Stronghold Triangulation Calculator

An Eye of Ender flies toward the nearest stronghold, but following it one throw at a time costs a stack of eyes. Throw twice from two places, note the angle each time, and the two lines cross at the stronghold. This calculator does that intersection, gives Overworld and Nether coordinates, and checks the result against the Java Edition stronghold rings so you can spot a misread angle before you start digging.

How to use this tool

1. Stand still, throw an eye, and put your crosshair on it while it hovers.
2. Press F3 and copy your X and Z plus the first number after "Facing" into Throw 1.
3. Walk or ride at least 200–300 blocks sideways — not toward the eye — and repeat for Throw 2.
4. Go to the coordinates shown; in the Nether, use the Nether coordinates.

Formula

direction = (−sin θ, cos θ) t = ((x₂ − x₁)·d₂z − (z₂ − z₁)·d₂x) ÷ (d₁x·d₂z − d₁z·d₂x)

θ is the F3 facing angle: 0° points south (+Z), 90° west (−X), ±180° north and −90° east. The stronghold is throw 1 plus t blocks along its direction. The error figure shows how far the answer moves if each angle is off by 0.1°.

Example

Throw 1 at X 200, Z 100 reads −127.6°; throw 2 at X 600, Z 400 reads −145.3°. The lines cross at an angle of 17.7° at about X 1,502, Z −903, 1,585 blocks from throw 2 and 1,752 blocks from 0, 0 — inside ring 1. In the Nether that is X 187, Z −113. A 0.1° misreading would move the answer by up to about 19 blocks.