Minecraft End Portal Finder (stronghold triangulation from 2 eye of ender throws)

Understanding the Minecraft End portal finder — concept and principle

To reach the End in Minecraft you need a stronghold, and eyes of ender point toward the nearest one. This calculator finds the stronghold from two throws: enter where you stood and the facing angle (yaw) you read on the F3 screen for each throw, and it works out where the two lines cross, with the matching Nether coordinates.

How it is calculated

Direction of each throw: d = (−sin yaw, cos yaw)

Solve P₁ + t₁ × d₁ = P₂ + t₂ × d₂ for t₁ and t₂

Stronghold = P₁ + t₁ × d₁

Nether coordinates = stronghold X ÷ 8, Z ÷ 8

• P₁ and P₂ are the (X, Z) positions of the two throws.
• In Java Edition, yaw 0° points south (+Z), 90° west (−X), ±180° north (−Z) and −90° east (+X).
• The angle between throws is shown; larger angles give more reliable results.

The principle

Each eye of ender flies toward the stronghold, so from where you stand it defines a line on the map. One line tells you the direction but not the distance. A second line from a different spot crosses the first at the stronghold, just as surveyors and sailors find positions by taking bearings from two points (triangulation). The yaw angle converts to a direction vector with sine and cosine, and solving two linear equations gives the crossing point. A small error in reading the angle shifts the crossing point less when the two lines meet at a wide angle.

Worked example

Default inputs: throw 1 at (0, 0), yaw −118.1°; throw 2 at (300, 300), yaw −132.5°.

1. Directions: d₁ = (0.882, −0.471), d₂ = (0.737, −0.676).
2. Solving the two line equations gives t₁ ≈ 1,704 and t₂ ≈ 1,632 blocks.
3. Stronghold ≈ (0 + 1,704 × 0.882, 0 − 1,704 × 0.471) = 1503, −803.
4. In the Nether: 1503 ÷ 8 and −803 ÷ 8, rounded down = 187, −101.
5. Distance from throw 2 = 1,632 blocks; from throw 1 = 1,704; angle between throws = 14.4°; distance from 0, 0 = 1,704.

How to read the result

The result is an estimate within a few dozen blocks, depending on how carefully you read the angles. Travel to the spot, often via the Nether to save time, then throw another eye nearby: when it flies downward, dig down. Strongholds are underground, so you may need to search the area. If the angle between throws is under about 10°, walk further sideways and throw again.

Common mistakes

• Reading the yaw while not looking straight at the eye.
• Taking both throws from almost the same direction, which makes the crossing point unreliable.
• Using Bedrock Edition angle conventions without checking.

Frequently asked questions

How far apart should my throws be?

Far enough that the angle between them is at least about 10°, often a few hundred blocks sideways.

Why use the Nether coordinates?

One block in the Nether equals eight in the Overworld, so travelling there is much faster.

What does the eye do when I am close?

It flies downward toward the stronghold below you.

Sources: PixelRayn (2025), "Locating Strongholds with Triangulation and Estimating Measurement Error" (self-published technical note); standard analytic geometry for line intersection