End Portal Finder — Minecraft Stronghold Triangulation
Throw an Eye of Ender from two positions, note your facing yaw angle from the F3 debug screen each time, and this calculator triangulates the exact Overworld block coordinates of the nearest stronghold using 2-D line intersection.
°
°
Overworld block coordinate — see Z and Nether coordinates in the stats below
- 1
Ray 1 direction (dx, dz)
(0.5592, 0.829)Direction vector from yaw: 0° = south (+Z), ±90° = west/east, ±180° = north. - 2
Ray 2 direction (dx, dz)
(-0.7071, 0.7071) - 3
Determinant (parallelism check)
-0.7071 × 0.829 − 0.5592 × 0.7071 = -0.981627Zero means the two rays are parallel — no unique intersection. - 4
Intersection parameter t
360.171Distance along ray 1 to the stronghold. Negative = you were pointing away. - 5
Stronghold X
round(0 + 360.171 × 0.5592) = 201
How does this calculator work?
Point at the Eye of Ender from two positions and record your X, Z, and facing yaw (from F3) each time. Direction vector: dx = −sin(yaw), dz = cos(yaw). Solve the 2×2 system where both rays meet — those are the Overworld X, Z of the stronghold. Divide by 8 for Nether equivalent travel. Dig around Y=35–45 and look for stone-brick corridors.
Formula
How this is calculated
When an Eye of Ender is thrown it flies in a straight line toward the nearest stronghold. That path defines a ray in the horizontal (X-Z) plane. From two different starting points, two such rays are produced — and their intersection is the stronghold location.
Minecraft records your facing direction as a yaw angle (−180° to 180°) shown on the F3 debug screen next to "Facing". The convention is 0° = south (+Z direction), 90° = west (−X), −90° = east (+X), ±180° = north (−Z). The unit direction vector for a given yaw θ is (dx, dz) = (−sin θ, cos θ). Knowing the starting coordinates (X, Z) and the direction, each throw defines a parametric ray: (X + t·dx, Z + t·dz). Setting two such rays equal and solving the 2×2 linear system gives the intersection — the stronghold.
For best results, stand at two positions at least 200–500 blocks apart in a direction roughly perpendicular to the stronghold. If the two angles differ by less than 5–10°, the lines are nearly parallel and small angle errors produce large positional errors. Dig around Y = 30–45 near the computed coordinates and look for stone-brick corridors. The stronghold portal room is typically within 30–80 blocks of the triangulated point.
Frequently asked questions
Press F3 to open the debug overlay. Look for the "Facing" line — it shows a cardinal direction and the yaw angle in degrees in parentheses, e.g. "south (0.1 / 5.2)". Use the first (horizontal) number. Do not use the second number — that is the vertical pitch angle. Throw the Eye, face the direction it flew, and read the angle.
A negative t means the intersection is behind Position 1 — you were pointing away from the stronghold. This usually means you read the angle you were facing before the Eye flew, rather than aligning yourself with the Eye's direction of travel afterward. Turn around and re-measure, or try a different second position.
Theoretically exact if angles are perfect. In practice the F3 yaw updates discretely, and you may align yourself slightly off. Two positions separated by 300–700 blocks with an angle difference of 30–90° give the best accuracy. Errors of 30–80 blocks are typical; the stronghold's portal room is inside a roughly 100×100 chunk cluster, so you usually only need to explore a moderate area.
Also known as
TG we-Calculate Editorial Team. (2026). End Portal Finder — Minecraft Stronghold Triangulation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/end-portal-finder-calculator
TG we-Calculate Editorial Team. "End Portal Finder — Minecraft Stronghold Triangulation." TG we-Calculate. 2026. https://we-calculate.com/calculator/end-portal-finder-calculator.
TG we-Calculate Editorial Team, "End Portal Finder — Minecraft Stronghold Triangulation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/end-portal-finder-calculator
@misc{wecalculate_end_portal_finder_calculator, title = {End Portal Finder — Minecraft Stronghold Triangulation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/end-portal-finder-calculator}}, year = {2026}, note = {TG we-Calculate} }
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