How this calculator works
An eye of ender drifts toward the nearest stronghold, so the direction you see is a line from your position to that stronghold. One throw gives a line but not a point. Two throws from different positions give two lines, and their intersection is the estimate. The arithmetic treats each throw as a ray in the horizontal plane: the throw position is the start, and the bearing gives the direction. If the bearings are too similar, the lines cross at a shallow angle and a small direction error moves the estimate a long way, so separate the throws as much as you reasonably can.
Formula
A bearing theta clockwise from north gives the direction dx = sin(theta) and dz = -cos(theta), because Minecraft +X is east and +Z is south. For throws at P1 and P2 with directions d1 and d2, the intersection parameter along the first ray is t1 = ((P2 - P1) x d2) / (d1 x d2), using the 2D cross product a x b = ax x bz - az x bx. The stronghold is P1 + t1 x d1. The distance from each throw is t1 or t2, and the distance from the world origin is sqrt(X^2 + Z^2).
Worked example
Throw one from X 0, Z 0 at bearing 45 degrees, and throw two from X 100, Z 0 at bearing 315 degrees. Both rays have a horizontal component of about 0.707, and they meet at X 50, Z -50. Each distance is about 70.7 blocks. Since 70.7 is inside 1,280 blocks, the estimate is closer to the origin than a regular Java Edition stronghold, which suggests a bearing or a position was entered incorrectly, or that this is Bedrock Edition, where strongholds are not placed in fixed rings.
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Frequently asked questions
How do I measure a bearing in Minecraft?
A bearing is an angle clockwise from north. North is negative Z, east is positive X, south is positive Z and west is negative X. Use the debug screen facing value, or estimate from a map, then convert to the 0 to 360 convention. The more accurate the two bearings, the closer the intersection.
Why does a small bearing error move the result so far?
At a distance of 1,000 blocks, one degree of error moves the line about 17 blocks sideways, and the crossing point can move more when the two lines meet at a shallow angle. Taking the throws far apart, and reading each direction carefully, matters more than the arithmetic.
Are strongholds always in rings?
In Java Edition, yes: the game places them in eight rings from 1,280 to 24,320 blocks from the origin, with 128 strongholds in total. Bedrock Edition places them differently, with a few near the origin and the rest more random. The ring table on this page is for Java Edition and is a check on the estimate, not a correction.
What if the two lines are parallel?
Parallel bearings never meet, so there is no intersection to report. This happens when the two directions point the same way to within the rounding of your measurements. Move to a position that gives a clearly different angle and throw again.
Does the estimate account for terrain or the Nether?
No. It is a flat-map triangulation in the overworld. Terrain, caves and the End portal room position do not change the stronghold location, and a Nether shortcut does not change the coordinates either. Dig down near the estimate and explore the stronghold once you find it.