Angle between two vectors calculator

The angle is arccos of the dot product divided by both vector magnitudes.

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Vector components

Second vector

Answer

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The angle is arccos of the dot product divided by both vector magnitudes.

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Formula and assumptions

Returns the smaller angle from 0 to 180 degrees. Zero vectors have no defined direction. Normalizing before the dot product limits overflow.

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Updated 2026-09-26

Using Angle between two vectors calculator

The angle is arccos of the dot product divided by both vector magnitudes.

Returns the smaller angle from 0 to 180 degrees. Zero vectors have no defined direction. Normalizing before the dot product limits overflow.

Next: Basic calculator

A worked example

With vector components = 3, 4, second vector = 1, 2, the angle (degrees) is 10.304846468766044.

Before you use the result

Returns the smaller angle from 0 to 180 degrees. Zero vectors have no defined direction. Normalizing before the dot product limits overflow.

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