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Vector Dot Product Calculator
Compute the dot product of two 3D vectors and the angle between them.
a.x
a.y
a.z
b.x
b.y
b.z
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How it works
a·b = axbx + ayby + azbz; angle = arccos(a·b ÷ (|a||b|))
The dot product multiplies matching components and sums them. It is zero when the vectors are perpendicular, positive when they point the same general way, and negative when opposed.
Worked example
(1,2,3)·(4,−5,6) = 4 − 10 + 18 = 12.
Frequently asked questions
What does a zero dot product mean?
The two vectors are perpendicular (90° apart).
For 2D vectors?
Set the z components to 0 — the math works the same.
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This calculator is for educational purposes. Double-check important results before acting on them.