Vector projection calculator

The projection of u onto v is ((u · v) ÷ (v · v)) × v.

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Vector components

Second vector

Answer

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The projection of u onto v is ((u · v) ÷ (v · v)) × v.

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Formula and assumptions

The second vector is the target direction and must be nonzero. Scalar projection is signed; a negative value points opposite to the target vector.

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Updated 2026-09-26

Using Vector projection calculator

The projection of u onto v is ((u · v) ÷ (v · v)) × v.

The second vector is the target direction and must be nonzero. Scalar projection is signed; a negative value points opposite to the target vector.

Next: Basic calculator

A worked example

With vector components = 3, 4, second vector = 1, 2, the projection vector is 2.2, 4.4.

Before you use the result

The second vector is the target direction and must be nonzero. Scalar projection is signed; a negative value points opposite to the target vector.

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