Calculate the scalar projection of one vector onto another.
Vector Components
Vector A (Project From)
Vector B (Project Onto)
Projection Results
3.00
Scalar Projection (comp_B A)
The length of the shadow of A on B.
Dot Product (A · B)15.00
Magnitude of B (|B|)5.00
About this calculator
What is Scalar Projection?
The scalar projection of vector A onto vector B (often written as comp_B A) is a scalar value that represents the 'component' of A in the direction of B. Geometrically, it's the signed length of the orthographic projection of A onto a line parallel to B.
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Pro Tips
The result is positive if the vectors point in the same general direction (< 90°).
The result is negative if the vectors point in opposite directions (> 90°).
Vector B cannot be a zero vector (|B| > 0).
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Fun Facts
"Scalar projection is the magnitude of the vector projection."
"In physics, work done by a constant force is the scalar projection of the force onto the displacement vector multiplied by displacement magnitude."
"The dot product itself is the scalar projection multiplied by the magnitude of the target vector."
