Vector Projection Calculator
Calculate the scalar projection of one vector onto another
About this calculator
The Vector Projection Calculator computes the scalar projection of one vector onto another, which represents the length of the shadow cast by the first vector when projected onto the second vector's direction. This mathematical operation is essential in physics for calculating work done by forces, in computer graphics for lighting calculations, and in engineering for analyzing component forces. The scalar projection helps determine how much of one vector lies in the direction of another, making it invaluable for decomposing vectors into directional components.
How to use
Enter the components of both vectors in their respective input fields (x, y, and z coordinates for 3D vectors, or x and y for 2D vectors). Click the calculate button to instantly compute the scalar projection value. The result shows how much of the first vector extends in the direction of the second vector, with positive values indicating the same general direction.
Frequently asked questions
What's the difference between scalar and vector projection?
Scalar projection returns a single number representing magnitude, while vector projection returns a vector showing both magnitude and direction along the target vector.
Can the scalar projection be negative?
Yes, negative scalar projection indicates the vectors point in generally opposite directions, with the magnitude showing the extent of opposition.
What happens if I project onto a zero vector?
Projection onto a zero vector is undefined mathematically, as division by zero occurs in the calculation formula.