Math

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Vector Projection Calculator.

Project one three-dimensional vector onto another.

On-device calculationNo signup
01

Set your values

Results update as you type.

Projection scalar: 3

Projection scalar

0.000000
x: 3

x

0.000000
y: 0

y

0.000000
z: 0

z

0.000000

Results update automatically as you type.

Use Cases

Physics: Resolving Forces

Decompose a force vector into components parallel and perpendicular to a direction, such as finding the component of gravity along an inclined plane.

Example: Project force F = (3, 4, 0) onto direction d = (1, 0, 0) to get the x-component.

Computer Graphics: Vector Decomposition

In 3D graphics, project a vector onto a surface normal or an axis to isolate directional components for lighting or movement calculations.

Example: Project a velocity vector onto a wall's normal to find the reflection direction.

Frequently Asked Questions

What does the vector projection calculator compute?
It computes the vector projection of vector A onto vector B using the formula (A·B / |B|^2) * B. You input the x, y, z components of both vectors, and it returns the projection vector components.
What is the difference between scalar projection and vector projection?
Scalar projection is the length of the projection (a scalar), while vector projection is the actual vector along B. This calculator gives the vector projection, which includes direction and magnitude.
Can I use this calculator for 2D vectors?
Yes, you can set the z components of both vectors to 0. The calculator will then compute the projection in the xy-plane.

Tips & Common Mistakes

Tips

  • Ensure all vector components are entered as real numbers; you can use decimals or fractions.
  • If vector B is zero (all components 0), the projection is undefined because division by zero occurs. Check your inputs.
  • The projection result is a vector, so it has both magnitude and direction. You can verify by checking that the result is parallel to vector B.
  • For quick 2D calculations, set the z components to 0.

Common Mistakes to Avoid

  • Forgetting to set z components to 0 for 2D vectors, leading to unintended 3D results.
  • Entering vector B as zero vector, which causes division by zero; the calculator cannot compute a projection onto a zero vector.
  • Confusing the order: projection of A onto B is not the same as projection of B onto A. Make sure you assign vectors correctly.

Last updated: August 13, 2026