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Projection Formula Calculator

Online vector projection: scalar and vector projection of a onto b.

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Scalar = a·b/|b|
Vector a
x
y
Vector b (direction)
x
y

📖 Tutorial | Projection

1. Definition
The scalar projection of a onto b is a·b/|b|; the vector projection is (a·b/|b|²)b.
2. Formula & Notation
Scalar, vectorAlong b
3. Properties & Laws
  • Scalar can be negative;
  • Vector along b;
  • b non-zero;
  • Scalar × unit b = vector.
4. Steps
  1. Enter two vectors;
  2. Click "Project";
  3. Or click "Load Example".
5. Worked Examples
Example: a=(3,4), b=(4,0): scalar 3, vector (3,0).
6. Common Pitfalls
Scalar can be negative;
Divide by |b|;
b non-zero.

❓ FAQ | Projection

Scalar?
Dot/|b|.
Vector?
Along b.
Sign?
Negative ok.
b zero?
Undefined.
Example?
3, (3,0).
Angle?
|a|cosθ.