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Vector Calculator
Perform the essential 3D vector operations, addition, subtraction, dot product, cross product and magnitude, in your browser.
HOW TO USE
- 1Enter the x, y and z components of vector A and vector B. Empty fields count as zero.
- 2Pick the operation: add, subtract, dot product, cross product or the magnitude of A.
- 3The result shows the outcome of the operation, along with the magnitude of both vectors and the angle between them in degrees.
- 4The angle is undefined when either vector is zero, and the cross product of parallel vectors is the zero vector.
EXAMPLE
INPUT
A = (1, 2, 3), B = (4, 5, 6)
OUTPUT
A + B = (5, 7, 9) · A · B = 32 · A × B = (−3, 6, −3) · angle ≈ 12.93°
FAQ
What does the dot product tell you?
The dot product of two vectors is a scalar: the product of their magnitudes times the cosine of the angle between them. A zero dot product means the vectors are perpendicular.
What does the cross product tell you?
The cross product of two 3D vectors is a third vector perpendicular to both, with a magnitude equal to the area of the parallelogram they span. Its direction follows the right-hand rule.
How is the angle between two vectors found?
Rearrange the dot product formula: cos(θ) = (A · B) / (|A| × |B|), then take the inverse cosine. The result is always between 0° and 180°.
Can this solve vector addition and subtraction homework?
Yes. Enter the components of A and B, pick add or subtract, and the solver shows the resulting vector plus both magnitudes and the angle between them.
When is the angle undefined?
When either vector is the zero vector — a direction cannot be defined for it, so the dot product formula divides by zero.
Is my data sent anywhere?
No. All calculations run entirely in your browser, your vectors never leave your device.