Math

Vector Operations Calculator

Run dot product, angle, magnitude, sum, difference, and cross product.

Last validated: 2026-02-14

Vector Operations Calculator performs dot product, magnitude, and angle-related operations on vectors. It is useful in physics, graphics, and linear algebra tasks. The tool streamlines repetitive component arithmetic. Use it to verify directional and projection calculations.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Vector Inputs

Use 2D or 3D vectors, e.g. 3,4,0.

Result

Dot product: 11.00000000

|A|: 5.00000000

|B|: 3.00000000

Angle (deg): 42.833428

A+B: [4.000000, 6.000000, 2.000000]

A-B: [2.000000, 2.000000, -2.000000]

A×B: [8.000000, -6.000000, 2.000000]

How to use this tool

Enter vector components in the required format.
Run the tool to compute selected vector operations.
Use results to analyze alignment, magnitude, or projection.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Vector a: 3, 4, 0
Vector b: 1, 2, 2
Dot product: 11.0
Magnitude a: 5.0
Magnitude b: 3.0
Angle degrees: 42.83342806606726

Expected Outputs

Parsed a 0: 3
Parsed a 1: 4
Parsed a 2: 0
Parsed b 0: 1

Interpretation

Parsed a 0 is 3.0. Use this as a decision input, not as a standalone conclusion.
Parsed a 1 is 4.0. Use this as a decision input, not as a standalone conclusion.
Parsed a 2 is 0.0. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Vector a

Vector b

Dot product

Magnitude a

Magnitude b

Angle degrees

Scenario B

Vector a

Vector b

Dot product

Magnitude a

Magnitude b

Angle degrees

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Algebra and arithmetic identities used by the selected formula.
Standard precision arithmetic; rounding shown for readability.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

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