Math

Vector Operations Calculator

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

Last validated: 2026-02-14

Use this free online Vector Operations Calculator to perform dot product, magnitude, and angle-related operations on vectors. It is useful when you need a focused browser-based utility that turns a specific set of inputs into a practical result quickly. The form focuses on Vector A, Vector B and returns Vector Inputs, Result, so you can move from input to answer without setting up a spreadsheet or custom script. Run one realistic example, adjust the inputs, and compare how the result changes before you copy or share it. Save the inputs with the result when the output will be shared, audited, or used as part of a larger workflow.

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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 A, Vector B for the vector operations calculator, keeping units, dates, or text format consistent with the form labels.
Check optional fields and assumptions before running so the result matches the workflow you have in mind.
Click "Run the tool" and review Vector Inputs, Result for the primary output.
Copy or share the result together with the inputs so the output can be reproduced later.

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.

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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Vector Operations Calculator

Input Pattern

Vector Inputs

Result

How to use this tool

Worked Example

Example Inputs

Expected Outputs

Interpretation

Confidence and limitations

Formula References

Assumptions

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