Scalar Meaning Calculator
Vector Calculator works out Result and Result (scalar) from Operation, Vector A and Vector B. The default figures on this page give result of A = (1, 2, 3), B = (4, -5, 6); change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
1 step
- A = (1, 2, 3), B = (4, -5, 6)
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Vector Calculator calculates
Adds, subtracts and scales vectors and computes dot and cross products, magnitude, unit vectors, the angle between vectors, projections and the scalar triple product.
How to use this Vector Calculator
Enter Operation, Vector A, Vector B and Vector C. Result updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Result, Result (scalar) and Result (vector).
The method follows Gilbert Strang, Introduction to Linear Algebra, ch. 1 (vectors, dot products, lengths and angles) and Wikipedia, Cross product and Vector projection.
Cross product of (1,2,3) and (4,-5,6) example
With Operation: cross, Vector A: 1,2,3, Vector B: 4,-5,6, the calculator returns A x B: (27, 6, -13), A · B: 12, |A|: 3.74165739. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Result, Result (scalar) and Result (vector). The inputs you can vary are Operation, Vector A, Vector B, Vector C, Scalar k and Decimals shown.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do I calculate a cross product?
Adds, subtracts and scales vectors and computes dot and cross products, magnitude, unit vectors, the angle between vectors, projections and the scalar triple product. Open “How this is worked out” beside the result to see each step for your own figures.
How to cross product on calculator?
It needs Operation, Vector A, Vector B, Vector C, Scalar k and Decimals shown. Nothing else is required, and the figures stay in your browser.
How do I calculate the cross product in Excel?
The result gives Result, Result (scalar), Result (vector), |A|, |B| and A · B, each labelled with its unit so the figure can be read on its own.
What is the cross product trick?
On the figures this page opens with, the result is A = (1, 2, 3), B = (4, -5, 6). No single number fits everyone: it follows Operation, Vector A and Vector B, so enter your own above and the answer updates as you type.
What information do I need for the Vector Calculator?
You need Operation, Vector A, Vector B, Vector C, Scalar k and Decimals shown. The page opens with default figures that give result of A = (1, 2, 3), B = (4, -5, 6), so you can see the scale before entering your own.
What does this Vector Calculator show?
It shows Result, Result (scalar), Result (vector), |A|, |B|, A · B, A x B and |A x B|, with the working and any warnings for your entries.