Vector calculator

Add and subtract matching vector components, then find their dot product and magnitudes.

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Vector calculator processes your input in this browser. Inputs and results are excluded from analytics. Recent tools save tool names, visit counts and last-visit times. Saved tools store only their names. Draft saving is optional and stays on this device; delete saved text with the draft controls. Loading text from a URL is optional and contacts that server; its URL and your IP address are visible to the server. An optional “Use in” action keeps a handoff in this tab. The next tool removes it on arrival and ignores it if more than a minute has passed.

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Spaces separate values; 1,000 is one value.

First vector components

Second vector components

Answer

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Add and subtract matching vector components, then find their dot product and magnitudes.

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Saved scenario

Save the current answer, then change an input to compare. This clears when you leave.

Formula and assumptions

Vectors must share a coordinate basis and dimension. Magnitude = √Σx²; dot product = Σaᵢbᵢ. Up to ten components, including zero vectors.

In a list, use spaces, new lines, semicolons, or commas followed by a space. A comma between groups of three digits is a thousands separator.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

Scratch calculator

Check another calculation

Use +, −, ×, ÷, parentheses and %. A percentage is divided by 100. This does not change the main tool.

Reset reloads the tool with its starting values and releases open files and device controls. Saved drafts stay on this device until you delete them.

Links include your inputs and settings. Anyone with the link can see them, so leave out private text. Files and generated results are left out; random draws run again.

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Updated 2026-09-26

Using Vector calculator

Add and subtract matching vector components, then find their dot product and magnitudes.

Vectors must share a coordinate basis and dimension. Magnitude = √Σx²; dot product = Σaᵢbᵢ. Up to ten components, including zero vectors.

Next: Unit vector calculator

A worked example

Example inputs: first vector components = 1 2 3, second vector components = 4 5 6. Sum vector = 5 7 9.

Before you use the result

Vectors must share a coordinate basis and dimension. Magnitude = √Σx²; dot product = Σaᵢbᵢ. Up to ten components, including zero vectors.

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ToolOctopus. “Vector calculator.” Updated 2026-09-26. https://tooloctopus.com/vector-calculator.

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