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DIY Cost Tools

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Dot Product Calculator

Use the scalar product to compare vector directions, check perpendicularity or verify one step of a linear-algebra calculation. Enter coordinates in the same orthonormal basis and keep matching components in the same positions. For a two-dimensional vector, enter zero for z. A positive dot product indicates an acute angle between nonzero vectors; a negative value indicates an obtuse angle. The result is a scalar, not a new vector.

Enter every field, including explicit zeros. Decimal and scientific notation are accepted; commas, fractions and blank fields are rejected. Each input must be finite and no larger than 1 billion in absolute value.

A · B32

How to use this calculator

  1. Match each input to its labeled coordinate, coefficient or matrix position.
  2. Check the signs and use one consistent coordinate convention.
  3. Select Calculate, or press Enter, and read the labeled results.

Formula and method

A · B = AxBx + AyBy + AzBz.

The calculation runs locally in your browser. Changing an input requires selecting Calculate again. If an input or mathematical condition is invalid, the previous result is hidden instead of leaving a stale answer visible.

Worked example

For A = (1, 2, 3) and B = (4, 5, 6), multiply matching components: 1×4 + 2×5 + 3×6 = 32.

Limitations and interpretation

A zero dot product does not establish a right angle if either vector is zero. This tool uses real Cartesian coordinates, not complex inner products or non-Euclidean metrics. Physical units multiply: meters dotted with meters produce square meters.

Results are displayed to approximately 10 significant digits. The underlying calculation uses ordinary floating-point numbers and is not exact symbolic arithmetic. Rounded results can differ slightly from hand calculations. For a measured quantity, choose precision that reflects the measurements rather than all the digits shown. Verify consequential calculations independently.

Frequently asked questions

Can I use two-dimensional vectors?

Yes. Set both z components to zero; the x and y terms remain.

Can I enter negative or decimal values?

Yes, provided the values meet the mathematical conditions described above. Type a normal hyphen for a negative sign. Do not type units, commas or a fraction such as 1/2; enter 0.5 instead.

Why did the calculator hide my previous result?

A missing or invalid input, undefined operation or unstable numerical case produces an explanation. Correct the input and calculate again to obtain a result for the current values.

Review notes and reference

Reviewed October 3, 2026. The stated default example and a boundary or algebraic check were tested against expected values. Input validation checks included blank fields, nonnumeric text and values outside the supported range. Wolfram MathWorld formula reference provides mathematical background. This tool is for calculation and education; its output alone does not validate a professional design.

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