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MATH / VECTORS

Angle Between Vectors Calculator

Calculate the smaller angle between two nonzero three-dimensional vectors. Review the symbolic equation, substituted values, interpretation boundary, and result in one guided workspace.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Equation inputs

Preparing the calculator...

Use boundary

Calculation path

Calculate the smaller angle between two nonzero three-dimensional vectors. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.

Calculation path

theta=cos^-1[(a dot b)/(|a||b|)]

What you provide

What you provide

  • Vector A x, using the same scenario as the other inputs
  • Vector A y, using the same scenario as the other inputs
  • Vector A z, using the same scenario as the other inputs
  • Vector B x, using the same scenario as the other inputs
  • Vector B y, using the same scenario as the other inputs
  • Vector B z, using the same scenario as the other inputs

What you receive

What you receive

  • Angle between vectors in deg from the stated equation
  • A symbolic formula plus substituted working with your values
  • Visible assumptions, field guidance, and an authoritative learning reference

Use boundary

Choose the maximum decimal places shown. This does not increase source accuracy.

Both vectors must be nonzero and expressed in one Cartesian basis.

Use internally consistent units and retain extra precision when carrying the result into another calculation.

Reviewed reference factors

Reviewed reference factors

OpenStax Introductory Statistics 2e

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