homechevron_rightStudychevron_rightMathchevron_rightGeometry

# Angle between two vectors

This online calculator finds the angle between two vectors This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8249/. Also, please do not modify any references to the original work (if any) contained in this content.

This calculator finds the angle between two vectors given their coordinates. The formula and the explanation can be found below the calculator. Angle

### Finding the angle between two vectors

We will use the geometric definition of the Dot product to produce the formula for finding the angle.

Geometrically the dot product is defined as

thus, we can find the angle as

To find the dot product from vector coordinates, we can use its algebraic definition.

Thus, for two vectors, and , formula can be written as

This is the formula used by the calculator.

URL copied to clipboard

#### Similar calculators PLANETCALC, Angle between two vectors