Math

Free Dot Product Calculator

Dot product and angle between two 2D vectors.

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Inputs

Result

Dot product

5.0000

Angle between vectors70.35°
Orthogonal?No

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Short answer

Dot product and angle between two 2D vectors.

What is the Dot Product Calculator?

Dot product and angle between two 2D vectors.

How does the Dot Product Calculator work?

Enter the inputs above and read the result.

Formula

a·b = x1x2 + y1y2 = |a||b|cos(θ)

Variables

  • θAngle between the vectors

Explanation

The dot product measures how much two vectors point in the same direction.

Examples

Applications

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          Tips

            Related concepts

            The Dot Product Calculator sits inside the Math Calculators hub, in the geometry & shapes cluster. Length, area, volume and angle in two and three dimensions. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            areaperimetervolumesurface areaanglecoordinate plane

            Practical use cases and industry applications

            Understanding Dot Product

            Dot product and angle between two 2D vectors. Within math calculators, dot product belongs to the geometry & shapes cluster, where it shares terminology and assumptions with closely related tools.

            Learning how dot product is calculated

            The dot product measures how much two vectors point in the same direction. Working through the variables one at a time — θ — makes the result reproducible by hand and easier to sanity-check.

            Using dot product to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How dot product compares with related measures

            area, perimeter, volume, surface area all describe adjacent aspects of geometry & shapes. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

            Related calculators

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