Math

Free Vector Addition & Magnitude Calculator

Add two 2D vectors and find the resultant magnitude.

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Inputs

Result

Resultant vector

(4.000, 2.000)

Magnitude4.4721
Direction26.57°

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Short answer

Add two 2D vectors and find the resultant magnitude.

What is the Vector Addition & Magnitude Calculator?

Add two 2D vectors and find the resultant magnitude.

How does the Vector Addition & Magnitude Calculator work?

Enter the inputs above and read the result.

Formula

R = (x1+x2, y1+y2), |R| = √(Rx² + Ry²)

Variables

  • RResultant vector

Explanation

Vectors add component-wise; the magnitude follows from the Pythagorean theorem.

Examples

Applications

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          Tips

            Related concepts

            The Vector Addition & Magnitude 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 Vector Addition & Magnitude

            Add two 2D vectors and find the resultant magnitude. Within math calculators, vector addition & magnitude belongs to the geometry & shapes cluster, where it shares terminology and assumptions with closely related tools.

            Learning how vector addition & magnitude is calculated

            Vectors add component-wise; the magnitude follows from the Pythagorean theorem. Working through the variables one at a time — R — makes the result reproducible by hand and easier to sanity-check.

            Using vector addition & magnitude to make a decision

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

            How vector addition & magnitude 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

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