Vector Addition Calculator with Graph

Add two or three vectors with flexible inputs. See components, magnitude, angle, and direction instantly. Plot every vector and review clean downloadable summaries easily.

Calculator Inputs

Use components or magnitude-angle inputs. Angles are measured counterclockwise from the positive x-axis.

This label appears beside component and magnitude values.
Choose between 1 and 6 decimal places.
Active vectors are added together. Use Vector 3 when needed.

Vector 1

Vector 2

Vector 3

Reset Form

Interactive Vector Graph

The graph plots each selected vector from the origin and highlights the resultant vector.

Example Data Table

This example shows three vectors and their combined resultant.

Vector Input Mode X Y Magnitude Angle (°)
Vector 1 Components 3.000 4.000 5.000 53.130
Vector 2 Magnitude + Angle 5.196 3.000 6.000 30.000
Vector 3 Components -1.000 2.000 2.236 116.565
Resultant Sum 7.196 9.000 11.524 51.360

Formula Used

For component inputs: The vector is already given as (x, y).

For magnitude-angle inputs: x = r cos(θ), y = r sin(θ)

Resultant components: Rx = Σx, Ry = Σy

Resultant magnitude: |R| = √(Rx2 + Ry2)

Resultant angle: θ = atan2(Ry, Rx)

Angles are displayed in degrees and measured counterclockwise from the positive x-axis.

How to Use This Calculator

  1. Select at least two vectors using the Include checkboxes.
  2. Enter a label for each active vector.
  3. Choose either component mode or magnitude-angle mode.
  4. Type the known values for each vector.
  5. Set the number of decimal places you want.
  6. Press Calculate Vectors to see the result above the form.
  7. Review the graph, summary cards, and detailed results table.
  8. Use the CSV or PDF buttons to download your results.

FAQs

1) What is vector addition?

Vector addition combines two or more vectors into one resultant vector. The calculator adds x-components and y-components, then computes the final magnitude and direction.

2) Can I mix component inputs with magnitude-angle inputs?

Yes. Each vector can use its own input mode. The calculator converts all active vectors into x and y components before adding them.

3) How is the angle measured?

The angle is measured in degrees from the positive x-axis. Positive rotation moves counterclockwise, which matches the usual coordinate-plane convention in mathematics.

4) What do negative components mean?

A negative x-component points left. A negative y-component points downward. Negative values simply describe direction within the coordinate plane.

5) What is the equilibrant?

The equilibrant has the same magnitude as the resultant but points in the opposite direction. It would balance the vector sum perfectly.

6) Why does the calculator use atan2?

atan2 determines the correct quadrant for the resultant angle. That makes the direction more reliable than using a basic inverse tangent alone.

7) Can I add three vectors here?

Yes. Vectors 1 and 2 are ready by default, and Vector 3 can be included anytime. The graph updates to show every active vector.

8) What does the graph show?

The graph plots each chosen vector from the origin and draws the resultant vector too. This makes the combined direction and size easier to interpret visually.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.