Math

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Vector Addition Calculator.

Add two three-dimensional vectors and calculate the result magnitude.

On-device calculationNo signup
01

Set your values

Results update as you type.

x: 5

x

0.000000
y: 7

y

0.000000
z: 9

z

0.000000
Magnitude: 12.4499

Magnitude

0.000000

Results update automatically as you type.

Use Cases

Physics: Net Force or Displacement

Combine two force vectors or displacement vectors in 3D space to find the resultant vector, useful in mechanics and kinematics problems.

Example: Add force A (3, -2, 5) N and force B (1, 4, -2) N to get resultant (4, 2, 3) N.

Engineering: Structural Analysis

Sum load vectors or reaction forces acting on a structure to determine the net effect, aiding in design and stability checks.

Example: Combine wind load (0, 0, -100) and weight (0, -500, 0) to get net force.

Frequently Asked Questions

How does the vector addition calculator work?
It adds corresponding components of two 3D vectors: the x-components (Aₓ and Bₓ), y-components (Aᵧ and Bᵧ), and z-components (A_z and B_z). The result is a new vector with those sums, computed instantly using a deterministic formula.
What fields do I need to fill in?
You need to enter the three components of vector A (Aₓ, Aᵧ, A_z) and the three components of vector B (Bₓ, Bᵧ, B_z). All fields are required for a complete 3D addition.
Can I use this calculator for 2D vectors?
Yes, you can set the z-components (A_z and B_z) to zero. The calculator will then add the x and y components as usual, effectively handling 2D vectors in the xy-plane.

Tips & Common Mistakes

Tips

  • Double-check the signs of your components: negative values are allowed and affect the direction of the resultant vector.
  • If you only need 2D addition, set the z-components (A_z and B_z) to zero.
  • Use consistent units for all components (e.g., all in meters or all in newtons) to get a meaningful result.
  • After getting the resultant, you can verify by adding the components manually to ensure accuracy.

Common Mistakes to Avoid

  • Forgetting to enter all six components – leaving a field blank may cause an error or incomplete result.
  • Mixing up the order of components: ensure you enter Aₓ, Aᵧ, A_z for vector A and Bₓ, Bᵧ, B_z for vector B.
  • Using different units for different components, which leads to an incorrect resultant vector.

Last updated: August 13, 2026