Soma de Vetores
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
soma por componente
About this calculator
The Vector Addition Calculator performs the sum of two vectors in up to three dimensions (2D or 3D). The user enters the coordinates of each vector (x, y, and optionally z components) and the tool calculates the resulting vector by adding each corresponding component. For example, for vectors u = (u₁, u₂) and v = (v₁, v₂), the sum is u+v = (u₁+v₁, u₂+v₂). The calculator displays the result clearly and also shows the step-by-step calculation.
This tool is useful for students of linear algebra, physics, or engineering who need to solve problems involving displacements, forces, or velocities. For instance, calculating the resultant force on an object or the trajectory of a two-dimensional motion. It is also helpful for professionals working with vectors in computer graphics or data analysis.
Vector addition is simple: just add the corresponding coordinates. However, it is important to ensure that the vectors have the same dimensionality (both 2D or both 3D). The calculator validates this condition and displays an error if the dimensions do not match. Also, remember that vector addition is commutative (u+v = v+u) and associative, properties that can simplify more complex calculations.
Cautions: when entering coordinates, use decimal numbers with a dot (e.g., 3.5) and avoid commas. Make sure all components are correctly filled. For 2D vectors, leave the z field blank or zero. The calculator does not handle vectors of dimension higher than 3, nor does it perform subtraction or dot product (these are features of other tools on the site).
Frequently asked questions
Can I add vectors of different dimensions, like a 2D and a 3D?
No. The calculator requires both vectors to have the same number of components. If one is 2D and the other 3D, an error will appear.
Does the calculator show the step-by-step result?
Yes. In addition to the resulting vector, the tool displays the sum of each individual component (e.g., u₁+v₁, u₂+v₂, u₃+v₃).
Can I use negative numbers or decimals?
Yes. The calculator accepts real numbers, including negatives and decimals. Use a dot (.) as the decimal separator.
What happens if I leave the z field blank for a 3D vector?
If you filled x and y for both vectors but left z empty, the calculator will treat them as 2D vectors. For 3D vectors, fill all components.
Does this calculator work for vector subtraction?
No. It only performs addition. For subtraction, you could add the first vector to the negative of the second (multiply by -1), but this is not implemented automatically.