Add multiple 2D or 3D vectors component-wise and find the resultant vector with magnitude.
Last updated
Dimensions
Vector 1
Vector 2
Component-wise addition
Each component of the result equals the sum of the corresponding components across all input vectors.
Magnitude from Pythagoras
The magnitude of the resultant vector is the square root of the sum of its squared components.
Result
The resultant of 2 vectors has magnitude 7.2111.
Step-by-step
Interpretation
The resultant vector represents the net displacement or force when all input vectors are combined tip-to-tail.
Linear Algebra
A vector addition calculator adds two or more vectors by summing their corresponding components. It returns the resultant vector and its magnitude.
To add vectors, sum each component separately: (a₁+b₁, a₂+b₂, a₃+b₃). This works for any number of vectors.
The resultant vector represents the combined effect of all input vectors. Its magnitude is found using the standard distance formula.
R = v₁ + v₂ + ... + vₙ
Component-wise vector addition. This is the specific relationship the calculator applies when building the result.
A worked example helps translate the vector addition calculator maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
Use the vector addition calculator output as a planning aid, then compare it with the assumptions, units, and caveats shown elsewhere on the page before acting on the number alone.
That extra interpretation step matters because a calculator can simplify the arithmetic but still cannot replace real-world context such as local rules, contract terms, or individual circumstances.
Frequently asked questions
Yes — the order of addition does not matter. v₁ + v₂ = v₂ + v₁.
No — all vectors must have the same number of dimensions to be added.
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
Also in Linear Algebra
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Subtract two vectors component-wise in 2D or 3D, with magnitude and step-by-step work.
Perform vector operations including addition, subtraction, dot product, cross product, and scalar multiplication.
Calculate the magnitude of a 2D or 3D vector with squared magnitude, unit vector, and direction angles.
Use this dot product calculator to compute the scalar product of 2D or 3D vectors, angle between vectors, cosine similarity, orthogonality, scalar projection.
