Add multiple 2D or 3D vectors component-wise and find the resultant vector with magnitude.
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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.
Also in Linear Algebra
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.
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.
Related
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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.
Calculate the dot product of two vectors in 2D or 3D, with angle and orthogonality detection.
Compute the cross product of two 3D vectors, with magnitude and direction information.
