➡️Vector Calculator
2D and 3D vector operations with steps and a visualization.
Vector u
Vector v
Free Vector Calculator
Perform any common vector operation with our free vector calculator. Enter two 2D or 3D vectors and instantly get their sum, difference, dot product, cross product (3D), magnitudes, unit vectors, and the angle between them — all with step-by-step working shown.
A live 2D visualization plots your vectors as arrows from the origin, with the result vector overlaid for addition and subtraction, so you can see the geometry, not just the numbers. The angle between vectors is computed via the dot-product formula and shown in both degrees and radians, with the zero-vector edge case handled explicitly rather than crashing.
Whether you're studying physics, engineering, or linear algebra, get accurate vector arithmetic with the reasoning shown. No sign-up, no downloads required.
About the Vector Calculator
Features
2D and 3D modes
Toggle dimensions; cross product available only in 3D.
Full operation set
Sum, difference, dot and cross product, magnitude, and unit vectors.
Angle between vectors
Computed via the dot-product formula, with the zero-vector case handled explicitly.
2D visualization
Vectors and their sum plotted as arrows from the origin.
Frequently Asked Questions
What operations are supported?
Addition, subtraction, scalar multiplication, dot product, cross product (3D), magnitude, unit vector, and angle between vectors.
Does it support 2D and 3D vectors?
Yes, toggle between them; cross product is only available in 3D since it's undefined in 2D.
How is the angle between vectors calculated?
Using cos θ = (u·v)/(|u||v|), then taking the inverse cosine — shown in both degrees and radians.
What if one vector is the zero vector?
The angle is undefined in that case, and the tool flags this clearly rather than dividing by zero.
Does it show a visualization?
Yes, a 2D plot shows both vectors as arrows from the origin, plus the sum vector.
Does it show the steps?
Yes, component-wise arithmetic and the cross-product determinant expansion are shown.
What is a unit vector?
A vector with the same direction but magnitude 1, computed as v / |v| — shown for both input vectors.
Are results shown as fractions or decimals?
Decimal values rounded to a sensible precision.
Is it free?
Completely free, no sign-up or limits.
Does it work on mobile?
Yes, fully responsive.