2D Vector Calculator — Add, Dot Product & Angle
Quick answer: Enter two 2D vectors to compute dot product, magnitudes, angle between them, sum, difference, and cross magnitude.
Perform all essential 2D vector operations: addition, subtraction, dot product, cross product magnitude, individual magnitudes, angle between vectors, and scalar projection. Enter two vectors A and B as (x, y) components.
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Last reviewed: April 2026Report an error
Vector A = (ax, ay)
Vector B = (bx, by)
Dot Product
11
A·B = 11. |A| = 5, |B| = 2.236068. Angle between: 10.3048°.
|A| Magnitude
5
|B| Magnitude
2.236068
Dot Product A·B
11
Angle Between
10.3048°
A + B
(4, 6)
A − B
(2, 2)
|A×B| Cross Mag
2
Scalar Proj A→B
4.91935
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How to Use This Vector Calculator Calculator
- 1Enter the x and y components of Vector A.
- 2Enter the x and y components of Vector B.
- 3Read all operations: dot product, magnitudes, angle, sum, difference, and cross product magnitude.
Frequently Asked Questions
- A·B = ax×bx + ay×by. It equals |A||B|cos(θ). If A·B = 0, the vectors are perpendicular.
- |A| = √(ax² + ay²). It is the length of the vector, equivalent to the Pythagorean theorem.
- θ = arccos(A·B / (|A||B|)). If the dot product is positive, the angle is acute (<90°). If negative, obtuse (>90°).
- A + B = (ax+bx, ay+by). Add corresponding components.
- The 2D cross product magnitude |A×B| = |ax×by − ay×bx|. It equals |A||B|sin(θ) and represents the area of the parallelogram formed by A and B.
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