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Angle Between Two Vectors Calculator

θ = arccos(a·b / (|a||b|)) in 2D or 3D, in degrees and radians, with the dot product, both magnitudes, the projections and a parallel / perpendicular / acute / obtuse verdict.

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Open Angle Between Two Vectors Calculator and you get an answer straight away, with no account to create. You will find it under Matrices & vectors, with Distance between two points and Angle Bisector Calculator (triangle) for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Angle Between Two Vectors Calculator?

θ = arccos(a·b / (|a||b|)) in 2D or 3D, in degrees and radians, with the dot product, both magnitudes, the projections and a parallel / perpendicular / acute / obtuse verdict.

When would I actually use this?

Checking a decomposition done by hand, solving a linear system, and finding the eigenvalues that describe how a transformation stretches space.

What is the most common mistake?

Inverting a matrix to solve a system. Elimination or a factorisation is both faster and far more stable numerically; an explicit inverse amplifies rounding error, especially when the matrix is close to singular.

How is Angle Between Two Vectors Calculator different from Distance between two points?

They sit next to each other but answer different questions: Distance between two points is the one to open when you need it to compute the straight-line distance between two points on a plane. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Angle Bisector Calculator (triangle) is the closest one after this: Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.

What else is worth having open alongside it?

Column Space Calculator (basis of Col(A), rank, pivot columns) and Cramer's Rule Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The decompositions follow their textbook definitions with partial pivoting where it applies. Results are exact for small integer matrices and subject to floating-point rounding otherwise.

Further reading

All guides →
How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.