Vector Angle Calculator
Calculate the angle between two equal-dimensional vectors.
How the vector angle calculator works
The included angle between two vectors comes from dividing their dot product by the product of their magnitudes. That ratio is the cosine of the angle and removes differences in vector length. This calculator accepts any equal dimension, computes the dot product and both lengths, clamps tiny floating-point overshoots to the valid cosine range, and converts the inverse cosine to degrees.
The default vectors 1, 0 and 0, 1 have dot product zero and both magnitudes equal one. Their cosine is therefore zero, and the verified angle is 90 degrees. This matches the coordinate-plane picture of the positive x and y axes. Identical nonzero vectors would instead have cosine one and angle zero.
Reading vector angle calculator results privately
A zero vector has no direction, so its angle with another vector is undefined and is rejected. Both vectors must have the same number of finite components. The reported angle lies from zero through 180 degrees and does not encode clockwise orientation. Near-parallel decimal data may be limited by ordinary floating-point precision. This vector angle calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why divide the dot product by both magnitudes?
Normalization removes vector length, leaving only directional alignment as a cosine between minus one and one.
Why is the angle undefined for a zero vector?
A zero vector has magnitude zero and no direction, so the normalization would divide by zero.
Is the vector angle calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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