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Angle Between Two Planar Vectors

Online angle between two planar vectors. Nonzero two-dimensional vectors; angle from zero to 180 degrees.

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angle between two planar vectors calculator online

Use angle between two planar vectors online for ax, ay, bx, by. Nonzero two-dimensional vectors; angle from zero to 180 degrees. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.

How to use it

Enter ax. Set ay, bx, by. Select Calculate and check the labeled output. Copy or download the JSON result.

Options and example settings

OptionChoices / valueExample default
axMain input. Signed finite values. 1
ayOption. Signed finite values. 0
bxOption. Signed finite values. 1
byOption. Signed finite values. 1

Calculation method

angle_deg = acosd(max(-1,min(1,(ax*bx+ay*by)/(positive(hypot(ax,ay))*positive(hypot(bx,by)))))) (^ means exponentiation; trig functions ending in d use degrees).

Worked examples

Apply angle between two planar vectors to the case below, keeping the displayed units and assumptions. Nonzero two-dimensional vectors; angle from zero to 180 degrees.

Angle Between Two Planar Vectors — worked case

Settings: ay: 0; bx: 1; by: 1

Input:

1

Calculated result for these inputs:

Output:

{
  "angle_deg": 45.00000000000001
}

Choose the right tool

Choose number theory for exact integer relationships, distribution tools for a declared random model, and geometry tools for coordinates. A density is not a probability and a statistical model does not establish a real-world outcome.

Limitations and common mistakes

  • Nonzero two-dimensional vectors; angle from zero to 180 degrees. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.
  • Use the displayed unit in every field. Ratios and percentages are different inputs; percent fields use values such as 25 rather than 0.25.

Frequently asked questions

How can I use angle between two planar vectors calculator online?

Enter ax. Set ay, bx, by. Select Calculate and check the labeled output. Copy or download the JSON result.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.

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