Angle Between Two Vectors Calculator
Calculate the angle between two 2D or 3D vectors from their dot product.
The same formula powers search engines
Cosine similarity — the cosine value above, before the arccos — is how text documents are compared once they are turned into vectors of word frequencies. Two documents about the same subject point in similar directions regardless of length, which is exactly the property that makes the measure useful.
The formula
cos θ = (a · b) / (|a| · |b|)
Every result on this page comes from this formula. Nothing is rounded until the final display, so figures match a spreadsheet to the cent.
How to use the Angle Between Two Vectors Calculator
- Fill in each field with your own figures — the defaults are only there as an example.
- The result updates as you type, so there is no button to press.
- Check the breakdown under the main result for the supporting numbers.
- Use the copy button to take the result with you, or share the link to reload the same inputs.
Angle Between Two Vectors Calculator — frequently asked questions
Is this angle between two vectors calculator free to use?
Yes. Every calculator on the site is free, needs no sign-up, and runs entirely in your browser, so your figures never leave your device.
How accurate is the result?
The maths is exact for the formula shown on the page. Accuracy in the real world depends on your inputs and on assumptions the formula cannot see, so treat the output as a well-grounded estimate rather than a quote.
Can I use it on my phone?
Yes. The page is responsive, weighs a few kilobytes and works offline once loaded, so it behaves the same on a phone as on a desktop.
What people search for
This page answers each of these searches. They are the exact phrases visitors use to find the angle between two vectors calculator.
- angle between two vectors calculator
- 3d vector angle
- cosine similarity calculator
- dot product angle
- vector angle calculator
- angle between two vectors
About this calculator
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes.
Last reviewed August 23, 2026 · Calculation runs client-side · No data collected · Report an error