---
title: "Dot Product Calculator — Angle Between Vectors with Steps"
description: "Calculate the dot product (scalar product) of two vectors in 2D, 3D, 4D, or 5D. Shows step-by-step working, angle between vectors, and orthogonality check. Essential for linear algebra, physics, and ML."
url: "https://worldcalculators.org/calculators/dot-product/"
canonical: "https://worldcalculators.org/calculators/dot-product/"
---

# Dot Product Calculator

Calculate the dot product (scalar product) of two vectors in 2D, 3D, 4D, or 5D. Shows step-by-step working, angle between vectors, and orthogonality check. Essential for linear algebra, physics, and ML.

## Quick answer

Vector A

## Frequently Asked Questions

Because the result is always a scalar (a single number), not a vector. This contrasts with the cross product, which produces a vector. "Dot product" refers to the dot notation (A · B), while "scalar product" describes the type of result. Both terms are used interchangeably in UK A-Level and IB curricula.
Yes. Unlike the cross product (which is only defined in 3D and 7D), the dot product generalizes to any dimension: A · B = Σᵢ aᵢbᵢ. This makes it central to machine learning where feature vectors may have thousands of dimensions. In functional analysis, the dot product generalizes to an inner product in infinite-dimensional spaces.

Source: https://worldcalculators.org/calculators/dot-product/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.