Math & Algebra Tool
Dot Product Calculator
Calculate the scalar product of two vectors in 2D or 3D space.
x
y
z
x
y
z
Scalar Result (A · B)
0
Σ The Formula
A · B = ∑ (A_i × B_i)
Real World Examples
2D Vectors
[2, 3] · [4, -1] = (2×4) + (3×-1) = 5.
Orthogonal Vectors
[1, 0] · [0, 1] = 0 (means they are perpendicular).
# About This Calculator
The Dot Product (or scalar product) is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.
It is fundamental to physics and engineering for:
- Calculating work (Force · Displacement).
- Determining the angle between two vectors.
- Projecting one vector onto another.
How To Use
- Choose the **Dimension** of your vectors (2 or 3).
- Enter the components for **Vector A**.
- Enter the components for **Vector B**.
- The **Dot Product** scalar value is calculated instantly.
Frequently Asked Questions
What does it mean if the dot product is zero?+
If the dot product of two non-zero vectors is zero, it means the vectors are orthogonal (perpendicular) to each other.
Is dot product the same as cross product?+
No. Dot product results in a scalar (a single number), while cross product results in a vector (a direction in 3D space).
Is Dot Product Calculator free to use?+
Yes, Dot Product Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.
How accurate is Dot Product Calculator?+
We use standard mathematical formulas and high-precision computing algorithms to ensure results for Dot Product Calculator are accurate for academic and professional use.
Can I use Dot Product Calculator on my phone?+
Yes! Dot Product Calculator is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.
Do you save my data?+
No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.