Dot Product Calculator
Enter two vectors of equal length and instantly get their dot product with a full step-by-step breakdown.
Vector Inputs
3
(2 – 10)
Enter vectors on the left and click Calculate
Dot Product (A · B)
These vectors are orthogonal (perpendicular to each other).
Step-by-Step Breakdown
A · B = Σ aᵢ × bᵢ
Sum (dot product)
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Summary
Enter two vectors of equal length and instantly get their dot product with a full step-by-step breakdown.
How it works
- Enter the number of dimensions (2D, 3D, or a custom size up to 10).
- Type the components of Vector A and Vector B into the input fields.
- Click "Calculate" or press Enter to compute the dot product.
- The result panel shows each component product and their sum.
- Use the "Copy Result" button to copy the final scalar value.
Use cases
- Check work on linear algebra homework involving vector projections.
- Verify dot products used in physics for work done by a force (W = F · d).
- Compute similarity scores between feature vectors in machine learning.
- Check orthogonality: a dot product of zero means the vectors are perpendicular.
- Evaluate lighting equations in 3D graphics (normal · light direction).
- Confirm angle calculations between two vectors in geometry.
- Debug matrix-vector multiplication one row at a time.
- Explore properties of inner products in a numerical way.
Frequently Asked Questions
Last updated: 2026-06-11 ·
Reviewed by Nham Vu