Dot Product Calculator
Dot product of 2-D or 3-D vectors, with exact fractions and the working.
Change the values and press Calculate to work out your own figures.
Enter the vector components (leave z blank for 2-D).
Show the working
- a · b = 3 × 1 + 4 × 2 = 11
How to use it
Enter the vector components (leave z blank for 2-D).
Enter coordinates as whole numbers, decimals or fractions (3/4). Show the working gives the formula with your numbers.
Key facts
a · b = a_x b_x + a_y b_y + a_z b_z
Components
Enter the x-, y- and (optionally) z-components; leave z blank for vectors in a plane.
Questions
How is the dot product worked out?
a · b = a_x b_x + a_y b_y + a_z b_z
Can I use fractions?
Yes, such as 1/2 or -3/4.
Formulas
a · b = a_x b_x + a_y b_y + a_z b_z
Sources
Limitations
- Vectors have two or three components (leave z blank for 2-D).
- Earth distances assume the WGS 84 ellipsoid (sea level).