The** Work (dot product)** calculator uses the equation, W= F⋅d, to computes the work done when a force (F) is applied to move a mass some displacement (d).

INSTRUCTIONS: Choose the preferred units and enter the following:

- (`F_x`) - This is the force applied in the x direction
- (`F_y`) - This is the force applied in the y direction
- (`F_z`) - This is the force applied in the z direction
- (`d_x`) - This is the distance the mass is moved in the x direction
- (`d_y`) - This is the distance the mass is moved in the y direction
- (`d_z`) - This is the distance the mass is moved in the z direction

**Work (w)**: The calculator returns the work in Newton meters (N•m). However, this can be automatically converted to compatible units via the pull-down menu.

### The Math / Science

This specific work calculator is an example of using the dot product. The dot product is used to multiply two vectors and output a scalar quanitity. Since force and displacement are vectors, and work is the multiplication of those two vectors, we are left with using the dot product! The dot product simply examines vectors in their specific cartesian directions, and then multiplies like terms to get a new vector in the appropriate direction. It is a powerful tool and is used commonly in Vector Calculus and Physics.

### Related Calculators:

### References:

Light and Matter Textbook Chapter 13.7