Mathematical modelling and computer-based tools

Mathematics is needed in all aspects of product designing, and being able to model a project on screen can help work out information before production.


Spreadsheets are a good way of organising collected data about a product. They give the user the ability to manipulate data, eg adding, sorting and numbering data, to be able to present a design to a client. Results of testing, cost of materials, opinions of user groups and product orders all offer data that can be entered into a spreadsheet to be used repeatedly in making decisions or producing evidence to support a hypothesis.

Presentation tools

Information collated onto a spreadsheet can then be entered onto graphs or charts to provide a visual and easy to understand guide to show clients information.

A businesswoman giving a presentation to five people sat around a table with tablets.


A database is an organised collection of data that can be accessed by designers to collect information relevant to their designs. There are databases available to access ergonomic and anthropometric data for millions of measurements, which saves a designer the time and resources of having to create their own database.

CAD modelling

When a computer aided design (CAD) drawing has been made, a product can be shown from all angles on screen, and colour, materials and components can be quickly changed. This allows designers to discover aspects of the product, eg the most economical way of cutting a material or how stresses and loads will perform on it, without costly physical modelling. Ideas can also be shared quickly around the world using the Internet.

A man in a suit working at a computer on computer aided design (CAD) in an office.

CAM modelling

Computer aided manufacture (CAM) can help produce full-size or to scale 3D models of a product. A designer can create the design in CAM, or input an existing 2D CAD drawing. The coordinates are automatically generated and use X, Y and Z values to build a model on a 3D printer, using points on an invisible grid.

X, Y and Z coordinates

All drawings start from the ‘origin’, which is the point where x and y meet.

As x increases, the point on the axis moves further away from where x and y meet, and when x decreases, the point moves back towards the intersection. As y increases, the point moves further up, away from the x and y meeting point, and when y decreases, the point moves down again.

x and y axis, showing where two lines, x and y meet and move away from each other.

An x and y coordinate creates a point on a 2D grid that can be used on machines, such as a laser cutter, that only cut flat materials. A z coordinate is added to make the point become 3D and can be used to build objects on machines such as a 3D printer.

Cube with x, y and z coordinates, showing where 3 lines meet and move away from each other.