Welcome to Spinning Numbers. Learn about electricity and electrical engineering.

New — Circuit Sandbox is now available in italiano (September 2023).


Become familiar with the most important electrical quantities: charge, current, and voltage.

News: The definition of the Ampere changed in 2019.

Circuit elements

Circuits are made of resistors, capacitors, inductors, and power sources.

Resistor circuits

Resistors in series and parallel, the voltage divider, delta-wye resistor networks.

DC circuit analysis

Kirchhoff’s Laws, node voltage method, mesh and loop current methods.

Special topics in DC analysis

Linearity and superposition. Source transformation. Thévenin and Norton equivalents.

Natural and forced response

Capacitor and inductor $i$-$v$ equations. Natural response is what a circuit does with its internal stored energy. Forced response is due to energy applied from outside.

AC circuit analysis

If we limit signals to only sine waves, we get AC analysis based on complex exponentials.

Special topics in AC analysis

Decibels and RMS.


The operational amplifier is the building block of analog electronics.


Using a diode in a circuit.


Electric force is described by Coulomb’s Law. Electric field. Formal definition of voltage.

Digital electronics

Basic concepts underlying digital hardware design.


Basic concepts of signal processing. Properties of sine waves. (under development)

Circuit sandbox simulator

circuit sandbox Circuit Sandbox simulator with selectable language,

English Español Italiano Português

Can you help translate Circuit Sandbox into other languages? It’s easy!

Rarely asked questions

A collection of amusing, interesting, (and possibly useful), engineering questions.

What’s with the name?

Where does the name Spinning Numbers come from?


Tips on the best way to print articles from Spinning Numbers.


List of everything on Spinning Numbers—topics, articles, videos, images, and on and on.


These videos and articles began at Khan Academy where I had the honor of being the Electrical Engineering Content Fellow in 2016. The concepts are explained at the level of an undergraduate EE student. Motivated middle school and high school students can get a lot from the course.

Spinning Numbers web site came to life in 2016 after I completed my fellowship at KA. All the articles have been reviewed and significantly improved, and several new articles have made their appearance. A nice new feature is the Circuit Sandbox simulator. Many articles include simulation models to let you try your test your understanding and bring the concepts to life.

Good luck on your journey into electronics and electrical engineering. Please leave a comment if you enjoy your visit, and ask questions. I’m here to help.

- Willy McAllister