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

Breaking News: May 20, 2019 — The definition of the Ampere has changed! It is now based on the charge of the electron rather than a force measurement.
Define the standard electrical units

Circuit sandbox simulator circuit sandbox

Circuit sandbox in English, en español, 用简体中文 (Chinese), 日本語で (Japanese).
Can you help translate Circuit Sandbox into other languages? It’s easy!


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

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

Natural response is what a circuit does with its own internal stored energy.

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.

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.

External resources

Glossary of electrical terms

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.

I set up this Spinning Numbers web site after completing my KA fellowship. I’ve reviewed and significantly improved all the articles, and added several new articles. A nice new feature is the Circuit Sandbox simulator. You will find simulation models included in most articles, to let you try your hand and bring the concepts to life.

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

- Willy McAllister