Welcome to Spinning Numbers! Learn about electricity and electrical engineering, explained at the level of an undergraduate EE student.

Circuit sandbox

Circuit sandbox is a simulator. Run it in English, o en español, 或简体中文 (Chinese).
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.


The operational amplifier is the building block of analog electronics.


Using a diode in a circuit.


The force between charged objects is described by Coulomb’s Law.


A list of everything on Spinning Numbers. Topics, articles, videos, images, and on and on.

Where does the name Spinning Numbers come from?

These videos and articles began at Khan Academy where I was the Electrical Engineering Content Fellow in 2016. Since completing my fellowship, I set up this web site and so far have reviewed and significantly improved all the articles. There are several new articles as well. A nice new feature of Spinning Numbers is the circuit simulator. Most articles include simulation models of the circuits to bring the concepts to life.

I hope this site helps you learn about electronics and electrical engineering.

- Willy McAllister