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

Circuit sandbox

A circuit simulator. Run Circuit sandbox it in English or en Español.
Can you help translate Circuit Sandbox into other languages? Write to me at willy@spinningnumbers.org.


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.


Here’s a list of everything on Spinning Numbers. Topic areas, articles, videos, images, etc.

Where does the name Spinning Numbers come from?

These videos and articles began as my contribution to Khan Academy where I was the Electrical Engineering Content Fellow in 2016. In the past year all the articles you find here have been significantly improved. I hope you enjoy them.
- Willy McAllister