The Smith Chart

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The Smith chart was developed by the electrical engineer Phillip H. Smith around 1939. It is a useful graphical aid for matching impedances of circuit elements, to optimize their performance.


In this Demonstration, you can vary the resistance ( in ohms Ω), inductance ( in nanohenries nH=H), and capacitance ( in picofarads pF= F) of the circuit element, as well as the frequency of the propagated signal ( in megahertz MHz=Hz). The complex reduced impedance is then marked on the Smith chart.


Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: reactance equals zero when capacitive and inductive contributions cancel

Snapshot 2: increasing inductive reactance (by increasing or ) gives a clockwise rotation about a red circle contour; increasing capacitive reactance would result in a counterclockwise rotation

Snapshot 3: the circumference of the Smith chart represents a resistance of zero

A more complete, full-scale Smith chart is given on this website. See also: P. H. Smith, Electronic Applications of the Smith Chart in Waveguide: Circuit and Component Analysis, 2nd ed., Raleigh, NC: SciTech Publishing, 2000.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.