In physics, he is known for studying the movement of charged particles in the magnetosphere and the formation of aurorae, and for his book on these subjects, From the Depths of Space to the Heart of the Atom.

In the years 1893-1897, he documented daily life on the streets of Oslo using a miniature CP Stirn spy camera.

[7] For instance it included one of Henrik Ibsen strolling down Karl Johans gate, the main road in Oslo.

[11][12] Størmer's first mathematical publication, published when he was a beginning student at the age of 18, concerned trigonometric series generalizing the Taylor expansion of the arcsine function.

Machin's original formula, is of this type, and Størmer showed that there were three other ways of representing π as a rational combination of two Gregory numbers.

He then investigated combinations of three Gregory numbers, and found 102 representations of π of this form, but was unable to determine whether there might be additional solutions of this type.

In particular, a four-term representation found by Størmer, was used in a record-setting calculation of π to 1,241,100,000,000 decimal digits in 2002 by Yasumasa Kanada.

[16] By modeling the problem using differential equations and polar coordinates, Størmer was able to show that the radius of curvature of any particle's path is proportional to the square of its distance from the sphere's center.

Størmer's work on this subject applies to what are today called the magnetospheric ring current[1] and Van Allen radiation belts.

He measured their heights and latitudes by triangulation from multiple observatories, and showed that the aurora are typically as high as 100 kilometers above ground.

[19][20] Størmer's book, From the Depths of Space to the Heart of the Atom, describing his work in this area, was translated into five different languages from the original Norwegian.

In his review of this book, Canadian astronomer John F. Heard calls Størmer "the acknowledged authority" on aurorae.

[24] The Lie-Størmer Center at UiT - The Arctic University of Norway is named after him In 1902, Størmer was decorated with King Oscar II's Medal of Merit in gold.