It is a very simple device, consisting of a rod with its ends bent
at right angles. One end, the tracer point T, is sharpened
to a point, while the other end, C, is sharpened to a chisel edge
parallel to the rod. The chisel edge is usually slightly rounded, making
it look similar to a hatchet, and consequently the device is also known
as a "hatchet planimeter." Prytz referred to it as a "stang planimeter,"
"stang" being Danish for "rod." |

Here is a Prytz planimeter traversing an ellipse.

The tracer point goes around the ellipse. Note that the chisel point does not return to the point where it started. The angle between the initial and final positions of the chisel is roughly proportional to the area of ellipse. The constant of proportionality is the square of the length of the planimeter. The longer the planimeter, the more accurately the area is measured. |

Differential geometers will be interested to know that the Prytz planimeter is a simple example of parallel translation on an S

Animations of Prytz planimeters

How a Prytz planimeter measures area

Differential Geometry Day Presentation

Kalamazoo College presentation

Main Planimeter Page |
Last update 1 August 2001
Robert
Foote |