Lay a line across two scales. Read the third.
A nomogram is a chart that computes. Each scale stands for one quantity in a formula, and any straight line that crosses them all lands on values that satisfy it. For about seventy-five years they did quick, accurate arithmetic in engineering offices, pharmacies and aircraft cockpits. Then pocket calculators arrived.
This site draws them again, one formula to a sheet, and works them in the browser: drag a ring and the red line, the index line, moves with it. The claim of the site is that the old instrument is still the better way to understand a formula, if not to compute one. A calculator gives the answer and hides the shape. A nomogram prints the shape. Where its ticks crowd together the formula is slack; where they spread apart it is sensitive; where two scales stand tells you how the inputs trade off. Each sheet comes with remarks on what its scales show.
Drawing register
| No. | Sheet | Computes | Scales |
|---|---|---|---|
| 01 | Dew point | The temperature at which dew forms, from air temperature and humidity. Why a simple rule of thumb holds in moist air and fails in dry. | Three parallel, sum form |
| 02 | Body surface area, two ways | Skin area from weight and height, by a 1916 formula built on nine people and a 2000 refit of the same paper’s data, read with one line. | Three parallel, logarithmic, middle scale doubled |
The name
The index line, also called the isopleth, is the line a straightedge makes when you lay it across a nomogram. Here it is a red stroke. The French engineer Maurice d’Ocagne is credited with inventing nomography in 1884. Everything else on one of his sheets is printed once and never changes; the index line is the only part that moves.
Source: “Nomogram,” Wikipedia, for d’Ocagne and 1884, the seventy-five years, the fields of use, and the terms index line and isopleth.