Nomogram

TL;DR

• A nomogram is a graphical calculator that maps input variables to an output value using aligned scales.
• It speeds routine calculations in fields like engineering, medicine, and finance by replacing arithmetic with a visual alignment.
• Accuracy depends on the data and assumptions used to create the nomogram; it may not replace more detailed calculations when required.

Definition

A nomogram is a graphical tool that allows for the rapid calculation of a specific value based on a set of input variables.

Explanation

Nomograms display one or more input variable scales plotted on a graph alongside an output scale. A user locates the values for the input variables on their respective scales and draws (or visualizes) a line connecting those points. The intersection of that line with the output scale provides the calculated value without performing algebraic computation. They are commonly applied where calculations must be performed quickly and repeatedly.

Examples

Body Mass Index (BMI) nomogram

This nomogram determines an individual’s BMI, a measure of body fat based on height and weight. The nomogram consists of two scales, one for height and one for weight, plotted on a graph. The user inputs their height and weight on the respective scales and draws a line connecting the two points. The line intersects with a third scale, which represents the BMI. By reading the BMI value at the intersection of the line, the user can determine their BMI without performing calculations.

Friction Factor nomogram

This nomogram is used in engineering to calculate the friction factor, which measures resistance to flow in a pipe or conduit. The nomogram consists of three scales: one for the Reynolds number, one for the roughness coefficient, and one for the friction factor. The user inputs the Reynolds number and roughness coefficient on their scales and draws a line connecting those points. The line intersects the friction factor scale, allowing the user to determine the friction factor without calculations.

Use cases

• Rapid routine calculations in engineering, medicine, and finance.
• Situations where quick visual determination of a value from multiple inputs reduces time and error.

Notes or pitfalls

• Nomograms are only as accurate as the data and assumptions used to create them.
• They should not be used as a substitute for more detailed calculations in situations that require higher precision or where underlying assumptions may not hold.

Related terms

• Body mass index (BMI)
• Reynolds number
• Roughness coefficient
• Friction factor
• Scale (graphical)