This web page allows you to convert the different curvature units and answers the following questions in particular: What are units of curvature used to measure? When were the first units of curvature developed and what were they called? What are the different units of curvature commonly used in modern engineering? What are some reference or record values in different units of measurements of curvature? How do you convert units of curvature from one unit to another?
Units of curvature are used to measure the bending, or curvature, of a line when it has a non-zero line integral or length. This can be measured quantitatively, as in mathematical calculus, or as an estimated value. Different units of curvature are used, depending on how the curve is measured or how it is being applied.
The first units of curvature were developed by mathematicians and physicists during the 18th century. The unit of curvature in this period was called ‘radius’, though this had little to do with any real-world measurements.
The first use of the term ‘radius’ as a measure of curvature in the real world came in the 19th century when Jean-Victor Marie Poncelet proposed the term in his ‘Analytical Mechanics of Gears and Chains’. During the 20th century, various units of curvature have been developed and are still in use today.
The most commonly used units in modern engineering, such as those related to circular and elliptical gears, are:
Other units, such as microradians, nanoradians, and arcseconds, are used in astronomy and geodesy. These units are less commonly used in engineering.
The following are some reference or record values in the different units of measurements of curvature:
Converting the different curvature units is relatively straightforward. To convert from one unit of curvature to another, you simply need to multiply by the respective conversion factor. For example, if you are converting from degrees per meter to radians per meter, you would multiply by the conversion factor of 0.017453. Similarly, to convert from meter inverse to cycles per meter, you would multiply by the conversion factor of 2π.