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'''Shape factors''' are [[dimensionless quantity|dimensionless quantities]] used in [[image analysis]] and [[microscopy]] that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured [[dimension]]s, such as [[diameter]], [[Chord (geometry)|chord]] lengths, [[area]], [[perimeter]], [[centroid]], [[Moment (mathematics)|moments]], etc. The dimensions of the particles are usually [[Measure (mathematics)|measured]] from two-dimensional [[Cross section (geometry)|cross-sections]] or [[Orthographic projection|projections]], as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a [[Metallography|metallurgical]] or [[Ceramography|ceramic microstructure]], or the microorganisms in a [[Microbiological culture|culture]], for example. The dimensionless quantities often represent the degree of [[Deviation (statistics)|deviation]] from an ideal shape, such as a [[Roundness (object)|circle]], sphere or equilateral [[polyhedron]].<ref>L. Wojnar & K.J. Kurzydłowski, et al., ''Practical Guide to Image Analysis'', [[ASM International (society)|ASM International]], 2000, p 157-160, {{ISBN|0-87170-688-1}}.</ref> Shape factors are often ''normalized'', that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube.
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==An application of shape factors==
[[Greenland]], the largest island in the world, has an area of 2,166,086 km<sup>2</sup>; a coastline (perimeter) of 39,330 km; a
:<math>A_R = \frac{1290}{2670} = 0.483</math>
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