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circular inch is a unit of area. it uses in Imperial/US system. it exactly equal π⁄4 sq in and approximately ≈ 5.067075 × 10−4 m2
A barn (symbol: b) is a unit of area equal to 10−28 m2 (100 fm2). Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is also used in all fields of high-energy physics to express the cross sections of any scattering process, and is best understood as a measure of the probability of interaction between small particles.