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Abstract We exhibit a theoretical calculation of the parameter $$\beta $$ β appearing in the generalized uncertainty principle (GUP) with only a quadratic term in the momentum. A specific numerical value is obtained by comparing the GUP-deformed Unruh temperature with the one predicted within the framework of Caianiello’s theory of maximal acceleration. The physical meaning of this result is discussed in connection with constraints on $$\beta $$ β previously fixed via both theoretical and experimental approaches.