We deal with solutions of the Cauchy problem to linear both homogeneous and nonhomogeneous parabolic second-order equations with real constant coefficients in the layer , where and . The homogeneous equation is considered with initial data in , . For the nonhomogeneous equation we suppose that initial function is equal to zero and the function in the right-hand side belongs to , pamp;gt;n + 2 and . Explicit formulas for the sharp coefficients in pointwise estimates for the length of the gradient to solutions to these problems are obtained.