Impact testing of pedestrian headforms is usually conducted at one velocity and with one mass of headform, but real impacts occur at a range of velocities and masses. A method is proposed to predict the Head Injury Criterion (HIC) and similar quantities at other velocities from their values observed under test conditions. A specific assumption is made about acceleration during the impact as related to displacement, its differential (instantaneous velocity), mass of headform, and initial velocity: namely, that it is the product of a power function of displacement (representing a possibly nonlinear spring) and a term that includes a type of damping. This equation is not solved, but some properties of the solution are obtained: HIC, maximum acceleration, and maximum displacement are found to be power functions of mass of headform and initial velocity. Expressions for the exponents are obtained in terms of the nonlinearity parameter of the spring. Simple formulae are obtained for the dependence of HIC, maximum acceleration, and maximum displacement on velocity and mass. These are relevant to many types of impact.