A method and apparatus for determining the caliper and/or the ultrasonic transit time through the thickness direction of a moving web of material using ultrasonic pulses generated by a rotatable wheel ultrasound apparatus. The apparatus includes a first liquid-filled tire and either a second liquid-filled tire forming a nip or a rotatable cylinder that supports a thin moving web of material such as a moving web of paper and forms a nip with the first liquid-filled tire. The components of ultrasonic transit time through the tires and fluid held within the tires may be resolved and separately employed to determine the separate contributions of the two tire thicknesses and the two fluid paths to the total path length that lies between two ultrasonic transducer surfaces contained within the tires in support of caliper measurements. The present invention provides the benefit of obtaining a transit time and caliper measurement at any point in time as a specimen passes through the nip of rotating tires and eliminates inaccuracies arising from nonuniform tire circumferential thickness by accurately retaining point-to-point specimen transit time and caliper variation information, rather than an average obtained through one or more tire rotations. Morever, ultrasonic transit time through the thickness direction of a moving web may be determined independent of small variations in the wheel axle spacing, tire thickness, and liquid and tire temperatures.