A road paver with a movable screed and with a layer thickness measuring device, which includes at least two sensors. The sensors are formed to carry out a distance measurement to the paving plane at intervals to determine a distance between the sensor and a point on the surface of the plane, said point being registered by the sensor. One of the two sensors defines a coordinate system. The layer thickness measuring device is formed to add as vectors the distance to the plane measured by the sensor that defines the coordinate system and a movement, relative to the plane and resulting from the driving of the road paver, of the coordinate system that is defined by the one sensor. In this way, a first vector can be determined which, together with a second vector, is used by the measuring device for determining the layer thickness of the laying material.