The height measurement that considers the geoid is known as?

The height measurement that takes into account the geoid is referred to as orthometric height. Orthometric height is derived by measuring the distance from a point on the Earth's surface to the geoid, which represents the mean sea level extended across the Earth's surface. This measurement is crucial in geodesy as it reflects the gravitational potential differences and provides a reference for elevations that can be used in practical applications such as mapping and construction.

In contrast, ellipsoidal height is the measurement from a point to the mathematical ellipsoid, which does not account for the Earth's gravitational field or the physical shape of the Earth. Measured height and absolute height may refer to different contexts or standards in measurement but do not specifically denote the consideration of the geoid, making them less relevant to the question about height measurement that incorporates geoidal effects.

Thus, orthometric height is the correct term that aligns with the notion of referencing the geoid in height measurements.