New technologies in the concrete industry like 3D printing, complex construction projects, or simulations, require very accurate measurements of the flow behavior, i.e., stress dependency on local shear rate and shear history. Unfortunately, most commercial systems, often called concrete viscometers, only feature relative measurements or compute pseudo-absolute values from complex flow fields which cannot be described analytically. The assumptions are usually of good quality but carry the risk of producing misleading results. Therefore, a new concrete rheometer, the Adaptive Coaxial Concrete Rheometer (ACCR), was built to measure absolute values comparable to commercial small-scale rheometers. The experimental setup of the rheometer and the necessary theory are described in detail, including some specific features to fulfill the requirements of ISO 3219 for coaxial rheometers. The important gap correction for serrated measuring systems to inhibit wall slip is explained, and examples are given for rotational plate-plate and coaxial systems. The calibration and validation measurements are presented to demonstrate the high accuracy of the ACCR and the good comparability for different flow behaviors. Then, a practical study of the flow behavior for an industrial Self Compacting Concrete (SCC) concrete is presented and discussed. Finally, the yield stress of the SCC was investigated using classical extrapolation methods and compared to an optical method using the ACCR.