The surface area (SA) and three-dimensional (3D) morphology of reef-building corals are central to their physiology. A challenge for the estimation of coral SA has been to meet the required spatial resolution as well as the capability to preserve the soft tissue in its native state during measurements. Optical Coherence Tomography (OCT) has been used to quantify the 3D microstructure of coral tissues and skeletons with nearly micron-scale resolution. Here, we develop a non-invasive method to quantify surface area and volume of single coral polyps. A coral fragment with several coral polyps as well as calibration targets of known areal extent are scanned with an OCT system. This produces a 3D matrix of optical backscatter that is analyzed with computer algorithms to detect refractive index mismatches between physical boundaries between the coral and the immersed water. The algorithms make use of a normalization of the depth dependent scatter intensity and signal attenuation as well as region filling to depict the interface between the coral soft tissue and the water. Feasibility of results is judged by inspection as well as by applying algorithms to hard spheres and fish eggs whose volume and SA can be estimated analytically. The method produces surface area estimates in calibrated targets that are consistent with analytic estimates within 93%. The appearance of the coral polyp surfaces is consistent with visual inspection that permits standard programs to visualize both point clouds and 3-D meshes. The method produces the 3-D definition of coral tissue and skeleton at a resolution close to 10 µm, enabling robust quantification of polyp volume to surface area ratios.