A high sensitivity, low power (∼1μW to 10 μW), room temperature, antenna coupled, THz (0.8 THz) detector is presented by means field effect transistor (FETs) fabricated on epitaxial-grown graphene on silicon carbide. The contact resistance across the source and drain are made high to study the effect of THz response. It is demonstrated that the energy coupled to the antenna is the important parameter in designing the ultra-sensitive THz detectors rather than the contact resistances and channel conductivity. The realised graphene based detectors shows quite good responsivity (>535 V/W) and noise equivalent power (NEP) (<100pW/Hz0.5). The individual contributions of photo voltage due to plasma wave generation (PWG) and photo thermo-electric effect (PTE) in the effective THz detection is estimated. It is also seen that the temperature of the hot carriers generated in the FET channel due to PTE is varying with the gate bias and not constant as assumed in earlier works. A new method is proposed in this work for calculating the antenna coupling factor which varies with incident THz-radiation power. A comprehensive analytical model is worked out to understand the graphene based detector performance.