Three-dimensional temperature (T)–pressure (P)–composition (X) phase diagrams of binary carbon-hydrogen (C–H) and carbon-oxygen (C–O) systems for activated low pressure diamond growth have been calculated. Based on an approximation of linear combination between C–H and C–O systems, a projective ternary carbonhydrogen-oxygen (C–H–O) phase diagram has also been obtained. There is always a diamond growth region in each of these phase diagrams. Once a supply of external activating energy stops, the diamond growth region will not exist. Nearly all of the reliable experimental data reported in the literature drop into the possible diamond growth region of the calculated projective ternary C–H–O phase diagram under the conditions of 0.01–100 kPa and above 700 K.