Stearoyl-CoA desaturase that utilizes O(2) and electrons from reduced cytochrome b5 to introduce the first double bond into saturated fatty acyl-CoA substrates. Catalyzes the insertion of a cis double bond at the delta-9 position into fatty acyl-CoA substrates including palmitoyl-CoA and stearoyl-CoA (PubMed:12815040, PubMed:16443825). Required for the biosynthesis of membrane phospholipids, cholesterol esters and triglycerides (By similarity). 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 + octadecanoyl-CoA = (9Z)-octadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O 2 Fe(II)-[cytochrome b5] + 2 H(+) + hexadecanoyl-CoA + O2 = (9Z)-hexadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Expected to bind 2 Fe(2+) ions per subunit. Detected in heart, but not in brain, liver, skin or adipose tissue. Up-regulated by agonists that activate NR1H3. Up-regulated by a fat-free high-carbohydrate diet. Not down-regulated by a high-carbohydrate diet supplemented with unsaturated fatty acids. Down-regulated by leptin. The histidine box domains are involved in binding the catalytic metal ions. Belongs to the fatty acid desaturase type 1 family.