To quantify antioxidant activity, you measure the material’s Oxygen Radical Absorbance Capacity, or ORAC for short, a method established by the US Department of Agriculture (USDA)’s Agricultural Research Service. These values appear in the USDA National Nutrient Database for Standard Reference, published on the department’s website, www.ars.usda.gov.
Total ORAC rates an ingredient’s activity against five free radicals: hydroxyl, peroxyl, peroxynitrite, singlet oxygen and superoxide anion. These five represent the lion's share of free radicals found in humans.
Antioxidant activity is more complex than this, of course. It involves multiple mechanisms: hydrogen atom or electron transfers to quench radicals, metal chelation, singlet oxygen quenching and more. And it takes place in both aqueous and lipid phases.
Actually, a number of methods can be used to screen for antioxidant activity, but at present, they have not been standardized for procedure or reporting. Another concern is that in vitro assays are not good models for what happens in humans and should not be the final factor on which to make dietary choices.
There’s also the matter of how much antioxidant to consume. USDA recommends 5,000 ORAC units per day, which can be provided by eating one apple or 1 oz of pecans. And remember, antioxidant activity is always reduced by exposure to heat, often by as much as 90%.