1. The pyrophosphatase activity in cytosolic and mitochondrial fractions of rat liver was 1.7 and 0.26 units/mg of protein respectively when assayed at 37 degrees C in the presence of physiological [Mg2+] (0.3 mM). 2. Approx. 80% of the mitochondrial pyrophosphatase was inaccessible to extramitochondrial PPi, of which 40% represented soluble matrix enzyme (0.38 unit/mg of matrix protein). 3. Ca2+ inhibited the soluble matrix enzyme; the effective K0.5 for inhibition increased as [Mg2+], an essential cofactor of the enzyme, increased. Measured values were 0.39, 1.15, 3.7, 8.3 and 12.5 microM at 0.04 mM-, 0.1 mM-, 0.3 mM-, 0.6 mM- and 1 mM-Mg2+ respectively. 4. The data were analysed by a kinetic model similar to that for yeast pyrophosphatase, which assumes the substrate to be MgPPi (Km 5 microM) with Mg2+ also activating at an additional site (K0.5 23 microM). Ca2+ inhibits through the formation of CaPPi, a strong competitive inhibitor (Ki 0.067 microM). 5. Heart mitochondria also contain a soluble matrix pyrophosphatase of similar activity to that of liver mitochondria and with the same sensitivity to [Ca2+]. 6. The data provide an explanation for the increase in mitochondrial PPi, mediated by Ca2+, which is responsible for the increase in matrix volume induced by gluconeogenic hormones [Davidson & Halestrap (1988) Biochem. J. 254, 379-384].