THE gas of the solar corona is at a temperature of several million degrees, orders of magnitude hotter than the underlying photosphere, The nature of the physical process that heats the solar corona (and the coronae of solar-type stars more generally) has been a long-standing puzzle, A number of plausible heating mechanisms have been proposed, but observations have so far been unable to discriminate between them(1). Here we show that coronal heating exhibits scaling properties that should provide a powerful diagnostic of the underlying mechanism. The coronal magnetic field organizes the coronal plasma into loop-like features, which form the basic structural elements of the corona(2). We demonstrate that the pressures and lengths of the coronal loops are statistically related, suggesting that the heating rate scales inversely with approximately the square of the loop length. Existing coronal heating theories make different predictions about what this scaling should he, and a model(3,4) of energy dissipation bg stressed coronal magnetic fields appears at present to be the most consistent with our observational result.