Magma chamber volume is critical for volcano hazards assessment and forecasting. Standard geodetic methods constrain volume change, not the total volume. Here, we show that the deformation response of the magma chamber to trapdoor faulting events at Sierra Negra volcano, Galapagos, depends on the product of the absolute chamber volume and the magma compressibility. Bubble-free magma provides the lower limit on compressibility, thus an upper bound on the chamber volume of 13.6 to 20.6 km3, depending on fault dip. We estimate an upper limit on compressibility using a conduit model relating volatile content to lava fountain height, compared with observations from the 2005 eruption, constrained by volatile content of olivine melt inclusions. This yields a lower bound on chamber volume roughly half the upper bound. We find that the best fitting trapdoor fault is near-vertical; reverse dips are slightly favored (88 degrees).