A systematic survey of 3 years of L band interferometric synthetic aperture radar (InSAR) measurements of the Central American Volcanic Arc shows a striking lack of magmatic deformation. We make measurements at 20 of the 26 historically active volcanoes and demonstrate that none were deforming magmatically (2007–2010), although we do measure shallow subsidence associated with flow deposits and edifice loading at three volcanoes. The minimum detection rates for our survey, as estimated from the variance in time series of radar path delay, are relatively high due to strong variability of tropospheric water vapor. We compare the average detection threshold (2.4 cm/yr) to published InSAR measurements and show that the majority (~78%) of deformation events would have been measurable with the same level of noise as Central America. We calculate that if magmatic volcano deformation were spread evenly across historically active volcanoes worldwide, the probability of none of Central America's 26 volcanoes deforming would be < 1%. The lack of magmatic deformation in Central America may be indicative of differences in magma storage relative to other well-studied continental arcs. The high proportion of basalts that ascend directly from depth relative to andesites stored in the shallow crust may limit the potential for high magnitude deformation. Magma stored in vertically elongated reservoirs and high parental melt volatile contents that result in bubble-rich, compressible magmas at shallow depths may also reduce surface deformation. We consider the measurement and analysis of a lack of deformation at active volcanoes to be essential for realizing the potential of regional scale InSAR surveys.