Estimates of carbon concentrations in Earth’s mantle vary over more than an order of magnitude, hindering our ability to understand mantle structure and mineralogy, partial melting, and the carbon cycle. CO₂ concentrations in mantle-derived magmas supplying hotspot ocean island volcanoes yield our most direct constraints on mantle carbon, but are extensively modified by degassing during ascent. Here we show that undegassed magmatic and mantle carbon concentrations may be estimated in a Bayesian framework using diverse geologic information at an ocean island volcano. Our CO₂ concentration estimates do not rely upon complex degassing models, geochemical tracer elements, assumed magma supply rates, or rare undegassed rock samples. Rather, we couple volcanic CO₂ emission rates with probabilistic magma supply rates, which are obtained indirectly from magma storage and eruption rates. We estimate that the CO₂content of mantle-derived magma supplying Hawai‘i’s active volcanoes is 0.97_−0.19^+0.25 wt%—roughly 40% higher than previously believed—and is supplied from a mantle source region with a carbon concentration of 263₋₆₂⁺⁸¹ ppm. Our results suggest that mantle plumes and ocean island basalts are carbon-rich. Our data also shed light on helium isotope abundances, CO₂/Nb ratios, and may imply higher CO₂ emission rates from ocean island volcanoes.