We present the photometric calibration of the twelve optical passbands observed by the Javalambre Photometric Local Universe Survey (J-PLUS). The proposed calibration method has four steps: (i) definition of a high-quality set of calibration stars using Gaia information and available 3D dust maps; (ii) anchoring of the J-PLUS gri passbands to the Pan-STARRS photometric solution, accounting for the variation of the calibration with the position of the sources on the CCD; (iii) homogenization of the photometry in the other nine J-PLUS filters using the dust de-reddened instrumental stellar locus in (X - r) versus (g - i) colours, where X is the filter to calibrate. The zero point variation along the CCD in these filters was estimated with the distance to the stellar locus. Finally, (iv) the absolute colour calibration was obtained with the white dwarf locus. We performed a joint Bayesian modelling of eleven J-PLUS colour-colour diagrams using the theoretical white dwarf locus as reference. This provides the needed offsets to transform instrumental magnitudes to calibrated magnitudes outside the atmosphere. The uncertainty of the J-PLUS photometric calibration, estimated from duplicated objects observed in adjacent pointings and accounting for the absolute colour and flux calibration errors, are ~19 mmag in u, J0378 and J0395, ~11 mmag in J0410 and J0430, and ~8 mmag in g, J0515, r, J0660, i, J0861, and z. We present an optimized calibration method for the large area multi-filter J-PLUS project, reaching 1-2% accuracy within an area of 1 022 square degrees without the need for long observing calibration campaigns or constant atmospheric monitoring. The proposed method will be adapted for the photometric calibration of J-PAS, that will observe several thousand square degrees with 56 narrow optical filters.
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