Context: The main sequence binary star 61 Cyg (K5V+K7V) is our nearest stellar neighbour in the northern hemisphere. This proximity makes it a particularly well suited system for very high accuracy interferometric radius measurements. Aims: Our goal is to constrain the poorly known evolutionary status and age of this bright binary star. Methods: We obtained high accuracy interferometric observations in the infrared K band, using the CHARA/FLUOR instrument. We then computed evolutionary models of 61 Cyg A & B with the CESAM2k code. As model constraints, we used a combination of observational parameters from classical observation methods (photometry, spectroscopy) as well as our new interferometric radii. Results: The measured limb darkened disk angular diameters are theta_LD(A) = 1.775 +/- 0.013 mas and theta_LD(B) = 1.581 +/- 0.022 mas, respectively for 61 Cyg A and B. Considering the high accuracy parallaxes available, these values translate into photospheric radii of R(A) = 0.665 +/- 0.005 Rsun and R(B) = 0.595 +/- 0.008 Rsun. The new radii constrain efficiently the physical parameters adopted for the modeling of both stars, allowing us to predict asteroseismic frequencies based on our best-fit models. Conclusions: The CESAM2k evolutionary models indicate an age around 6 Gyrs and are compatible with small values of the mixing length parameter. The measurement of asteroseismic oscillation frequencies in 61 Cyg A & B would be of great value to improve the modeling of this important fiducial stellar system, in particular to better constrain the masses.
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