We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of the considered probes, thus relieving analysis pipelines from having to develop a full SSC modeling, and reducing the computational load. The approximation is asymptotically exact for fine redshift bins $Delta z rightarrow 0$. We furthermore show how it can be implemented at the level of a Gaussian likelihood or a Fisher matrix forecast, as a fast correction to the Gaussian case without needing to build large covariance matrices. Numerical application to a Euclid-like survey show that, compared to a full SSC computation, the approximation recovers nicely the signal-to-noise ratio as well as Fisher forecasts on cosmological parameters of the $w$CDM cosmological model. Moreover it allows for a fast prediction of which parameters are going to be the most affected by SSC and at which level. In the case of photometric galaxy clustering with Euclid-like specifications, we find that $sigma_8$, $n_s$ and the dark energy equation of state $w$ are particularly heavily affected. We finally show how to generalize the approximation for probes other than angular spectra (correlation functions, number counts and bispectra), and at the likelihood level, allowing for the latter to be non-Gaussian if needs be. We release publicly a Python module allowing to implement the SSC approximation, as well as a notebook reproducing the plots of the article, at https://github.com/fabienlacasa/PySSC
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