Fractional uncertainty (δN_AGN/N_AGN) on the number of AGN detectable in at least one Euclid band in bins of redshift (Δz = 0.25) and bolometric luminosity (Δ log₁₀[L_bol/erg s⁻¹] = 0.25) for the EWS (left) and EDS (right). The fractional uncertainties were derived using three hundred realisations of the adopted XLF probing the ±1σ interval of each parameter given in Table 1. For reference, we plot curves corresponding to the 50% completeness flux limits of the 7 Ms exposure of the Chandra Deep Field-South (red, F_{2 − 7 keV} = 2.5 × 10⁻¹⁶ erg s⁻¹ cm⁻²; Luo et al. 2017) and medium-depth X-ray survey XMM-COSMOS (black, F_{2 − 10 keV} = 5.6 × 10⁻¹⁵ erg s⁻¹ cm⁻²; Cappelluti et al. 2009). We additionally show the sample limiting flux of the XXL 1000 brightest AGN sample (XXL-1000-AGN) as used in Fotopoulou et al. (2016b) for SED fitting (blue; F_{2 − 10 keV} = 4.8 × 10⁻¹⁴ erg s⁻¹ cm⁻²; Fotopoulou et al. 2016b). The flux limits were homogenised to the 2–10 keV band assuming an X-ray power law with photon index Γ = 1.9, where applicable, and converted to the bolometric domain assuming the X-ray bolometric correction of Duras et al. (2020).