Context. Recent studies with, for example, Spitzer and Herschel have suggested that star formation in dense molecular gas may be governed by essentially the same “law” in Galactic clouds and external galaxies. This conclusion remains controversial, however, in large part because different tracers have been used to probe the mass of dense molecular gas in Galactic and extragalactic studies. Aims. We aimed to calibrate the HCN and HCO+ lines commonly used as dense gas tracers in extragalactic studies and to test the possible universality of the star-formation efficiency in dense gas (≳104 cm-3), SFEdense. Methods. We conducted wide-field mapping of the Aquila, Ophiuchus, and Orion B clouds at ~0.04 pc resolution in the J = 1 − 0 transition of HCN, HCO+, and their isotopomers. For each cloud, we derived a reference estimate of the dense gas mass MHerschelAV > 8, as well as the strength of the local far-ultraviolet (FUV) radiation field, using Herschel Gould Belt survey data products, and estimated the star-formation rate from direct counting of the number of Spitzer young stellar objects. Results. The H13CO+(1–0) and H13CN(1–0) lines were observed to be good tracers of the dense star-forming filaments detected with Herschel. Comparing the luminosities LHCN and LHCO+ measured in the HCN and HCO+ lines with the reference masses MHerschelAV > 8, the empirical conversion factors αHerschel − HCN (=MHerschelAV > 8/LHCN) and αHerschel − HCO+ (=MHerschelAV > 8/LHCO+) were found to be significantly anti-correlated with the local FUV strength. In agreement with a recent independent study of Orion B by Pety et al., the HCN and HCO+ lines were found to trace gas down to AV ≳ 2. As a result, published extragalactic HCN studies must be tracing all of the moderate density gas down to nH2 ≲ 103 cm-3. Estimating the contribution of this moderate density gas from the typical column density probability distribution functions in nearby clouds, we obtained the following G0-dependent HCN conversion factor for external galaxies: αHerschel − HCNfit′ = 64 × G0-0.34. Re-estimating the dense gas masses in external galaxies with αHerschel − HCNfit′(G0), we found that SFEdense is remarkably constant, with a scatter of less than 1.5 orders of magnitude around 4.5 × 10-8 yr-1, over eight orders of magnitude in dense gas mass. Conclusions. Our results confirm that SFEdense of galaxies is quasi-universal on a wide range of scales from ~ 1–10 pc to > 10 kpc. Based on the tight link between star formation and filamentary structure found in Herschel studies of nearby clouds, we argue that SFEdense is primarily set by the “microphysics” of core and star formation along filaments.