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We investigate the free magnetic energy and relative magnetic helicitybudgets of solar quiet regions. Using a novel non-linear force-free methodrequiring single solar vector magnetograms we calculate the instantaneous freemagnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vectormagnetograms. As in a previous work on active regions, we construct here forthe first time the (free) energy-(relative) helicity diagram of quiet-Sunregions. We find that quiet-Sun regions have no dominant sense of helicity andshow monotonic correlations a) between free magnetic energy/relative helicityand magnetic network area and, consequently, b) between free magnetic energyand helicity. Free magnetic energy budgets of quiet-Sun regions represent arather continuous extension of respective active-region budgets towards lowervalues, but the corresponding helicity transition is discontinuous due to theincoherence of the helicity sense contrary to active regions. We furtherestimate the instantaneous free magnetic-energy and relative magnetic-helicitybudgets of the entire quiet Sun, as well as the respective budgets over anentire solar cycle. Derived instantaneous free magnetic energy budgets and, toa lesser extent, relative magnetic helicity budgets over the entire quiet Sunare comparable to the respective budgets of a sizeable active region, whiletotal budgets within a solar cycle are found higher than previously reported.Free-energy budgets are comparable to the energy needed to power fine-scalestructures residing at the network, such as mottles and spicules.

Energy and helicity budgets of solar quiet regions