We show that γ-ray burst (GRB) afterglow observations strongly suggest, within the fireball model framework, that radiating electrons are shock accelerated to a power-law energy distribution, dn e /dγ e ∝ γ −p e , with universal index p ≈ 2.2, and that the fraction of shock energy carried by electrons, ξ e , is universal and close to equipartition, ξ e ∼ 1/3. For universal p and ξ e , a single measurement of the X-ray afterglow flux on the time scale of a day provides a robust estimate of the fireball energy per unit solid angle, ε, averaged over a conical section of the fireball of opening angle θ ∼ 0.1.Applying our analysis to BeppoSAX afterglow data we find that: (i) Fireball energies are in the range of 4πε = 10 51.5 to 10 53.5 erg; (ii) The ratio of observed γ-ray to total fireball energy per unit solid angle, ε γ /ε, is of order unity, satisfying | log 10 (ε γ /ε)| ∼ < 0.5; (iii) If fireballs are jet like, their opening angle should satisfy θ ∼ > 0.1. Our results imply that if typical opening angles are θ ∼ 0.1, a value consistent with our analysis, the total energy associated with a GRB event is in the range of 10 50 erg to 10 51.5 erg.