Small volume, finite conductivity, and high frequencies are major imperatives in the design of communications infrastructure. The radiation efficiency ηr impacts on the optimal gain, quality factor, and bandwidth. The current efficiency limit applies to structures confined to a radian sphere ka (k is the wavenumber and a is the radius). Here, we present new fundamental limits to ηr for arbitrary antenna shapes based on k2S, where S is the conductor surface area. For a dipole with an electrical length of 10−5 our result is two orders of magnitude closer to the analytical solution when compared with previous bounds on the efficiency. The improved bound on ηr is more accurate, more general, and easier to calculate than other limits. The efficiency of an antenna cannot be larger than the case where the surface of the antenna is peeled off and assembled into a planar sheet with area S, and a uniform current is excited along the surface of this sheet.