Archimedes' principle is well known to state that a body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. Herein, Archimedes' principle is derived from first principles by using conservation of the stress-energy-momentum tensor in general coordinates. The resulting expression for the force is applied in Schwarzschild coordinates and in rotating coordinates. Using Schwarzschild coordinates for the case of a spherical mass suspended within a perfect fluid leads to the familiar expression of Archimedes' principle. Using rotating coordinates produces an expression for a centrifugal buoyancy force that agrees with accepted theory. It is then argued that Archimedes' principle ought to be applicable to non-gravitational phenomena, as well. Conservation of the energy-momentum tensor is then applied to electromagnetic phenomena. It is shown that a charged body submerged in a charged medium experiences a buoyancy force in accordance with an electromagnetic analogue of Archimedes' principle.