As originally stated in terms of DC resistive circuits only, the Thévenin's theorem holds that:

• Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source V_th in series connection with an equivalent resistance R_th.
• This equivalent voltage V_th is the voltage obtained at terminals A-B of the network with terminals A-B open circuited.
• This equivalent resistance R_th is the resistance obtained at terminals A-B of the network with all its independent current sources open circuited and all its independent voltage sources short

In circuit theory terms, the theorem allows any one-port network to be reduced to a single voltage source and a single impedance.
The theorem also applies to frequency domain AC circuits consisting of reactive and resistive impedances.
The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.^{[1][2][3][4][5][6]}
Thévenin's theorem and its dual, Norton's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response.^[7][8] Thévenin's theorem can be used to convert any circuit's sources and impedances to a Thévenin equivalent; use of the theorem may in some cases be more convenient than use of Kirchhoff's circuit laws.^[6][9]