text: The FRET efficiency () is the quantum yield of the energy-transfer transition, i.e. the probability of energy-transfer event occurring per donor excitation event:
  where  the radiative decay rate of the donor,  is the rate of energy transfer, and  the rates of any other de-excitation pathways excluding energy transfers to other acceptors.
  The FRET efficiency depends on many physical parameters that can be grouped as: 1) the distance between the donor and the acceptor (typically in the range of 1–10 nm), 2) the spectral overlap of the donor emission spectrum and the acceptor absorption spectrum, and 3) the relative orientation of the donor emission dipole moment and the acceptor absorption dipole moment.
   depends on the donor-to-acceptor separation distance  with an inverse 6th-power law due to the dipole–dipole coupling mechanism:
  with  being the Förster distance of this pair of donor and acceptor, i.e. the distance at which the energy transfer efficiency is 50%.
  The Förster distance depends on the overlap integral of the donor emission spectrum with the acceptor absorption spectrum and their mutual molecular orientation as expressed by the following equation all in SI units:
  where  is the fluorescence quantum yield of the donor in the absence of the acceptor,  is the dipole orientation factor,  is the refractive index of the medium,  is the Avogadro constant, and  is the spectral overlap integral calculated as
  where  is the donor emission spectrum,  is the donor emission spectrum normalized to an area of 1, and  is the acceptor molar extinction coefficient, normally obtained from an absorption spectrum.
  The orientation factor  is given by
  where  denotes the normalized transition dipole moment of the respective fluorophore, and  denotes the normalized inter-fluorophore displacement.
   = 2/3 is often assumed. This value is obtained when both dyes are freely rotating and can be considered to be isotropically oriented during the excited-state lifetime. If either dye is fixed or not free to rotate, then  = 2/3 will not be a valid assumption. In most cases, however, even modest reorientation of the dyes results in enough orientational averaging that  = 2/3 does not result in a large error in the estimated energy-transfer distance due to the sixth-power dependence of  on . Even when  is quite different from 2/3, the error can be associated with a shift in , and thus determinations of changes in relative distance for a particular system are still valid. Fluorescent proteins do not reorient on a timescale that is faster than their fluorescence lifetime. In this case 0 ≤  ≤ 4.
  The units of the data are usually not in SI units. Using the original units to calculate the Förster distance is often more convenient. For example, the wavelength is often in unit nm and the extinction coefficient is often in unit , where  is concentration .  obtained from these units will have unit . To use unit Å () for the , the equation is adjusted to 
  :     (Å)
  For time-dependent analyses of FRET, the rate of energy transfer () can be used directly instead:
  where  is the donor's fluorescence lifetime in the absence of the acceptor.
  The FRET efficiency relates to the quantum yield and the fluorescence lifetime of the donor molecule as follows:
  where  and  are the donor fluorescence lifetimes in the presence and absence of an acceptor respectively, or as
  where  and  are the donor fluorescence intensities with and without an acceptor respectively.