FRET Efficiency and Forster Radius Calculator
Convert between FRET efficiency, donor-acceptor distance and the Forster radius, and derive R0 from spectral overlap.
🔬 What is FRET Efficiency and the Förster Radius?
FRET, Förster resonance energy transfer, is the non-radiative transfer of excitation energy from an excited donor fluorophore to a nearby acceptor through dipole-dipole coupling. No photon is emitted and reabsorbed. The efficiency of that transfer is E = 1 ÷ (1 + (r ÷ R₀)⁶), where r is the donor-acceptor separation and R₀ is the Förster radius, the distance at which transfer is exactly half efficient. Because the coupling energy falls as 1/r³ and the rate goes as the square of the coupling, the efficiency collapses as the sixth power of distance.
That steepness is what makes FRET the most widely used molecular ruler in biophysics. Single-molecule FRET tracks a protein folding and unfolding in real time by watching a dye pair on the two termini move apart and back together. Genetically encoded FRET biosensors report calcium concentration, kinase activity or membrane voltage by coupling a conformational change to a change in dye separation. FRET microscopy maps protein-protein interactions inside living cells, and FRET-based assays detect nucleic acid hybridisation, protease cleavage and ligand binding in high-throughput screens.
The most common misconception is that FRET measures any distance. It does not. It measures distances close to R₀, and only there. At r = 0.5R₀ the efficiency is already 98.5 percent and at r = 2R₀ it is 1.5 percent, so outside roughly half to one and a half times R₀ the signal carries essentially no distance information. The second common trap is the orientation factor κ². The textbook value of 2/3 assumes both dyes tumble freely and rapidly, and a rigidly held dye can put κ² anywhere between 0 and 4, which propagates into R₀ as a sixth-root uncertainty.
This calculator covers all three directions of the problem. Given R₀ and a distance it returns the efficiency, the quenched donor lifetime and the transfer rate. Given a measured efficiency it recovers the distance in nanometres and angstroms. Given the orientation factor, refractive index, donor quantum yield and spectral overlap integral it computes R₀ itself. Every mode plots its own curve so you can see immediately where on the response your measurement sits.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Dye Pair Slightly Beyond R₀
R₀ = 5.4 nm, r = 6.0 nm, donor lifetime 2.6 ns (efficiency mode)
Example 2 — Compact Conformation Well Inside R₀
R₀ = 5.4 nm, r = 4.0 nm, donor lifetime 2.6 ns (efficiency mode)
Example 3 — Recovering a Distance from a Measured Efficiency
Measured E = 72 %, R₀ = 5.4 nm (distance mode)
Example 4 — Förster Radius from Spectral Overlap
κ² = 0.667, n = 1.4, QD = 0.6, J = 1 × 10₁⁵ M⁻¹cm⁻¹nm⁴ (radius mode)
❓ Frequently Asked Questions
🔗 Related Calculators
What is FRET efficiency and how is it calculated?
FRET efficiency is the fraction of donor excitations that transfer to the acceptor, E = 1 / (1 + (r/R0)^6), where r is the donor-acceptor separation and R0 is the Förster radius of the dye pair. It can also be measured as E = 1 - (tau_DA / tau_D) from donor lifetimes, or from the drop in donor intensity when the acceptor is present.
What is the Forster radius R0?
The Förster radius is the donor-acceptor distance at which energy transfer is exactly 50 percent efficient. It is a property of the dye pair and its environment, typically 4 to 7 nm for common fluorescent proteins and organic dyes, and it sets the entire usable distance range of a FRET experiment.
How do I calculate distance from FRET efficiency?
Invert the efficiency equation: r = R0 x ((1/E) - 1)^(1/6), with E as a fraction between 0 and 1. For example a measured efficiency of 0.72 with R0 = 5.4 nm gives r = 4.61 nm. The sixth root makes the answer remarkably tolerant of small efficiency errors near E = 0.5.
What is the formula for the Forster radius?
R0^6 = 8.79e-5 x kappa^2 x n^-4 x Q_D x J, giving R0 in angstroms when the overlap integral J is expressed in M^-1 cm^-1 nm^4. Equivalently R0 (in angstroms) = 0.211 x (kappa^2 n^-4 Q_D J)^(1/6). The calculator reports R0 in both angstroms and nanometres.
What is the orientation factor kappa squared?
Kappa squared describes the relative orientation of the donor emission dipole and the acceptor absorption dipole. It ranges from 0 (perpendicular dipoles, no transfer) to 4 (collinear dipoles). The conventional value 2/3 assumes both dyes rotate isotropically and rapidly during the donor excited-state lifetime.
Why does FRET depend on the sixth power of distance?
The transfer is a dipole-dipole coupling. The interaction energy between two dipoles falls as 1/r^3, and the transfer rate depends on the square of that coupling, so the rate falls as 1/r^6. That steep dependence is exactly what makes FRET a precise molecular ruler over a narrow distance window.
What distance range can FRET actually measure?
Roughly 0.5 x R0 to 1.5 x R0, which for a typical R0 of 5 nm means about 2.5 to 7.5 nm. Below that band the efficiency saturates near 1 and above it the signal disappears into noise, so in both regimes small efficiency changes correspond to enormous distance changes.
How does the donor lifetime change when FRET occurs?
The donor lifetime shortens to tau_DA = tau_D x (1 - E). A donor with a 2.6 ns unquenched lifetime undergoing 35 percent transfer will show 1.70 ns. Lifetime-based FRET measurements are preferred because they need no correction for local dye concentration.
What is the spectral overlap integral J?
J measures how much the donor emission spectrum overlaps the acceptor absorption spectrum, weighted by the fourth power of wavelength and by the acceptor extinction coefficient. Typical values run from 1e14 to 1e16 M^-1 cm^-1 nm^4. Because R0 depends on J^(1/6), even large differences in J shift R0 only modestly.
What refractive index should I use for the Forster radius?
Use about 1.4 for a dye pair embedded in a protein or membrane environment, and about 1.33 for two dyes freely dissolved in water. The term enters as n^-4, so moving from 1.33 to 1.4 lowers R0^6 by roughly 22 percent, which is only a 4 percent change in R0 itself.