FRET pair calculator
Förster radius from real spectra, and the artefacts that will spoil the measurement.
Quantum yield 0.93 and a near single-exponential lifetime: the default FRET donor for lifetime work.
Fast-maturing yellow, the usual FRET acceptor for a cyan donor. Bleaches quickly.
Centre to centre.
Optional. Measures donor leak.
The dynamic isotropic average, and the assumption behind every published Förster radius. Sound for dyes on flexible linkers.
Förster radius
67.8% transfer at 5 nm. Efficiency is measurable between about 3.9 and 8.2 nm and saturates outside that.
Transfer efficiency against separation
The numbers behind it
- Overlap integral J
- 2.319e+15 M⁻¹cm⁻¹nm⁴
- Donor quantum yield
- 0.93
- Acceptor ε
- 104,000 M⁻¹cm⁻¹
- κ²
- 0.667
- Refractive index
- 1.4
- Acceptor excited at 434 nm
- 3% of its peak
- Donor leak into acceptor filter
- 29% of acceptor
Transfer depends on the donor’s emission (filled) lying under the acceptor’s excitation (dashed). Where those two overlap is the overlap integral.
mTurquoise2 contributes strongly to the acceptor channel through that filter. A donor-only sample is needed to subtract it, and a narrower or redder acceptor filter would reduce it.
J = ∫F_D(λ)ε_A(λ)λ⁴dλ ÷ ∫F_D(λ)dλ; R₀ = [9000·ln10·κ²·Φ_D·J ÷ (128π⁵N_A n⁴)]^(1/6); E = 1 ÷ (1 + (r/R₀)⁶)- Förster resonance energy transfer, the original derivation — Annalen der Physik, 1948
- Förster radius, the overlap integral and the orientation factor — Principles of Fluorescence Spectroscopy, 3rd edition, 2006
- Fluorophore spectra, extinction coefficients and quantum yields — FPbase, Nature Methods, 2019
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κ² is the weak point of every Förster radius ever published, including this one. It is almost always taken as 2/3, which assumes both dipoles rotate freely and fast compared with the donor lifetime — sound for a dye on a long linker, and questionable for a fluorescent protein whose chromophore is held rigid inside a β-barrel. R₀ depends on it only as the sixth root, so the error is smaller than it looks: the entire physical range moves the radius by a factor of about 2.9, and a plausible range for a tethered pair by well under a fifth. The acceptor absorption is taken from its excitation spectrum, which is exact for a single-species fluorophore and slightly low where a dark absorbing state exists.
When to use this
Use this when choosing a donor and acceptor for a FRET biosensor or an interaction assay, or to check whether the distance you are trying to measure falls inside the range a pair can report at all. It computes the Förster radius from the actual spectra rather than quoting a table. It does not tell you whether two proteins interact — it tells you whether you would be able to see it if they did.
Worked example
A cyan-to-yellow biosensor with the two fluorophores expected to sit about 5 nm apart.
- Donor
- mTurquoise2
- Acceptor
- mVenus
- Orientation κ²
- 2/3 (free rotation)
- Refractive index
- 1.4 (protein interior)
- Separation
- 5 nm
Result
A good working point: efficiency is measurable between about 3.9 and 8.2 nm, and 5 nm sits inside that with room to move in both directions, which is what a sensor needs in order to have a signal to change.
What people get wrong
- Choosing a pair on Förster radius alone. Direct excitation of the acceptor by the donor line, and donor emission leaking into the acceptor channel, sink more intensity-based FRET experiments than a short R₀ does — and both need their own single-label controls rather than a better pair.
- Believing κ² = 2/3 without asking whether it applies. It assumes both dipoles rotate freely and fast compared with the donor lifetime, which is reasonable for a dye on a long linker and questionable for a fluorescent protein whose chromophore is rigidly held inside a β-barrel.
- Reading a change in acceptor intensity as a change in distance. Acceptor signal also rises with expression, with maturation, and with direct excitation; ratiometric measurements and donor lifetime exist precisely because raw acceptor intensity does not mean what it appears to.
- Picking a pair whose emissions are close together. EGFP into EYFP has a perfectly respectable Förster radius and is nearly useless ratiometrically, because no filter cleanly separates the two channels. Such pairs belong in a lifetime measurement on the donor.
Questions
+Why is my R₀ slightly different from the published value?
Published radii assume a particular quantum yield, refractive index and κ², and papers differ on all three — a value quoted at n = 1.33 is about 2% larger than the same pair at 1.4. The spectra themselves also vary between measurements. Agreement to within a few per cent is as close as this quantity gets.
+How much does the orientation factor really matter?
Less than its reputation suggests, because R₀ depends on it only as the sixth root. The entire physical range from 0 to 4 moves the radius by a factor of about 2.9, and the plausible range for a tethered protein pair moves it by well under a fifth.
+Is the static κ² of 0.476 the average of κ²?
No, and this is worth being careful about. The mean of κ² is 2/3 whether the dipoles are moving or frozen; 0.476 is the square of the mean of |κ|, an average appropriate to the static limit. The two differ by 40%, and they are frequently confused.
+Can I use this for single-molecule FRET?
Yes — Cy3 to Cy5 is in the catalogue and comes out near the published 5.4 nm. For smFRET the dyes are on flexible linkers, so κ² = 2/3 is far better justified there than it is for a fluorescent protein pair.
Related tools
- Fluorescence spectra viewer — Overlay excitation and emission spectra and see which pairs will separate.
- Filter set and channel checker — Check a multi-colour panel against your filters before you stain anything.
- Fluorophore brightness comparison — Rank fluorophores by what your setup will actually detect, not by ε × Φ alone.
Science last reviewed .