Fluorescence Lifetime and Quantum Yield Calculator
Convert between fluorescence lifetime, quantum yield, and decay rate constants, and determine relative quantum yield against a reference standard.
💡 What is Fluorescence Lifetime and Quantum Yield?
Fluorescence lifetime is the average time a molecule spends in its excited electronic state before returning to the ground state, and fluorescence quantum yield is the fraction of absorbed photons that come back out as emitted photons. The two quantities are not independent. After absorbing a photon, an excited fluorophore has exactly two competing options: emit (at the radiative rate kr) or lose the energy silently through internal conversion, intersystem crossing, or collisional quenching (at the combined nonradiative rate knr). The lifetime is the reciprocal of the total rate, tau = 1/(kr + knr), and the quantum yield is the radiative share of that total, Phi = kr/(kr + knr). Multiply them and you recover the identity Phi = kr times tau, which is why a change in lifetime almost always signals a matching change in brightness.
These numbers do real work in the laboratory. Fluorescence lifetime imaging microscopy separates two dyes that emit at the same wavelength but decay at different speeds, and it reports FRET efficiency in live cells because energy transfer to an acceptor shortens the donor lifetime in a way that intensity alone cannot prove. Materials chemists compare quantum yields when screening new emitters for OLED panels and solar concentrators, where a few percentage points of yield decide whether a device is viable. Analytical chemists use the fact that a dynamic quencher shortens lifetime and yield by identical factors to distinguish dynamic from static quenching in a Stern-Volmer plot, and biosensor designers exploit lifetime shifts that are immune to probe concentration and photobleaching in ways that intensity measurements are not.
Two points cause repeated confusion. First, the natural radiative lifetime tau zero, equal to 1/kr, is not something you measure directly; it is what the lifetime would be if nonradiative decay vanished, and it is always longer than the observed lifetime by exactly a factor of 1 over the quantum yield. Second, the comparative quantum yield method is not a simple intensity ratio. It compares the gradients of integrated emission against absorbance for the sample and a reference standard, and it needs a refractive index correction of (n sample over n standard) squared whenever the two sit in different solvents. Skipping that correction between water and ethanol already introduces a 4% error.
This calculator covers all three routes people actually take. Enter rate constants and it returns lifetime, quantum yield, natural radiative lifetime, and the total decay rate. Enter a measured lifetime and yield and it separates them back into kr and knr, which is the standard way to attribute a brightness loss to a specific decay channel. Enter the paired emission, absorbance, and refractive index values for a sample and a standard and it runs the comparative method end to end. Each mode plots the relationship being computed, so you see the quantum yield curve collapse as quenching grows, the observed decay trace fall away from the quench-free radiative decay, and the two comparative gradient lines whose slope ratio is the whole measurement.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A Bright Fluorophore from Its Rate Constants
kr = 0.23 /ns, knr = 0.02 /ns (a fluorescein-like dye)
Example 2 — The Same Dye Under Heavy Quenching
kr = 0.23 /ns unchanged, knr raised to 0.77 /ns by a quencher
Example 3 — Extracting Rate Constants for Rhodamine 6G
Measured τ = 4.08 ns and Φ = 0.95 in ethanol
Example 4 — A Dim Probe Dominated by Nonradiative Decay
Measured τ = 2.6 ns and Φ = 0.31 for a protein-bound probe
Example 5 — Relative Quantum Yield Against Quinine Sulfate
Sample in ethanol: Fx = 452, Ax = 0.048. Quinine sulfate standard: Fst = 388, Ast = 0.052, Φst = 0.546, nx = 1.361, nst = 1.333
❓ Frequently Asked Questions
🔗 Related Calculators
What is the relationship between fluorescence lifetime and quantum yield?
Both come from the same competition between radiative and nonradiative decay. The lifetime is tau = 1/(kr + knr) and the quantum yield is Phi = kr/(kr + knr), so Phi = kr times tau. If the radiative rate is unchanged, lifetime and quantum yield always move together in exact proportion.
How do you calculate fluorescence lifetime from rate constants?
Add the radiative and nonradiative rate constants and take the reciprocal: tau = 1/(kr + knr). With kr = 0.23 per ns and knr = 0.02 per ns, the total decay rate is 0.25 per ns and the lifetime is 1/0.25 = 4.00 ns.
What is the natural radiative lifetime?
The natural radiative lifetime tau zero is 1/kr, the lifetime the fluorophore would show if nonradiative decay were switched off completely. It also equals tau divided by Phi. It is always longer than the measured lifetime, and the ratio tau zero over tau is exactly 1 over the quantum yield.
How do you get kr and knr from a measured lifetime and quantum yield?
Use kr = Phi/tau and knr = (1 - Phi)/tau. For rhodamine 6G with tau = 4.08 ns and Phi = 0.95, kr = 0.95/4.08 = 0.23284 per ns and knr = 0.05/4.08 = 0.01225 per ns. This is the standard way to separate the two decay channels experimentally.
What is the comparative or relative quantum yield method?
You measure integrated emission and absorbance for both your sample and a reference standard of known quantum yield, then apply Phi_x = Phi_std x (Grad_x/Grad_std) x (n_x/n_std)^2, where Grad is integrated emission divided by absorbance and n is the solvent refractive index. It avoids the need for an integrating sphere.
Why is the refractive index squared in the relative quantum yield formula?
The amount of emitted light collected by the detector depends on how the solvent refracts light leaving the cuvette, and that collection efficiency scales with the square of the refractive index. Comparing water at 1.333 with ethanol at 1.361 gives a correction factor of 1.0425, a 4.25% change in the reported yield.
Can the quantum yield ever exceed 1?
Not for ordinary single-photon fluorescence, where the yield is the fraction of absorbed photons re-emitted and cannot exceed unity. Values above 1 are only physically possible in multiplication processes such as singlet fission or quantum cutting. If your comparative measurement returns more than 1, suspect inner filter effects, a wrong standard value, or a scatter contribution.
Why is my measured lifetime shorter than the natural radiative lifetime?
Because nonradiative pathways compete with emission. Internal conversion, intersystem crossing to the triplet state, collisional quenching by oxygen or iodide, and energy transfer to an acceptor all drain the excited state without emitting a photon, adding to knr and shortening tau below tau zero.
What units should I use for the rate constants?
This calculator uses inverse nanoseconds (1/ns), which keeps typical organic fluorophore values in a readable range around 0.01 to 1. To convert to SI, multiply by 10 to the ninth: 0.23 per ns equals 2.3 times 10 to the eighth per second. Lifetimes are entered and returned in nanoseconds.
How does a quencher change lifetime and quantum yield together?
A dynamic quencher adds a term kq[Q] to knr, so both the lifetime and the quantum yield fall by exactly the same factor. That equality is the diagnostic test for dynamic quenching in a Stern-Volmer analysis. If the quantum yield drops but the lifetime does not, the quenching is static, that is, a non-fluorescent ground-state complex has formed.
What is a good reference standard for relative quantum yield?
Quinine sulfate in 0.1 M sulfuric acid, with a quantum yield around 0.546 and a refractive index of about 1.333, is the classic blue-emitting standard. Fluorescein in 0.1 M sodium hydroxide (roughly 0.92) and rhodamine 6G in ethanol (roughly 0.95) cover the green and orange regions.
Why must absorbance stay below 0.1 in the comparative method?
Above about 0.1 absorbance, the excitation beam is attenuated significantly across the cuvette and re-absorption of emitted light becomes measurable. Both effects are inner filter artefacts that break the assumed linear relationship between integrated emission and absorbance, biasing the gradient and therefore the calculated quantum yield downward.