Fluorescence Lifetime Calculator
Model single and bi-exponential fluorescence decay curves. Calculate intensity-weighted average lifetimes.
Lifetime τ (1/e time)
5.00 ns
decay rate 1/τ = 2.00e+8 s⁻¹
Quantum yield Φ
0.500
⟨τ⟩_amp / τ_rad, non-radiative rate 1.00e+8 s⁻¹
Single: I(t) = I₀ · exp(−t/τ)
Bi-exponential: I(t) = I₀ · [α₁·exp(−t/τ₁) + (1−α₁)·exp(−t/τ₂)]
Intensity-weighted: ⟨τ⟩_int = Σ fᵢτᵢ = Σαᵢτᵢ² / Σαᵢτᵢ. Amplitude-weighted: ⟨τ⟩_amp = Σαᵢτᵢ / Σαᵢ.
α₁ is the fraction of the initial amplitude, not of the emitted light: the longer component contributes more photons (fᵢ). Use ⟨τ⟩_int to compare with a single-exponential fit or a phase/modulation lifetime, and ⟨τ⟩_amp for quantum yields and FRET efficiencies; Φ = ⟨τ⟩_amp/τ_rad assumes one radiative rate for all components. The log scale shows a single exponential as a straight line.
References: J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed. (2006), ch. 4; A. Sillen, Y. Engelborghs, Photochem. Photobiol. 67, 475 (1998).
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact definitions of the fractional intensities and of the intensity- and amplitude-weighted averages of a multi-exponential decay. Φ = ⟨τ⟩_amp/τ_rad assumes one radiative rate for all components.
- Lakowicz J. R. (2006). Principles of Fluorescence Spectroscopy, 3rd ed., ch. 4. Springer.
- Sillen A., Engelborghs Y. (1998). The Correct Use of ‘Average’ Fluorescence Parameters. Photochem. Photobiol. 67, 475–486. doi:10.1111/j.1751-1097.1998.tb09443.x