What it does
Living things build their proteins from L-amino acids. After death the amino acids slowly turn into their mirror images (D forms) until the two reach a balance. The D/L ratio in a shell, tooth, bone or eggshell therefore grows with age, and with a known rate it gives an age. The reaction runs both ways, so the ratio follows reversible first-order kinetics:
ln[(1 + D/L) / (1 − K′·D/L)] − C = (1 + K′)·k·t
Here k is the rate constant, t the time, K′ = 1 ÷ the equilibrium constant (1 for most amino acids, whose D/L levels off at 1; about 0.77 for the epimerisation of isoleucine, measured as A/I), and C is the same expression for the D/L at time zero: fresh material, or the small amount of racemisation that sample preparation causes.
How to use it
- Pick the reaction (or type K′), then the sample’s D/L with its uncertainty and the D/L at time zero.
- Give the rate: either calibrate it from a sample of known age (from radiocarbon, for example) that has a D/L you measured, or type a known k (per year) with the temperature it is for.
- Give the effective temperature of your sample and of the calibration site, and the activation energy Ea. The rate is moved between temperatures with k₂ = k₁ · exp[−(Ea/R)(1/T₂ − 1/T₁)]. The effective temperature is the steady temperature that would cause the same racemisation as the real, changing one; it is a little above the mean because warm spells count for more.
- Leave Monte Carlo on: it draws every input many times from its normal spread and shows the real, lopsided spread of the age.
Worked example
The made-up example calibrates the rate from a sample 8,000 ± 200 years old with D/L 0.20 ± 0.01 at 12 ± 1 °C, with a time-zero D/L of 0.02 ± 0.005. That gives k = 2.28 × 10⁻⁵ per year at 12 °C. The sample to date has D/L 0.35 ± 0.02 and lay at 10 ± 1 °C; with Ea = 120 ± 10 kJ/mol its k is 1.598 × 10⁻⁵ per year, and the age is 21,600 ± 5,850 years. The Monte Carlo median is about 21,600 years with a 95 % range of about 12,500 to 37,600 years, longer on the old side.
The budget table shows why: the two temperatures give 44 % and 43 % of the variance, far more than the measured ratios. One degree is a lot. If both sites had the same temperature (set the sample to 12 °C), the age would be 15,100 ± 4,040 years.
Tips
- D/L can only be dated below its equilibrium (1/K′). Close to it, small errors in D/L give huge errors in age.
- Rates differ between amino acids, materials and even species: calibrate within the same material and lab method.
- Older samples often deviate from simple first-order kinetics. Many labs use empirical fits (for example power functions) instead; this tool uses the classic model only.
FAQ
Which units? Years throughout. A known k must be per year.
Why do GUM and Monte Carlo differ? The age depends on temperature exponentially and on D/L through a logarithm, so its spread is lopsided. The first-order figure treats it as straight; Monte Carlo does not.
Is my data uploaded? No. Everything runs in your browser and works offline. For study and planning: it is not a substitute for a lab’s own calibration and judgement.
Where the numbers come from
- Reversible first-order racemisation kinetics, ln[(1 + D/L)/(1 − K′·D/L)] = (1 + K′)kt + constant, as set out by Bada and others (e.g. Bada, J. L. and Protsch, R., 1973, PNAS 70) and in standard geochronology texts; Arrhenius equation; GUM (JCGM 100:2008) and GUM Supplement 1 (JCGM 101:2008) for the uncertainty.
- Checked against scipy: the reversible reaction L ⇌ D integrated with scipy.integrate.solve_ivp and the age found with scipy.optimize.brentq (the calibrated rate constant found the same way), with scipy.constants.R. Ages agree to 1 part in 10⁹; the GUM uncertainty agrees with finite differences on that model; the Monte Carlo median and 68 % and 95 % ranges agree with a separate numpy run within 1 %.
- All example values (ratios, ages, temperatures, activation energy and rate constant) are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.