Molecular Clock Divergence Time Calculator

Understanding the molecular clock calculator — concept and principle

The molecular clock idea is that DNA or protein sequences accumulate changes at a roughly steady rate, so the number of differences between two species can be read as the time since they shared a common ancestor. This calculator converts a genetic distance and a substitution rate into a divergence time in millions of years (Myr). It is used in teaching, phylogeography and quick checks of published dates.

The distance is shared by both branches, so divide by twice the rate.

How it is calculated

T = d / (2r)

d = genetic distance between the two sequences, in substitutions per site.
r = substitution rate per site per million years along one lineage.
T = divergence time in Myr.

The factor 2 is there because d counts the changes on both branches.

The principle

After two lineages split, each one keeps accumulating substitutions independently. If each gains r substitutions per site per Myr, then after T Myr the two sequences differ by about r·T + r·T = 2rT per site. Solving d = 2rT for T gives the formula. The idea goes back to Zuckerkandl and Pauling in the 1960s, and Kimura's neutral theory explained why: neutral mutations become fixed at a rate equal to the mutation rate, independent of population size. The rate r is usually calibrated with fossils or dated geological events such as island formation.

Worked example

Inputs: d = 0.02 substitutions/site, r = 0.001 per site per Myr.
Combined rate of both lineages: 2 × 0.001 = 0.002 per Myr.
T = 0.02 / 0.002 = 10 Myr.

Each point is the calculator re-run with only “Substitution rate (per site per Myr)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Substitution rate (per site per Myr)	Divergence time (Myr)
0.00025	40
0.0005	20
0.00075	13.33333333
0.001	10
0.00125	8
0.0015	6.666666667
0.002	5

How to read the result

The answer scales directly with d and inversely with r, so the rate is the biggest source of error: a rate that is 50% too high gives a date one third too young. Be clear whether a published rate is per lineage or pairwise; a commonly quoted rule of thumb for mammalian mitochondrial DNA, about 2% divergence per Myr, is pairwise, which corresponds to r ≈ 0.01 per lineage. Rates differ between genes, codon positions and taxa, so use a rate estimated for your marker and group.

Common mistakes

Using a pairwise rate as r, which halves the age.
Using raw p-distance for divergent sequences; multiple substitutions at the same site hide changes, so apply a model correction such as Jukes-Cantor.
Assuming one rate fits all branches when generation time or metabolism differ.

Keep in mind: A strict clock rarely holds exactly. Modern studies use relaxed-clock models with several calibrations and report confidence intervals; treat this single-rate estimate as a rough first approximation.

Frequently asked questions

What does substitutions per site mean?

The average number of changes per aligned position. A d of 0.02 means about 2 differences per 100 sites after correction.

Why do different genes give different dates?

Genes evolve at different speeds and are calibrated differently; ancestral polymorphism can also make gene divergence older than species divergence.

Can I use protein distances?

Yes, if the rate is expressed for the same protein and distance measure.

Sources: E. Zuckerkandl and L. Pauling, "Evolutionary divergence and convergence in proteins", in Evolving Genes and Proteins, 1965 · M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, 1983 · T. H. Jukes and C. R. Cantor, "Evolution of protein molecules", in Mammalian Protein Metabolism, 1969

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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