# How old is the earth? Calculate it for yourself

### Introduction

In one respect, science and religion have been largely reconciled since the nineteenth century, when geologists such as Charles Lyell recognized the evidence for a very old earth, and, within a few decades, most mainstream religious denominations accepted this view as well.

But much to the consternation of scientists, young-earth creationism, which holds that the earth is only about 6000 years old, continues to be promoted in some quarters, and remains very popular with the public, especially in the United States. A 2010 Gallup poll found that 40% of Americans believe that “God created humans in their present form within the last 10,000 years” [Newport2010]. A 2009 poll found that 39% agreed that “God created the universe, the earth, the sun, moon, stars, plants, animals and the first two people within the past 10,000 years.” [Bishop2010]. (By contrast and more representative of OECD, about half as many Canadians espouse such beliefs [Science2.0].) Such notions are, of course, vastly different than the findings of modern science, which pegs the age of the earth at 4.56 billion years, and the age of the universe at 13.75 billion years.

While there are numerous experimental methods used to determine geologic ages, the most frequently employed technique is “radiometric dating,” which is based on measurements of various radioactive isotopes in rocks. The phenomenon of radioactivity is rooted in fundamental laws of physics and follows simple mathematical formulas. Dating schemes based on rates of radioactivity have been refined and scrutinized for several decades. The latest high-tech equipment permits reliable results to be obtained even with microscopic samples.

Radiometric dating is self-checking, because the data (after certain preliminary calculations are made) are fitted to a straight line (an “isochron”) by means of standard linear regression methods of statistics. The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date. Technical details on how these dates are calculated are given in Radiometric dating. Here is one example of an isochron, based on measurements of basaltic meteorites (in this case the resulting date is 4.4 billion years) [Basaltic1981, pg. 938]:

So, are radiometric methods foolproof? Just how reliable are these dates?

As with any experimental procedure in any field of science, these measurements are subject to certain “glitches” and “anomalies,” as noted in the literature. Skeptics of old-earth geology make great hay of these examples. For example, creationist writer Henry Morris [Morris2000, pg. 147] has highlighted the fact that measurements of specimens from a 1801 lava flow near a volcano in Hualalai, Hawaii gave apparent ages (using the Potassium-Argon method) ranging from 160 million to 2.96 billion years, citing a 1968 study [Funkhouser1968]. In the particular case that Morris highlighted, the lava flow was unusual because it included numerous xenoliths (typically consisting of olivine, an iron-magnesium silicate material) that are foreign to the lava, having been carried from deep within the earth but not completely melted in the lava. Also, as the authors of the 1968 article were careful to explain, xenoliths cannot be dated by the K-Ar method because of excess argon in bubbles trapped inside [Dalrymple2006]. Thus in this case, as in many others that have been raised by skeptics of old-earth geology, the “anomaly” is more imaginary than real.

The overall reliability of radiometric dating was addressed in some detail in a recent book by Brent Dalrymple, a premier expert in the field. He wrote [Dalrymple2004, pg. 80-81]:

These methods provide valid age data in most instances, although there is a small percentage of instances in which even these generally reliable methods yield incorrect results. Such failures may be due to laboratory errors (mistakes happen), unrecognized geologic factors (nature sometimes fools us), or misapplication of the techniques (no one is perfect).

We scientists who measure isotope ages do not rely entirely on the error estimates and the self-checking features of age diagnostic diagrams to evaluate the accuracy of radiometric ages. Whenever possible we design an age study to take advantage of other ways of checking the reliability of the age measurements. The simplest means is to repeat the analytical measurements in order to check for laboratory errors. Another method is to make age measurements on several samples from the same rock unit. This technique helps identify post-formation geologic disturbances because different minerals respond differently to heating and chemical changes. The isochron techniques are partly based on this principle.

The use of different dating methods on the same rock is an excellent way to check the accuracy of age results. If two or more radiometric clocks based on different elements and running at different rates give the same age, that’s powerful evidence that the ages are probably correct.

Along this line, Roger Wiens asks those who are skeptical of radiometric dating to consider the following [Wiens2002]:

There are well over forty different radiometric dating methods, and scores of other methods such as tree rings and ice cores. All of the different dating methods agree — they agree a great majority of the time over millions of years of time. Some [skeptics] make it sound like there is a lot of disagreement, but this is not the case. The disagreement in values needed to support the position of young-Earth proponents would require differences in age measured by orders of magnitude (e.g., factors of 10,000, 100,000, a million, or more). The differences actually found in the scientific literature are usually close to the margin of error, usually a few percent, not orders of magnitude!

Vast amounts of data overwhelmingly favor an old Earth. Several hundred laboratories around the world are active in radiometric dating. Their results consistently agree with an old Earth. Over a thousand papers on radiometric dating were published in scientifically recognized journals in the last year, and hundreds of thousands of dates have been published in the last 50 years. Essentially all of these strongly favor an old Earth.

### Radioactive isotopes and the age of the earth

Until recently, only large scientific laboratories could afford mass spectrometers, which are the principal tool used to measure dates of rock samples. But recently the prices of these devices have dropped to levels that even amateur meteorite hunters and others can afford. Used mass spectrometers are currently available at eBay.com for as little as USD\$99. Some have said that the last of the flat-earth believers did not give up until they could hold GPS receivers in their hand that give their latitude-longitude position. Will skeptics of old-earth geology wait until mass spectrometers are in every home before finally conceding that the earth is older than 6000 years?

In any event, there is a simple way to see that the earth must be at least 1.6 billion years old, which does not require any mass spectrometers, isochron graphs, calculus or statistical software (provided one accepts a few very-well-established measured rates of radioactivity). Consider the list of all known radioactive isotopes with half-lives of at least one million years but less than one quadrillion years, and which are not themselves produced by any natural process such as radioactive decay or cosmic ray bombardment [Nuclides2012]:

 Isotope Half-life (years) Found in nature? In-115 4.41 x 1014 yes Gd-152 1.08 x 1014 yes Ba-130 7.00 x 1013 yes Pt-190 6.50 x 1011 yes Sm-147 1.06 x 1011 yes La-138 1.02 x 1011 yes Rb-87 4.97 x 1010 yes Re-187 4.12 x 1010 yes Lu-176 3.76 x 1010 yes Th-232 1.40 x 1010 yes U-238 4.47 x 109 yes K-40 1.25 x 109 yes U-235 7.04 x 108 yes Pu-244 8.00 x 107 yes Sm-146 6.80 x 107 yes Nb-92 3.47 x 107 no Pb-205 1.73 x 107 no Cm-247 1.56 x 107 no Hf-182 8.90 x 106 no Pd-107 6.50 x 106 no Tc-98 4.20 x 106 no Bi-210 3.04 x 106 no Dy-154 3.00 x 106 no Fe-60 2.62 x 106 no Tc-97 2.60 x 106 no Cs-135 2.30 x 106 no Gd-150 1.79 x 106 no Zr-93 1.53 x 106 no

(In the above chart, years are displayed in scientific notation: i.e., 1 x 106 = 1 million; 1 x 109 = 1 billion, etc.)

All of the above isotopes are readily produced in nuclear reactors, so there is every reason to believe that they were formed along with stable isotopes, in roughly the same abundance as nearby stable isotopes of similar atomic weight, when the material forming our solar system was produced in an ancient stellar explosion. A quick calculation shows that after an elapsed period of 20 times the half-life of a given isotope, the fraction 1/220 = 1/1048576 (i.e., roughly one part in one million) of the original isotope will remain, which is a small but nonetheless detectable amount. Similarly, after 30 half-lives, roughly one part in one billion will remain, and after 40 half-lives, roughly one part in one trillion will remain, which is near the current limit of detectability.

Now note that an absolutely clear-cut fact is revealed in the above table: every isotope in the list with a half life less than 68 million years is absent in nature, evidently because all traces of these isotopes have decayed away, yet those isotopes with half-lives greater than 68 million years are present at some minute but detectable level. This is incontestable evidence that the material from which our earth and solar system was formed is at least 20 x 68 million (= 1.36 billion) years old, and more likely is at least 40 x 68 million (= 2.72 billion) years old. For details, see [Dalrymple2004, pg. 202-204; Miller1999, pg. 69-72].

### Conclusion

Radiometric dating, like any other experimental discipline, is subject to a variety of errors, ranging from human errors to rare anomalies resulting from highly unusual natural circumstances. But while errors and anomalies can occur, the burden of proof is not on scientists to fully explain each and every error. Instead, the burden of proof is on skeptics of old-earth geology to explain why tens of thousands of other carefully measured ages are all internally and externally consistent. Indeed, there is no known physical phenomenon that can yield consistent results in many thousands of measurements, year after year, except one: that these specimens really are as old as the data shows them to be. As biologist Kenneth Miller has observed, “The consistency of [radiometric] data … is nothing short of stunning.” [Miller1999, pg. 76].

[A version of this article previously appeared in the SMR blog, and in The Conversation.]