Calculate radiometric age from an isotope system or custom half-life using the daughter-to-parent ratio and get an estimated age in years.
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Absolute Age Formula
The calculator estimates absolute age from radioactive decay using the measured daughter-to-parent isotope ratio. The main formula is:
Age = T_{1/2} \cdot \log_2(1 + D/P)The same formula can also be written with natural logarithms:
Age = T_{1/2} \cdot \frac{\ln(1 + D/P)}{\ln(2)}- Age = estimated age of the sample
- T1/2 = half-life of the parent isotope
- D/P = daughter isotope amount divided by parent isotope amount
- D = radiogenic daughter isotope in the sample
- P = remaining parent isotope in the sample
- ln = natural logarithm
In isotope system mode, the calculator uses the selected isotope pair’s built-in half-life, then applies the daughter-to-parent ratio you enter.
In custom half-life mode, the calculator first converts your half-life entry to years using the selected unit. It then applies the same decay formula to estimate the sample age.
Common Half-Lives Used for Absolute Age Dating
| Isotope system | Parent isotope | Daughter isotope | Half-life |
|---|---|---|---|
| Uranium-238 to Lead-206 | U-238 | Pb-206 | 4.468 billion years |
| Uranium-235 to Lead-207 | U-235 | Pb-207 | 704 million years |
| Potassium-40 to Argon-40 | K-40 | Ar-40 | 1.251 billion years |
| Rubidium-87 to Strontium-87 | Rb-87 | Sr-87 | 48.8 billion years |
| Carbon-14 to Nitrogen-14 | C-14 | N-14 | 5,730 years |
| Thorium-232 to Lead-208 | Th-232 | Pb-208 | 14.05 billion years |
| Samarium-147 to Neodymium-143 | Sm-147 | Nd-143 | 106 billion years |
| Daughter / Parent ratio | Fraction of one half-life elapsed | Meaning |
|---|---|---|
| 0.1 | 0.138 | Only a small amount of parent has decayed. |
| 0.5 | 0.585 | Less than one half-life has passed. |
| 1.0 | 1.000 | One half-life has passed. Parent and daughter amounts are equal. |
| 3.0 | 2.000 | Two half-lives have passed. |
Absolute Age Examples
Example 1: Uranium-238 sample
A sample has a U-238 to Pb-206 system and a daughter-to-parent ratio of 0.25.
Age = 4.468 \text{ billion yr} \cdot \log_2(1 + 0.25)Age = 4.468 \cdot 0.3219 = 1.438 \text{ billion years}The estimated absolute age is about 1.438 billion years.
Example 2: Carbon-14 sample
A sample has a C-14 to N-14 daughter-to-parent ratio of 1.0.
Age = 5730 \text{ yr} \cdot \log_2(1 + 1)Age = 5730 \cdot 1 = 5730 \text{ years}The estimated absolute age is 5,730 years.
Absolute Age Calculator FAQ
What does the daughter-to-parent ratio mean?
The daughter-to-parent ratio compares the amount of decay product to the amount of original radioactive parent isotope still left in the sample. A ratio of 1 means the daughter and parent amounts are equal, which corresponds to one half-life. A ratio of 3 means there is three times as much daughter as parent, which corresponds to two half-lives.
Why does the formula use 1 plus the daughter-to-parent ratio?
The original parent amount equals the parent remaining plus the daughter produced by decay. If the daughter-to-parent ratio is D/P, then the original-to-remaining parent ratio is 1 + D/P. The logarithm converts that decay ratio into the number of half-lives that have passed.
What assumptions affect the calculated age?
The result assumes the daughter isotope entered is radiogenic, meaning it was produced by decay of the parent isotope. It also assumes the sample stayed closed after formation, so parent or daughter isotopes were not added or removed. If the sample had initial daughter isotope or later chemical alteration, the simple age estimate can be too old or too young.