Calculator
Use any consistent unit for isotope amounts, such as counts, moles, mass fractions, or normalized ratios.
Decay graph
The graph shows normalized parent remaining and radiogenic daughter growth across time. When a result exists, the marker highlights your calculated age.
Example data table
| Sample | Isotope system | Method | Half-life | Parent start | Parent now | Daughter now | Daughter start | Estimated age |
|---|---|---|---|---|---|---|---|---|
| Organic Remain | C-14 to N-14 | Parent remaining | 5730 years | 100 | 35 | 65 | 0 | 8678.50 years |
| Mineral A | Generic pair | Parent remaining | 1.25 Myr | 80 | 50 | 30 | 0 | 0.84759 Myr |
| Crystal B | U-238 to Pb-206 | Corrected parent-daughter | 4.468 Gyr | — | 72 | 28 | 0 | 2.11752 Gyr |
| Shard C | Generic pair | Corrected parent-daughter | 704 Myr | — | 40 | 90 | 10 | 1.11581 Gyr |
Formula used
Radiometric age dating relies on exponential decay. The decay constant is linked to half-life by:
λ = ln(2) / t½
For parent remaining data:
t = ln(P₀ / P) / λ
For corrected parent-daughter data:
D* = D − D₀
t = ln(1 + D* / P) / λ
P₀ is starting parent, P is current parent, D is current daughter, D₀ is initial daughter, and D* is radiogenic daughter produced after system closure.
How to use this calculator
- Enter a sample name and the isotope pair you are studying.
- Select the calculation method that matches your available measurements.
- Enter the half-life and choose its time unit.
- For parent remaining mode, provide starting parent and current parent.
- For corrected parent-daughter mode, enter current parent, current daughter, and any initial daughter estimate.
- Choose the desired output unit for the final age.
- Optionally add a ratio uncertainty percentage for a quick age spread estimate.
- Press Calculate Age to display the result above the form.
- Review the graph, compare percentages remaining, and export the summary if needed.
Interpretation notes
This calculator is useful for chemistry, geochemistry, and teaching workflows that compare decay rates, parent fractions, and daughter buildup. Accurate laboratory dating still depends on the correct isotope system, dependable half-life data, and a closed sample history.
Open-system behavior, contamination, isotopic loss, inherited daughter products, or incorrect initial assumptions can shift the apparent age. Use the graph and exported summary as analytical aids, not as substitutes for full isotope laboratory protocols.
FAQs
1. What does this calculator estimate?
It estimates sample age from radioactive decay data. You can use parent loss with a known starting amount or a corrected parent-daughter ratio with an initial daughter estimate.
2. Which formula is used?
For parent remaining data, age equals ln(P₀/P) divided by λ. For corrected parent-daughter data, age equals ln(1 + D*/P) divided by λ, where D* is radiogenic daughter and λ = ln(2)/half-life.
3. Why is half-life important?
Half-life fixes the decay constant. A longer half-life means slower decay and usually older ages for the same measured ratio.
4. What is radiogenic daughter?
It is the daughter isotope produced by decay after the system formed. The calculator subtracts any estimated initial daughter before computing age.
5. Can I use any isotope system?
Yes, if you know the appropriate half-life and your sample behaved as a closed system. The output is only as reliable as those assumptions.
6. What does uncertainty mean here?
The uncertainty field gives a quick age spread based on ratio uncertainty. It is an approximation, not a full laboratory propagation model.
7. Why might I get impossible results?
Impossible results usually come from negative values, daughter smaller than initial daughter, or current parent larger than starting parent. Check units and measurements carefully.
8. Does the graph show measured concentrations?
No. The graph shows normalized decay behavior from one starting parent amount. It helps visualize timing, not replace detailed isotope concentration plots.