Skip to main content

Radioactive Decay Calculator

Free radioactive decay calculator: remaining nuclei, half-life, decay constant λ, and activity in Bq and Ci — with reverse solvers and an 18-isotope reference table. This radioactive half life calculator runs 100% in your browser.

Remaining nuclei calculator

How to calculate radioactive decay: enter the starting quantity N₀, the elapsed time, and the half-life — or pick an isotope to fill its half-life. Works as a carbon 14 decay calculator, iodine 131 decay calculator, or for any isotope.

N(t) = N₀ × (1/2)t/T½ = N₀ × e−λt  ·  λ = ln(2)/T½

The radioactive decay formula above is shown in both forms for every result.

—

Doubles as a decay constant calculator — λ is reported per your chosen time unit with every result.

Decay curve

Radioactive decay graph calculator: the curve below plots your numbers over 5 half-lives.

Not this tool: drug/medication half-lives — how fast your body clears a medicine follows pharmacokinetic models, not nuclear physics. For medicines use our drug half-life calculator. Scuba diving nitrogen half-times are a separate domain too.

Method & sources

The lambda decay constant formula is λ = ln(2) / T½, and every result here satisfies N(t) = N₀·(1/2)t/T½ = N₀·e−λt with activity A = λN and 1 Ci = 3.7 × 1010 Bq exactly. Worked checks: 100 g of carbon-14 becomes 50 g after 5,730 years; 1 kg of uranium-238 carries 12.43 MBq of activity.

Half-life values are evaluated data from primary nuclear-data sources: NIST evaluated half-life data; the NNDC Chart of the Nuclides (Brookhaven National Laboratory); SRS Appendix B — Nomenclature and Half-Life for Radionuclides (Chart of the Nuclides, 16th ed.); DOE Appendix C — Radionuclide Nomenclature. Molar masses: IUPAC atomic weights. Year = 365.25 days.

Educational tool, not radiation-safety advice. Never handle radioactive material based on a web calculator; follow your national regulator's guidance.

Frequently asked questions

What is the radioactive decay formula?
The remaining quantity after time t is N(t) = N₀ × (1/2)^(t/T½), where N₀ is the starting quantity and T½ is the half-life. Example: 100 g of carbon-14 becomes 50 g after 5,730 years. The same law is often written with the decay constant λ as N(t) = N₀ × e^(−λt); this calculator shows both forms for every result.
How do I calculate how much of a radioactive isotope is left after a given time?
Enter the starting quantity, the elapsed time, and the half-life in the Remaining tab — or pick an isotope from the table to fill its half-life automatically. Example: iodine-131 (T½ = 8.02 days) after 24.06 days — exactly 3 half-lives — leaves 12.5% of the starting amount.
What is the decay constant λ and how does it relate to half-life?
The decay constant λ is the per-unit-time probability that a nucleus decays, and λ = ln(2) / T½. A short half-life means a large λ and fiercely intense radiation. Example: cobalt-60 (T½ = 5.271 years) has λ = 0.1315 per year.
Are (1/2)^(t/T½) and e^(−λt) really the same thing?
Yes. Since λ = ln(2)/T½, e^(−λt) = e^(−ln(2)·t/T½) = (e^ln(2))^(−t/T½) = 2^(−t/T½) = (1/2)^(t/T½). They are two notations for one law; the half-life form is intuitive for counting half-lives, the exponential form is standard in physics derivations.
What is radioactivity (activity) and how is it different from the number of atoms?
Activity A = λN is the number of decays per second. The SI unit is the becquerel (1 Bq = 1 decay/second); the traditional unit is the curie. Two samples can hold the same number of atoms but have wildly different activities if their half-lives differ — 1 g of Co-60 roars at 1,132 Ci while 1 g of Ra-226 hums at 0.9885 Ci.
How do I convert between becquerel and curie?
1 curie (Ci) = 3.7 × 10¹⁰ becquerel, exactly, by definition. So 1 millicurie = 3.7 × 10⁷ Bq and 1 microcurie = 3.7 × 10⁴ Bq. Use the Bq ↔ Ci converter in the Activity tab for any value, including sub-multiples like nCi and pCi.
How do I find the activity of a given mass of an isotope?
Combine A = λN with N = (mass / molar mass) × Avogadro's number. Pick the isotope and enter the mass in the Activity tab — the calculator does all three steps. Checks: 1 g of radium-226 gives 0.9885 Ci (the historical reason the curie was defined near 1 Ci per gram of radium), and 1 kg of uranium-238 gives 12.43 MBq.
How long until only a target fraction of the isotope remains?
Solve the decay law for time: t = T½ × log₂(1/f), where f is the target fraction. In the Reverse tab enter the half-life and the target percent. Example: iodine-131 falls to 1% of its starting activity after 53.28 days.
How do I find a half-life from two activity measurements?
Measure activity A₀ and, after time t, activity A₁ (with A₀ > A₁), then T½ = t × ln(2) / ln(A₀/A₁). Example: 1000 Bq decaying to 125 Bq over 24.06 days gives T½ = 8.02 days — the half-life of iodine-131. Use the second Reverse solver; it also reports λ.
How does carbon-14 dating work?
Living things hold a steady ¹⁴C level; after death the ¹⁴C decays with T½ = 5,730 years while stable ¹²C stays put. Measuring the remaining fraction dates the sample: 25% remaining means 2 half-lives, i.e. 11,460 years. The method works back to about 50,000 years — roughly 9 half-lives, after which too little ¹⁴C is left to measure.
Why is iodine-131 useful in medicine if it decays so quickly?
Its 8.02-day half-life is a feature: it delivers its dose and then essentially vanishes — after 53.28 days less than 1% remains. The thyroid absorbs iodine selectively, so I-131 concentrates where it is needed for therapy and diagnosis, then decays away instead of irradiating the patient for years.
Can temperature, pressure, or chemistry change a half-life?
For practical purposes, no. The half-life is a property of the nucleus, shielded by the atom's electrons from heat, pressure, and chemical bonds — that is why radiometric dating is trustworthy. (Exotic exceptions exist only under extreme laboratory conditions, far outside anything this calculator is for.)
Why does uranium-238 barely decay during a human lifetime?
Its half-life is 4.47 billion years, so in one year only about 0.0000000155% of a sample decays — the change is utterly negligible on human timescales, yet the same slow trickle powers radiometric dating of the oldest rocks and keeps 1 kg of U-238 at a steady 12.43 MBq of activity.
Is radioactive half-life the same as a drug's half-life?
No — different domains, different math. A drug's elimination half-life describes how fast your body metabolizes and excretes a medicine (pharmacokinetics, multi-compartment models). Radioactive half-life describes nuclear decay of atoms. For medicines, use our drug half-life calculator instead; this page covers nuclear physics only.
How accurate are the half-lives in the isotope table?
They are evaluated values from primary nuclear-data sources: NIST evaluated half-life data, the NNDC Chart of the Nuclides (Brookhaven), the SRS Appendix B nuclide table (Chart of the Nuclides, 16th ed.), and the DOE radionuclide nomenclature standard. Values are given to the precision those sources publish. This is an educational calculator, not radiation-safety advice — never handle radioactive material based on a web tool.
Related: drug half-life calculator (medicines — different domain, see boundary note above).
Radioactive Decay Calculator — free, 100% client-side. Half-lives: NIST/NNDC evaluated data (see sources).

Free tool by NRTechStudio

⚡ Related Utility Tools

Explore similar general tools and calculators. 100% free, accurate, and runs completely in your browser without sign-up.

General Free & Private

Therapy Cost Calculator — How Much Does Therapy Cost?

Therapy cost calculator: estimate per-session rates, insurance copays, sliding-scale fees and online therapy prices. Compare 5 ways to pay and budget your year.

Launch Calculator →
General Free & Private

Timing Belt Replacement Cost Calculator

Timing belt replacement cost calculator: price belt-only vs full kit with water pump by vehicle class, dealer vs independent labor, and the cost of waiting.

Launch Calculator →
General Free & Private

Trip Planner

Free trip planner: build a day-by-day travel itinerary with activities, times, per-day costs, reorderable days, a packing checklist generator, and printable export. 100% client-side, no signup.

Launch Calculator →
General Free & Private

True Position Calculator

GD&T true position calculator: TP = 2×√(ΔX²+ΔY²) from basic and measured coordinates. Pass/fail vs tolerance, RFS/MMC/LMC bonus, batch CMM data, zone diagrams.

Launch Calculator →
General Free & Private

Tummy Tuck Cost Calculator

Free tummy tuck cost calculator: mini, full & extended abdominoplasty prices with muscle repair, financing payments, and recovery downtime planner.

Launch Calculator →
General Free & Private

Urgent Care Cost Calculator

Estimate urgent care visit costs by reason, add-ons, and region. Compare urgent care vs ER vs PCP vs telehealth vs retail clinic with insurance math.

Launch Calculator →
Browse All General Tools (95) → Master Directory (2,700+ Tools)