Radioactive Decay Calculator
Weigh the vial and name the isotope: the page counts the atoms, prices the decay constant and prints the activity in becquerel and curie.
Radioactive Decay Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One isotope, no daughter activity build-up
- Table half-lives quoted approximate — sources spread
In short: One gram of radium-226 — the vial that named the curie — holds 1/226 mol, and 6.02214076e+23 particles per mole put 2.664664e+21 atoms on the bench. A half-life of 1,600 years prices the decay constant at 4.332170e-4 per year, 1.372782e-11 per second, so the sample ticks at 3.658002e+10 becquerel — 0.988649 curie, within a percent of the 3.7e+10 definition. A microgram of technetium-99m is fiercer: 1.948786e+11 Bq, about 5 curie, because a 6.01-hour half-life spends its atoms fast.
Formula
λ = ln 2/t½ · N = m/M·N_A · A = λ·N · 1 Ci = 3.7e+10 Bq
Activity is population times hazard: count the atoms, attach the per-second probability λ = ln 2/t½, and the product is decays per second — becquerel. The curie is the historical wrapper, defined as 3.7e+10 Bq after the original radium gram. Half-life in years converts with the Julian year of 365.25 days; a short half-life spends atoms faster, which is why a microgram of a 6-hour isotope outscreams a gram of radium.
Worked Example
- Pick or type the half-life in years.
- Type the sample mass and the isotope’s molar mass.
- Read the atom count, the decay constant and the activity.
- Compare against the curie card — the radium gram that named the unit.
Defaults: Ra-226, 1 g, 226 g/mol → 2.664664e+21 atoms, λ 1.372782e-11/s, A 3.658002e+10 Bq = 0.988649 Ci. Drive the microgram chip with Tc-99m: 1.948786e+11 Bq, 5.266990 Ci.
Strengths & Limits Of This Model
Where this engine is strong
- Mass to activity in one card
- The curie’s radium origin priced honestly
Where it stops
- No decay-chain ingrowth
- No dose conversion — activity is not dose
Practical Use Cases
Nuclear medicine
activity of a delivered dose
Inventory and licensing
declared activity of a stock
Teaching
the curie’s radium origin
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Radioactive Decay Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does a microgram beat a gram?
Activity is atoms times hazard, and the hazard scales with 1/t½. Technetium-99m’s 6.01-hour half-life is roughly 2.3 million times shorter than radium’s 1,600 years, so each atom is that much more eager to decay — a microgram of it outscreams a gram of radium by a factor of about five.
How is this different from the half-life page?
Direction. That page follows the survival curve — how much is left after a wait, or how long a wait to a remainder. This page weighs the vial once and prices how hot it is now: atoms, decay constant, clicks per second. Dose planning uses both ledgers together.
What exactly is a curie?
The activity the Curies’ radium gram appeared to have — later pinned at exactly 3.7e+10 becquerel. The modern arithmetic for one gram of radium-226 lands within a percent of the definition, because the half-life and molar mass printed on today’s tables carry the wobble the original measurement did.
Why does the page use the Julian year?
Because half-lives in years need a fixed bridge to seconds, and 365.25 days — 31,557,600 seconds — is the calendar-agnostic convention. The difference from a 365-day year is 0.07%, small next to the quoted half-life’s own precision.
What does a zero mass print?
An honest zero: nothing in the vial, nothing clicks — 0.000000 Bq. A negative mass is refused; the ledger has no borrowing.
Why quote the half-life in years down to 6.01 hours?
The chips convert: technetium-99m’s 6.01 hours is 0.000685 of a Julian year, iodine-131’s 8.02 days about 0.02196. One unit on the input keeps the constant honest — λ = ln 2/t½ in per-year, then one bridge to seconds. The chips carry the conversions so the typing does not have to.
What sets the precision of the activity figure?
The table values, not the arithmetic: the constants run at full precision but the half-life and molar mass are quoted approximate, so the activity inherits their spread. The curie card is the sanity rail — one gram of radium-226 landing within a percent of 0.988649 Ci against the 3.7e+10 definition says the whole chain is honest.
Is activity the same as dose?
No — and the distinction matters. Becquerel counts decays; dose weighs the energy those decays deposit and the tissue’s sensitivity. Equal activities of different isotopes can deliver very different doses. This page stops at the click count; dose belongs to licensed medical physics.