What is the formula for radioactive activity?

A = λN, where N is the number of radioactive atoms and λ = ln 2 / t½ is the decay constant in s⁻¹. With N from a mass, A = (ln 2 / t½) × (m / M) × Nₐ. Example: 1 g of Cs-137 (M = 136.907 g/mol, t½ = 30.08 y) gives N = 4.399×10²¹ atoms, λ = 7.302×10⁻¹⁰ s⁻¹ and A = 3.21×10¹² Bq, or about 86.8 Ci.

How do I calculate activity after a certain time?

Use A(t) = A₀·e^(−λt), which is the same as A₀·(½)^(t / t½). Example: a 370 MBq (10 mCi) I-131 dose after 24 hours keeps (½)^(24 / 192.6) = 91.7% of its activity, so about 339 MBq remains. After one half-life half remains; after 10 half-lives about 0.1% remains.

How do I convert becquerels to curies?

1 Ci = 3.7×10¹⁰ Bq exactly, so divide Bq by 3.7×10¹⁰. Handy pairs: 1 mCi = 37 MBq, 1 µCi = 37 kBq, 1 nCi = 37 Bq, and 1 MBq = 27.03 µCi. 1 Bq is one decay per second, which is 60 disintegrations per minute (dpm).

What is specific activity?

Specific activity is the activity per unit mass of the pure isotope: SA = (ln 2 / t½) × Nₐ / M. Short half-lives give very high values: F-18 is about 3.5×10¹⁸ Bq/g, Co-60 about 4.2×10¹³ Bq/g (1,130 Ci/g), Ra-226 about 3.7×10¹⁰ Bq/g (≈1 Ci/g), and U-238 only 1.24×10⁴ Bq/g.

Why is 1 curie close to the activity of 1 gram of radium?

The curie was originally defined as the activity of 1 g of Ra-226. It was later fixed at exactly 3.7×10¹⁰ Bq. With today's half-life of 1,603 years, 1 g of Ra-226 is 3.65×10¹⁰ Bq, or 0.987 Ci.

Which half-life values does this calculator use?

The presets use NNDC NuDat 3 (ENSDF) half-lives, for example Cs-137 30.08 y, Co-60 1,925.28 d, I-131 8.0252 d, Tc-99m 6.0072 h, F-18 109.77 min, C-14 5,700 y and Ra-226 1,603 y. Atomic masses come from the AME2020 evaluation. Radiocarbon ages still use the conventional Libby half-life of 5,568 years, not 5,700.

Is this calculation exact for real sources?

It assumes a pure, single isotope. Real sources can contain carrier or stable isotopes, which lower the specific activity, and decay chains such as Sr-90 → Y-90 or Ra-226 → Rn-222 add daughter activity that grows in over time. For licensing or dosimetry, use the activity on the source certificate.

Radioactive Activity Calculator

Get activity A = λN from sample mass and half-life, decay it to any date with A = A₀·e^(−λt), find the time to reach a target activity, and convert Bq, MBq, GBq, Ci, mCi and µCi.

Activity from mass and half-life

Isotope preset

Molar mass (g/mol)

Half-life

Quantity input

Sample mass (g)

Pick an isotope, enter a mass and click Calculate.

Decay over time: A(t) = A₀·e^−λt

Uses the half-life entered on the left.

Initial activity A₀

Elapsed time t

Activity after t—

Same in Bq / Ci—

Remaining—

Time to decay to (same unit as A₀)

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Activity unit converter (Bq ↔ Ci)

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kBq

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MBq

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GBq

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TBq

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mCi

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µCi

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nCi

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pCi

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dpm

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Half-lives and specific activity of common isotopes

Half-lives: NNDC NuDat 3 (ENSDF). Atomic masses: AME2020. Specific activity = (ln 2 / t½) × Nₐ / M for the pure isotope.

Isotope	Half-life	Atomic mass	Bq/g	Ci/g	Typical use
H-3	12.32 y	3.016	3.56 × 10¹⁴	9,621	Tritium lights, fusion research
C-14	5,700 y	14.003	1.66 × 10¹¹	4.48	Tracers, radiocarbon dating
F-18	109.77 min	18.001	3.52 × 10¹⁸	9.52 × 10⁷	PET imaging (FDG)
P-32	14.266 d	31.974	1.06 × 10¹⁶	2.86 × 10⁵	Molecular biology labels
K-40	1.248 × 10⁹ y	39.964	2.65 × 10⁵	7.17 × 10⁻⁶	Natural potassium, K–Ar dating
Co-60	1,925.28 d	59.934	4.19 × 10¹³	1,132	Radiotherapy, sterilization, gauges
Ga-68	67.71 min	67.928	1.51 × 10¹⁸	4.09 × 10⁷	PET imaging (PSMA, DOTATATE)
Sr-90	28.91 y	89.908	5.09 × 10¹²	138	Fission product, RTGs
Mo-99	65.924 h	98.908	1.78 × 10¹⁶	4.81 × 10⁵	Parent of Tc-99m in generators
Tc-99m	6.0072 h	98.906	1.95 × 10¹⁷	5.27 × 10⁶	SPECT imaging
I-125	59.4 d	124.905	6.51 × 10¹⁴	1.76 × 10⁴	Brachytherapy seeds, assays
I-131	8.0252 d	130.906	4.6 × 10¹⁵	1.24 × 10⁵	Thyroid therapy and imaging
Cs-137	30.08 y	136.907	3.21 × 10¹²	86.8	Calibration sources, gauges
Lu-177	6.6443 d	176.944	4.11 × 10¹⁵	1.11 × 10⁵	Radioligand therapy
Ir-192	73.829 d	191.963	3.41 × 10¹⁴	9,213	Industrial radiography, HDR brachytherapy
Po-210	138.3763 d	209.983	1.66 × 10¹⁴	4,494	Static eliminators
Rn-222	3.8222 d	222.018	5.69 × 10¹⁵	1.54 × 10⁵	Indoor radon
Ra-226	1,603 y	226.025	3.65 × 10¹⁰	0.987	Historical curie standard
U-235	7.04 × 10⁸ y	235.044	7.99 × 10⁴	2.16 × 10⁻⁶	Reactor fuel
U-238	4.468 × 10⁹ y	238.051	1.24 × 10⁴	3.36 × 10⁻⁷	Natural uranium, U–Pb dating
Pu-239	24,110 y	239.052	2.3 × 10⁹	0.062	Reactor fuel
Am-241	432.6 y	241.057	1.27 × 10¹¹	3.43	Smoke detectors

Summary

Computes radioactive activity from the decay law A = λN, where λ = ln 2 / t½ and N = (mass / molar mass) × Avogadro's number. Pick one of 22 isotopes (half-lives from NNDC NuDat 3 / ENSDF, atomic masses from AME2020) or enter your own values. The result includes the decay constant, mean life, atom count, activity in Bq, MBq, GBq and Ci, and specific activity in Bq/g and Ci/g. A decay panel applies A(t) = A₀·e^(−λt) to give the activity after any elapsed time and the time needed to fall to a target activity, and a unit converter covers Bq, kBq, MBq, GBq, TBq, Ci, mCi, µCi, nCi, pCi and dpm.

How it works

Select an isotope or enter its molar mass and half-life.
Enter the sample mass in grams (or switch to an atom count).
The decay constant is λ = ln 2 / t½, converted to s⁻¹ (1 year = 365.2422 days, as in NuDat).
The atom count is N = (m / M) × 6.02214076×10²³, and the activity is A = λN in becquerels (decays per second); 1 Ci = 3.7×10¹⁰ Bq exactly.
In the decay panel, A(t) = A₀·e^(−λt) = A₀·(½)^(t / t½) gives the activity after time t, and t = ln(A₀ / A) / λ gives the time needed to reach a target activity.

Use cases

Estimating the activity of a Cs-137 or Co-60 source from its mass, or the mass behind a labelled activity.
Decay-correcting a calibration source or check source from its certificate date to today.
Working out how long an I-131, Tc-99m or F-18 dose takes to fall to a release or disposal limit.
Converting between becquerels and curies (MBq ↔ mCi, kBq ↔ µCi) for licences, labels and shipping papers.
Checking specific-activity and decay-constant values in nuclear physics coursework.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu