Activity of a Radioactive Sample Calculator

Compute the activity A = λN of a radioactive sample from the number of atoms and half-life. Results are shown in Bq, Ci, mCi, MBq, GBq, with the decay constant λ and mean lifetime τ.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter the Number of Atoms (N)
Input the total count of radioactive atoms in your sample. Scientific notation is accepted (e.g., 1e20 for 1×10²⁰ atoms).
2
Specify the Half-life (t½) in Seconds
Enter the half-life of the radioactive isotope in seconds. Convert from years/days/hours as needed: 1 year ≈ 3.156×10⁷ s.
3
Review your seven results
The calculator displays activity in Becquerels, Curies, MBq, GBq, and millicuries (mCi), plus the decay constant (λ) and mean lifetime (τ).

Example Calculation

A nuclear physics student calculates the activity of a sample with 1×10²⁰ atoms of an isotope with a 5,730-second half-life.

Number of Atoms (N)

1e20

Half-life (t½, seconds)

5730

Results

Activity

1.2097×10¹⁶ Bq

3.2694×10⁵ Ci

λ = 1.2097×10⁻⁴ s⁻¹

1.2097×10¹⁰ MBq

1.2097×10⁷ GBq

3.2694×10⁸ mCi

τ = 8,266.64 s

Tips

Convert Half-life to Seconds First

The half-life must be in seconds. Carbon-14 (5,730 years) = 5,730 × 365.25 × 24 × 3,600 = 1.807×10¹¹ s. Technetium-99m (6 hours) = 6 × 3,600 = 21,600 s. Always convert before entering the value.

Use the Curie Value for Medical Context

Medical imaging uses millicuries (mCi) or microcuries (μCi). Divide the Ci result by 1,000 for mCi or by 1,000,000 for μCi. A typical PET tracer dose is 5–15 mCi; a bone scan is 15–25 mCi.

Mean Lifetime vs. Half-life

Mean lifetime (τ) is the average time a nucleus survives before decaying. It equals 1/λ = half-life/ln(2) ≈ 1.443 × half-life. For dose-rate calculations in radiation safety, mean lifetime is sometimes used instead of half-life.

Seven Radioactivity Metrics from Two Inputs

The Activity of a Radioactive Sample Calculator derives seven radiation metrics from the number of atoms and their half-life.

For N = 1×10²⁰ atoms with half-life 5,730 seconds: activity is 1.2097×10¹⁶ Bq (Extremely high), 3.2694×10⁵ Ci (above 1 Ci threshold), decay constant λ = 1.2097×10⁻⁴ s⁻¹, 1.2097×10¹⁰ MBq, 1.2097×10⁷ GBq, 3.2694×10⁸ mCi, and mean lifetime τ = 8,266.64 s.

The Radioactive Decay Formulas

All six outputs derive from the fundamental relationship between half-life and decay probability.

λ (decay constant) = ln(2) / halfLife          // s⁻¹
Activity (Bq)      = λ × N                     // disintegrations/second
Activity (Ci)      = Bq / 3.7×10¹⁰            // 1 Ci = 3.7×10¹⁰ Bq
Activity (MBq)     = Bq / 1×10⁶
Activity (GBq)     = Bq / 1×10⁹
Activity (mCi)     = Ci × 1,000               // 1 Ci = 1,000 mCi
Mean Lifetime (τ)  = 1 / λ = halfLife / ln(2)  // seconds

💡 When evaluating reaction rates in chemistry that involve radioactive tracers, our pH Calculator can help you quantify the acidity of the solution, which often affects how radioactive decay products behave chemically.

Calculating Activity for N = 1×10²⁰ Atoms at Half-life 5,730 s

A physics student has a sample of 1×10²⁰ atoms of an isotope with a half-life of 5,730 seconds and needs all seven activity metrics.

Decay Constant (λ): ln(2) / 5,730 = 0.6931 / 5,730 = 1.2097×10⁻⁴ s⁻¹ — Moderate decay rate.
Activity (Bq): 1.2097×10⁻⁴ × 1×10²⁰ = 1.2097×10¹⁶ Bq — Extremely high; far above any clinical use level.
Activity (Ci): 1.2097×10¹⁶ / 3.7×10¹⁰ = 3.2694×10⁵ Ci — Above 1 Ci; industrial/research scale.
Activity (MBq): 1.2097×10¹⁶ / 1×10⁶ = 1.2097×10¹⁰ MBq — Megabecquerel scale.
Activity (GBq): 1.2097×10¹⁶ / 1×10⁹ = 1.2097×10⁷ GBq — Gigabecquerel scale.
Activity (mCi): 3.2694×10⁵ × 1,000 = 3.2694×10⁸ mCi — Well above typical medical doses (5–25 mCi).
Mean Lifetime (τ): 1 / 1.2097×10⁻⁴ = 8,266.64 s — Average nucleus survives ~2.3 hours.

Full results: 1.2097×10¹⁶ Bq | 3.2694×10⁵ Ci | λ=1.2097×10⁻⁴ s⁻¹ | 1.2097×10¹⁰ MBq | 1.2097×10⁷ GBq | 3.2694×10⁸ mCi | τ=8,266.64 s.

💡 For reactions involving radioactive decay products that alter solution basicity, our pOH Calculator can help you determine hydroxide ion concentration alongside activity measurements.

Lab and Real-World Conditions

While the decay constant is an intrinsic nuclear property unaffected by external conditions, several practical factors influence how measured activity relates to the calculated value.

Sample purity is critical: if 10% of measured mass consists of stable impurities, the effective atom count and measured activity will be 10% lower than calculated from total mass.

Physical form matters for detection efficiency — a thick solid sample self-shields gamma and beta radiation, reducing detected counts below true activity.

For liquid samples, detector geometry and quenching in liquid scintillation counting can reduce measured efficiency by 10–30%.

Environmental temperature and pressure do not affect the nuclear decay rate, but they affect sample containment and detector electronics, which is why calibration at controlled conditions is required for traceable activity measurements.

Regulations and Standards

Activity measurements are governed by strict national and international frameworks.

In the United States, the Nuclear Regulatory Commission (NRC, 10 CFR Parts 20 and 30–40) sets specific activity thresholds for licensing, transport, and disposal.

The IAEA Safety Standards Series No. RS-G-1.9 defines categorization of radioactive sources by activity in Becquerels — Category 1 sources (≥10¹⁴ Bq for Cs-137) pose a severe public hazard; Category 5 (≤10¹⁰ Bq) are unlikely to cause permanent injury.

The default calculation produces 1.21×10¹⁶ Bq — well within Category 1 for most isotopes, illustrating why large atom counts require full regulatory oversight.

Transport regulations (IATA DGR, IMDG Code) classify radioactive packages into categories (I-White, II-Yellow, III-Yellow) based on dose rate and activity, with specific limits for each isotope.

Frequently Asked Questions

What is the difference between Becquerels and Curies?

A Becquerel (Bq) is the SI unit of radioactivity: 1 disintegration per second. A Curie (Ci) is the older unit: 3.7×10¹⁰ disintegrations per second (the activity of 1 gram of radium-226). For the defaults (N=1e20, t½=5730 s): Activity = 1.2097×10¹⁶ Bq = 3.2694×10⁵ Ci.

How does half-life affect activity?

Activity is inversely proportional to half-life for the same number of atoms: A = ln(2)×N/t½. Halving the half-life doubles the activity. Carbon-14 (t½=5,730 yr ≈ 1.807×10¹¹ s) at 1×10²⁰ atoms produces about 3.84×10⁸ Bq — orders of magnitude less than the same atom count of a short-lived isotope.

What does the decay constant λ represent?

The decay constant (λ) is the probability per second that any given nucleus will decay. For half-life 5,730 s: λ = ln(2)/5730 = 1.2097×10⁻⁴ s⁻¹, meaning approximately 0.012% of remaining nuclei decay every second. It directly equals activity divided by atom count.

Can the activity of a sample increase over time?

The activity of an isolated sample always decreases over time as atoms decay. However, if a daughter nucleus is also radioactive, the total activity of the sample (parent + daughter) can temporarily increase before both decay. This secular or transient equilibrium is important in nuclear medicine and waste management.