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Easily calculate radioactive decay and precisely determine remaining substance. Empower your research and feel confident with fast, accurate results.

Radioactive Half-Life Decay Calculator

Years

Days

Hours

Initial Quantity (N0) (g)

Half-Life (T) (years)

Time Elapsed (t) (years)

Radioactive Half-Life Decay Calculator Guidelines

It's simple—just follow these quick steps to get your result:

Enter the initial quantity (N0) in grams, MBq, or another consistent unit.
Specify the half-life (T) of the substance using matching time units.
Input the elapsed time (t) since measurement began.
Ensure half-life and elapsed time use the same unit (e.g., both in years).
Click Calculate to determine the remaining quantity (N(t)).
Use decimals for fractional half-lives or time values.

Radioactive Half-Life Decay Calculator Description

What Is Radioactive Decay?

Radioactive decay is a natural, stochastic process where unstable atomic nuclei lose energy by emitting radiation. Over time, the number of unstable atoms in a sample decreases, transforming into more stable atoms through a predictable pattern.

How Half-Life Works

The key metric in radioactive decay is the half-life (T). It represents the time it takes for half of the original radioactive atoms to decay. Regardless of the amount of material, after each half-life interval, 50% of the remaining atoms will have decayed.

Half-life is constant for a given isotope.
Decay continues exponentially—not linearly—over time.
The substance never fully disappears; it asymptotically approaches zero.

Pro Tip: Always match the time units between half-life and elapsed time to ensure accurate calculations (e.g., both in years or both in hours).

Mathematical Formula

Radioactive decay follows an exponential formula:

N(t) = N0 * (1/2)^t/T

N(t): Remaining quantity after time t
N0: Initial quantity
T: Half-life of the isotope
t: Elapsed time

Real-World Applications

Nuclear Medicine

Doctors use isotopes like Technetium-99m (half-life ~6 hours) for diagnostics. Understanding decay helps schedule scans and dosage.

Archaeology

Radiocarbon dating uses the known half-life of Carbon-14 (5,730 years) to estimate the age of organic artifacts like bones and textiles.

Geology

Dating rocks and Earth's crust uses long half-life isotopes like Uranium-238 (4.5 billion years).

Environmental Science

Monitoring radioactive pollutants (e.g., Cesium-137 in soil) relies on decay modeling for safety and cleanup planning.

Edge Cases to Consider

Zero Half-Life: Entire substance decays instantly; N(t) = 0 immediately.
Zero Initial Quantity: Result remains 0 regardless of time or half-life.
Extremely Long Half-Life: Minimal decay over typical human observation periods.
Multiple Half-Lives Elapsed: After n half-lives, only (1/2)^n of the original remains.
Fractional Time: Works accurately with decimals in time or half-life values.

Mini Case Studies

Medical Use of Technetium-99m

A hospital prepares 200 MBq of Technetium-99m at 8 AM. By 2 PM (after 6 hours, one half-life), only 100 MBq remains, ensuring a safe diagnostic dose for the patient.

Dating an Ancient Artifact

A wooden tool is analyzed and contains 25% of its original Carbon-14. Since 25% = (1/2)^2, two half-lives (~11,460 years) have passed, placing the tool’s age accordingly.

Alternate Formula

In terms of the decay constant λ, another common form is:

N(t) = N0 * e^(-λt), where λ = ln(2)/T

This continuous exponential form is often used in advanced physics and engineering contexts.

Start calculating now to confidently manage decay data, whether you're solving scientific problems or planning critical safety protocols.

Example Calculation

Initial Quantity (N0)	Half-Life (T)	Time Elapsed (t)	Remaining Quantity (N(t))
100 g	10 years	5 years	70.71 g
500 g	20 years	10 years	353.55 g
200 MBq	6 hours	12 hours	50 MBq
50 g	1000 years	3000 years	6.25 g
10 g	0 years	5 years	0 g

Frequently Asked Questions

The time required for half of the radioactive atoms in a sample to decay.

Using the formula N(t) = N0 * (1/2)^(t/T), where N(t) is the remaining quantity, N0 is the initial quantity, t is time elapsed, and T is the half-life.

Each additional half-life further reduces the remaining quantity by 50%. For example, after 3 half-lives, only 12.5% of the original sample remains.

Mathematically, it never reaches zero—it just becomes extremely small. However, practically it can become undetectable after many half-lives.

Yes, the formula supports decimal or fractional values for both time and half-life to allow precise calculations.

No, each radioactive isotope has its own unique decay constant and half-life, which determine how quickly it decays.

Ensure both half-life and elapsed time are in the same units (e.g., both in hours, days, or years) to get an accurate result.

After about 10 half-lives, less than 0.1% of the original substance remains, often considered negligible in practical scenarios.