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chemistry

Radioactive Decay Calculator

Calculate the remaining quantity of a radioactive isotope after a given time period using its half-life.

Reviewed by Christopher FloiedPublished Updated

This free online radioactive decay calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Starting quantity (grams, atoms, Bq, etc.).

Half-life of the isotope.

Time elapsed (same unit as half-life).

Results

Amount Remaining

25

Amount Decayed

75

Half-Lives Elapsed

2

Decay Constant (λ)

1.2097e-4

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Radioactive Decay Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Radioactive Decay Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Radioactive Decay Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

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About Radioactive Decay Calculator

The radioactive decay calculator determines how much of a radioactive isotope remains after a given period of time, using the isotope's half-life. Radioactive decay is a random nuclear process in which unstable atomic nuclei emit radiation and transform into different elements or isotopes. Despite the randomness at the individual atomic level, the statistical behavior of large numbers of atoms follows precise first-order kinetics with a characteristic half-life that is constant and specific to each isotope. This calculator is used in nuclear physics, radiochemistry, nuclear medicine (dosimetry), radiocarbon dating in archaeology, environmental science (monitoring contamination), and nuclear power engineering.

The Math Behind It

Radioactive decay follows first-order kinetics: the rate of decay is proportional to the number of undecayed nuclei present. The differential equation dN/dt = −λN integrates to N(t) = N₀e^(−λt), where λ = ln(2)/t½ is the decay constant. After one half-life, 50% of the original sample remains; after two half-lives, 25%; after n half-lives, (1/2)ⁿ. Half-lives span an enormous range: from fractions of a second (e.g., Po-214, t½ = 164 µs) to billions of years (e.g., U-238, t½ = 4.47 × 10⁹ years). The activity of a sample (decays per second, measured in becquerels or curies) is A = λN, which also decreases exponentially. Radiocarbon dating uses the known half-life of C-14 (5730 years) to determine the age of organic materials up to about 50 000 years old. Medical isotopes like Tc-99m (t½ = 6.01 hours) are chosen to provide diagnostic images while minimizing radiation dose to the patient.

Formula Reference

Radioactive Decay

N = N₀ × e^(−λt); λ = ln(2)/t½

Variables: N = remaining amount; N₀ = initial amount; λ = decay constant; t = elapsed time; t½ = half-life

Worked Examples

Example 1: Carbon-14 dating

A sample originally had 100 units of C-14. After 11 460 years (two half-lives), how much remains?

Step 1:λ = ln(2) / 5730 = 1.21 × 10⁻⁴ yr⁻¹.
Step 2:N = 100 × e^(−1.21×10⁻⁴ × 11460) = 100 × e^(−1.386) = 100 × 0.25.
Step 3:Or simply: 2 half-lives → (1/2)² = 25% remaining.

25 units of C-14 remain; 75 units have decayed.

Common Mistakes & Tips

  • !Using mismatched time units between the half-life and elapsed time.
  • !Confusing activity (decays per second) with the amount of substance remaining.
  • !Applying this model to non-first-order nuclear processes (which are extremely rare; virtually all radioactive decay is first-order).

Related Concepts

Half-Life (Chemistry)

The same mathematical framework applies to first-order chemical reactions.

Avogadro's Number

Convert between mass and number of atoms to determine activity.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Half-Life Calculator

Frequently Asked Questions

Does anything affect the rate of radioactive decay?

Under normal conditions, no. Radioactive decay rates are insensitive to temperature, pressure, chemical state, and electromagnetic fields. They are determined by nuclear forces, not chemical or physical environment.

How is radiocarbon dating accuracy limited?

It is reliable up to about 50 000 years (roughly 9 half-lives of C-14). Beyond that, the remaining C-14 is too scarce to measure accurately. Calibration using tree-ring data and other methods corrects for historical variations in atmospheric C-14 levels.

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