What formula does this calculator use?

It uses the standard radioactive decay law: N = N₀ × e^(−λt), where λ (the decay constant) equals ln(2) divided by the half-life. This is equivalent to N = N₀ × (1/2)^(t / t½).

Does the unit of time matter?

As long as the half-life and the elapsed time are expressed in the same unit, the result is correct. Select a unit from the dropdown and enter both values in that unit.

What is the decay constant (λ)?

The decay constant λ = ln(2) / t½ represents the probability per unit time that any given nucleus will decay. It is the natural way to express the rate of radioactive decay independent of sample size.

Can I use this for carbon dating calculations?

Yes. Carbon-14 has a half-life of about 5,730 years. Enter your initial C-14 quantity, 5730 as the half-life, and the sample age in years to find the fraction remaining.

What happens if I enter a very long elapsed time?

The remaining quantity will approach zero. For very large multiples of the half-life the result may display as 0.00 — this is mathematically correct given floating-point precision limits.

Radioactive Decay Calculator

Name: Radioactive Decay Calculator
Availability: InStock
Author: Nham Vu

Calculate how much of a radioactive substance remains after any elapsed time using the decay formula N = N₀ × e^(−λt).

Decay Parameters

Initial Quantity (N₀)

Any unit: grams, moles, Bq, atoms, etc.

Time Unit

Half-Life (t½)

Must be in the same unit selected above.

Elapsed Time (t)

Must be in the same unit selected above.

Quick Examples

Results

Remaining (N)

—

units

Decayed

—

units

% Remaining

—

of original

Decayed Remaining

0% 100%

Formula Breakdown

N₀ = —

t½ = —

λ = ln(2)/t½ = —

t = —

N = N₀ × e^(−λt) = —

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Summary

Calculate how much of a radioactive substance remains after any elapsed time using the decay formula N = N₀ × e^(−λt).

How it works

Enter the initial quantity (N₀) of the radioactive substance.
Select the time unit (seconds, minutes, hours, days, or years).
Enter the half-life of the isotope in the chosen unit.
Enter the elapsed time since the sample was measured.
The calculator applies N = N₀ × e^(−λt) and displays the remaining quantity, amount decayed, and percentage remaining.
The decay progress bar gives a visual sense of how far the sample has decayed.

Use cases

Estimate remaining activity of medical isotopes (e.g., I-131, Tc-99m) between preparation and administration.
Check carbon-14 remaining after thousands of years for radiocarbon dating exercises.
Solve homework and exam problems involving first-order nuclear decay.
Determine safe storage periods for radioactive waste or lab samples.
Visualize how quickly short-lived isotopes become negligible.
Verify half-life measurements against known decay constants.
Teach or learn exponential decay concepts interactively.
Compare decay rates of multiple isotopes side-by-side by running separate calculations.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu