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

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) = —

Copied!

Summary

This tool uses the standard exponential decay equation N = N₀ × e^(−λt), where λ = ln(2) / t½, to calculate the remaining quantity of any radioactive isotope. Simply enter the initial amount, the half-life (in any consistent time unit), and the elapsed time to instantly see the remaining quantity, the amount decayed, and the percentage remaining. Results update in real time as you type.

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: 2026-09-30 · Reviewed by Nham Vu