What formula does this use?

N(t) = N₀ × (1/2)^(t/t½), where N₀ is the initial quantity, t is elapsed time, and t½ is the half-life. The decay constant λ = ln(2) / t½ gives the probability of decay per unit time.

Do the time units have to match?

No. You can set the half-life in years and elapsed time in days, for example. The calculator converts both to seconds internally before computing.

What does "fraction remaining" mean?

It is N(t)/N₀ — the proportion of the original quantity still present. Multiply by 100 for the percentage remaining, or subtract from 100 for the percentage decayed.

Can I use this for Carbon-14 dating?

Yes. Set the half-life to 5730 years, the initial quantity to 100 (representing 100% modern carbon), and the elapsed time to the sample age. The remaining fraction tells you what percentage of C-14 should still be present.

What if my half-life or time is zero?

A half-life of zero is physically undefined. An elapsed time of zero returns the full initial quantity (100% remaining). Both values must be positive numbers.

Half-Life Decay Calculator

Name: Half-Life Decay Calculator
Availability: InStock
Author: Nham Vu

Enter an initial quantity, half-life, and elapsed time to find the remaining amount and percentage decayed.

Inputs

Initial Quantity (N₀)

Any unit: atoms, grams, Bq, etc.

Half-Life (t½)

Elapsed Time (t)

Common Isotopes

Remaining (N)

—

same unit as N₀

Fraction Remaining

—

Decayed

—

Decay Constant (λ)

—

per second

Remaining —

0% 100%

Decay Table

Half-lives elapsed	Fraction remaining	% remaining	Quantity

Enter values and click Calculate

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Summary

Enter an initial quantity, half-life, and elapsed time to find the remaining amount and percentage decayed.

How it works

Enter the initial quantity N₀ (any unit: atoms, grams, becquerels, etc.).
Set the half-life t½ and select its time unit.
Set the elapsed time t in the same or a different unit — the calculator converts automatically.
Results appear instantly: remaining quantity, decay constant λ, fraction remaining, and percentage decayed.
The decay table shows remaining quantity at 1, 2, 3, 5, and 10 half-lives for quick reference.

Use cases

Determine how much of a radioactive isotope remains after a given storage period.
Calculate radiation dose reduction over time for nuclear medicine planning.
Estimate the age of a sample using Carbon-14 dating principles.
Verify decay calculations in physics homework or lab reports.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu