Chimie et Science

Free Radioactive Half-Life & Exponential Decay Calculator

Understanding radioactive decay and first-order exponential kinetics is fundamental across chemistry, nuclear physics, radiology, and archaeological carbon dating. A substance's half-life ($t_{1/2}$) represents the time needed for half of its unstable atomic nuclei to decay. Our free half life calculator lets students and scientists evaluate radioactive decay calculator problems, apply the official calculate half life formula, and determine decay constant lambda finder parameters.

Radioactive Half-Life & Decay Calculator

Calculate remaining quantity N(t) = N₀ · (1/2)^(t / t½), decay constant λ, and half-life steps.

Initial Quantity N₀ (grams, moles, %)

Half-Life t½

Time Elapsed t

Time Unit

Remaining Quantity N(t)

25.000

25.00% of initial quantity remaining.

Half-Lives Elapsed:2.00 t½

Decay Constant (λ):1.2097e-1 /year

Half-Life Decay Progress Table

Half-Life Step	Time (years)	Remaining Quantity	% Remaining
0 t½	0.00 years	100.00	100.0%
1 t½	5.73 years	50.00	50.0%
2 t½	11.46 years	25.00	25.0%
3 t½	17.19 years	12.50	12.5%
4 t½	22.92 years	6.25	6.3%
5 t½	28.65 years	3.13	3.1%

Mathematical Formulas & Calculation Methods

Half-Life Exponential Decay Formulas

Decay rate equation relating initial mass, time, and half-life duration.

N(t) = N₀ × (½)^(t / t½) | Decay Constant λ = ln(2) / t½ | N(t) = N₀ × e^(-λt)

Worked Step-by-Step Examples

Example 1: 100 grams of Carbon-14 (t½ = 5,730 years) after 11,460 years (2 half-lives)

"Calculate remaining mass of Carbon-14."

Steps:

Half-lives elapsed = 11,460 / 5,730 = 2.0.
N(t) = 100 × (½)² = 100 × 0.25 = 25.0 grams.
Decay Constant λ = ln(2) / 5730 = 0.000121 per year.

Result: Remaining Mass = 25.0 grams (25% remaining).

What is Calculateur de Radioactive Half-Life & Decay?

A half life calculator computes exponential decay of isotopes, pharmaceuticals, and physical quantities over time.

A carbon dating calculator chemistry tool determines sample age based on remaining Carbon-14 ratios.

How to Use Calculateur de Radioactive Half-Life & Decay

1Enter Initial Quantity N₀ (grams, moles, or percentage).
2Enter Half-Life duration t½ and Time Elapsed t.
3Select time unit (seconds, minutes, hours, days, years).
4View instant Remaining Quantity N(t), Decay Constant λ, and step-by-step decay table.

Key Features

Calculates remaining quantity N(t) and percentage remaining.
Calculates decay constant λ and half-lives elapsed.
Displays interactive 5-step half-life decay table.

Benefits of Using Calculateur de Radioactive Half-Life & Decay

Saves chemistry and physics students from manual exponential equation errors.

Useful for radiology technicians calculating medical isotope decay.

Practical Use Cases

Chemistry & Physics Students

Solve nuclear chemistry, decay kinetics, and half-life homework.

Radiologists & Pharmacists

Track medical isotope activity and drug elimination half-lives.

Frequently Asked Questions

What is the half-life of Carbon-14?

The half-life of Carbon-14 is approximately 5,730 years, making it ideal for radiocarbon dating organic artifacts up to 50,000 years old.

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