Nuclear Decay Half-Life Calculator – Radioactive Decay

Calculate radioactive decay using half-life. Find remaining amount after time, or calculate time needed for specific decay.

Half-life

Initial Amount

Time Elapsed

How to Use This Half-Life Calculator

Enter the half-life

Input the half-life of the radioactive substance in your chosen time unit.

Input initial amount and elapsed time

Enter the starting quantity and how much time has passed since then.

Calculate remaining amount

Click Remaining to see how much of the substance is left after the elapsed time.

Half-Lives of Common Isotopes

Isotope	Half-Life	Common Use
Carbon-14	5,730 years	Radiocarbon dating
Uranium-238	4.5 billion years	Geological dating
Iodine-131	8 days	Medical treatment
Cesium-137	30 years	Industrial gauges
Tritium (H-3)	12.3 years	Glow-in-dark signs
Polonium-210	138 days	Static eliminators

Understanding Radioactive Decay

What Is Half-Life?

Half-life is the time required for half of a radioactive substance to decay. After one half-life, 50% remains. After two half-lives, 25% remains. After three, 12.5% remains. This exponential decay pattern is predictable and constant for each isotope.

The Decay Formula

The amount remaining follows: N(t) = N₀ × (1/2)^(t/T), where N₀ is initial amount, t is elapsed time, and T is half-life. This formula works for any time unit as long as t and T use the same unit. The decay is exponential, not linear.

Why Half-Life Matters

Half-life determines how long radioactive materials remain hazardous. Medical isotopes need short half-lives to minimize patient exposure. Nuclear waste has long half-lives, requiring secure storage for thousands of years. Carbon dating relies on C-14's predictable 5,730-year half-life.

Radioactive Decay Tips

Use consistent time units

Ensure half-life and elapsed time use the same unit (both seconds, both years, etc.).

Remember the 10 half-life rule

After 10 half-lives, less than 0.1% of the original material remains — effectively gone.

Decay is random but predictable

Individual atom decay is random, but large samples follow the half-life pattern precisely.

Half-life cannot be changed

Temperature, pressure, and chemical state do not affect radioactive decay rates.

Frequently Asked Questions

How do you calculate half-life decay?

Use the formula: remaining = initial × (1/2)^(time/half-life). For example, if you start with 100g of a substance with 5-day half-life, after 15 days (3 half-lives), you have 100 × (1/2)³ = 100 × 0.125 = 12.5g remaining.

Can half-life be affected by external factors?

No. Radioactive decay is a nuclear process unaffected by temperature, pressure, chemical bonds, or magnetic fields. This constancy makes half-life reliable for dating and medical applications. Only the nucleus itself determines decay rate.

What happens after many half-lives?

The amount approaches zero but never quite reaches it mathematically. Practically, after 10 half-lives, only 0.1% remains. After 20 half-lives, less than one millionth remains. For most purposes, the material is considered effectively gone.

How is half-life used in carbon dating?

Living organisms maintain constant C-14 levels. After death, C-14 decays with a 5,730-year half-life. Measuring remaining C-14 reveals how long ago the organism died. This works for samples up to about 50,000 years old (roughly 9 half-lives).

Why do some isotopes have short half-lives?

Unstable nuclei decay faster. Isotopes far from the stable neutron-proton ratio decay quickly. Very unstable isotopes may have half-lives of milliseconds. More stable isotopes can have half-lives of billions of years. Stability determines half-life.

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