How do I calculate the amount remaining after radioactive decay?

Divide the time elapsed by the half life to get the number of half lives, then multiply the initial amount by a half raised to that power. For an initial 100, a half life of 5,730 years and 11,460 years elapsed, that is 100 x (1/2) to the power of 2, which is 25.

What is the half life of carbon 14?

5,730 years. That is why radiocarbon dating works over a range of roughly the last 50,000 years, since after about nine half lives the remaining carbon 14 is too small to measure reliably against background radiation.

How long until half of a sample decays?

Exactly one half life. That is the definition. After two half lives half of that half has gone, leaving a quarter, and the pattern continues indefinitely, with the sample approaching zero but never reaching it.

What is the half life of carbon 14 used for?

Radiocarbon dating. Living organisms maintain a known ratio of carbon 14 to carbon 12 while alive. Once an organism dies the exchange stops and carbon 14 decays away at its 5,730 year half life, so the remaining ratio gives the time since death.

Why does the amount never reach zero?

Because each halving halves a positive number rather than subtracting a fixed amount. The remaining amount is always initial multiplied by a half raised to a positive power, which is always greater than zero. It approaches zero as the number of half lives grows without bound.

How do I find the time it takes to reach a certain amount?

Use the working backwards button, which applies t = half life x ln(initial divided by target) divided by ln(2). For an initial 100 with a 5,730 year half life and a target of 10 percent, that gives about 19,030 years.

What happens if the target amount is greater than the initial amount?

There is no such time. A decaying sample only ever gets smaller, so no amount of waiting produces a larger quantity. The calculator reports this rather than returning a negative time, which would be meaningless.

What is the decay constant lambda?

Lambda is ln(2) divided by the half life, and it appears in the exponential form of the decay equation N = N0 multiplied by e raised to minus lambda t. It describes the rate of decay per unit time and has units of the reciprocal of the time unit you are using.

How accurate is radiocarbon dating?

For samples under about 50,000 years the method is generally reliable, but the result is an estimate expressed with a range rather than an exact year. Calibration curves, contamination and the material sampled all introduce uncertainty that a reputable laboratory will report rather than hide.

Can I use this for a half life in hours or minutes?

Yes, as long as the half life and the time you are comparing it against use the same unit. A tracer with a six hour half life measured after 18 hours gives three half lives, leaving 12.5 percent. Converting one of the two to a different unit breaks the calculation.

How to Use the Half Life Calculator

This calculator works both forwards, to find how much of a decaying sample is left after a given time, and backwards, to find how long a decay will take to reach a target amount.

Step-by-Step Instructions

1 Enter the initial amount, which is the quantity at the moment decay starts. Any unit works as long as it is consistent throughout.
2 Enter the half life in the same time unit you intend to use for the elapsed time.
3 For a forward calculation, enter the time elapsed and read the amount remaining, percent remaining and number of half lives.
4 For a backward calculation, enter the amount you want to reach instead, then press Work backwards.
5 Use the How this is worked out panel to see the number of half lives and the arithmetic behind the result.

Understanding the Inputs

Initial amount

The starting quantity at the moment the clock starts, which for radiocarbon dating is the moment an organism died.

How to find it: A percentage such as 100, a mass in grams, a count rate in becquerels, or a dose in millicuries. The unit does not matter as long as it stays consistent with the target.

Why it matters: Every decay calculation is proportional to the starting amount. Half of nothing is nothing, which is why a zero initial amount can never be brought back to life by any amount of waiting.

Type: number · Default: 100

Half life

The time taken for half the sample to decay, in whatever unit you choose. Common values are 5,730 years for carbon 14, about 6 hours for the medical tracer technetium 99m, and roughly 4.5 billion years for uranium 238.

How to find it: Look it up for your isotope rather than estimating. Published half lives are measured values and are usually quoted to a few significant figures.

Why it matters: The half life sets the entire time scale of the decay. Doubling it doubles the time for every equivalent fraction to decay, which is why dating ranges are always quoted in half life multiples.

Type: number · Default: 5730

Time elapsed

In a forward calculation, how long the sample has been decaying. In a backward calculation, the amount you want to know the time to reach.

How to find it: Years for radiocarbon dating, hours or days for medical tracers and pharmaceuticals, or any consistent unit.

Why it matters: These two uses share one field because they are inverse problems. Solving for time and solving for the remaining amount are the same equation rearranged, and having both in one place makes it easy to check one against the other.

Type: number · Default: 11460

Tips & Best Practices

✓ Keep the half life and the elapsed time in matching units at all times.
✓ Think in half lives, so two half lives is a quarter and ten half lives is roughly a thousandth.
✓ Check a backward result by feeding the time it returns back into a forward calculation.
✓ Treat dating results as estimates with a range, never as an exact year.

Try the Half Life Calculator

by CalculatorPro Tools · Updated 10-12-2026