Half-Life Calculator
Find the amount remaining after radioactive decay.
Any unit — grams, atoms, becquerels. The answer keeps the same unit.
Use the same time unit for both fields.
Results update as you type.
How it works
Half-life describes how quickly an unstable substance decays, and this half-life calculator tells you exactly how much is left after a given time. Enter the initial amount, the half-life of the isotope, and the elapsed time in the same time unit, and it returns both the remaining quantity and the percentage of the original that survives. Half-life matters far beyond nuclear physics. It sets the timeline for carbon dating ancient artefacts, dictates how long a medical tracer stays active in the body, governs the storage of radioactive waste, and even models how a drug concentration falls between doses. Because decay is exponential rather than linear, intuition often misleads people, so a half-life calculator keeps the maths honest. The formula works because each half-life multiplies the remaining amount by one half, and the elapsed time divided by the half-life counts how many of those halvings have occurred. After one half-life, half remains; after two, a quarter; after three, an eighth, and so on along a smooth exponential curve. Students, chemists, radiologists, and archaeologists all use a half-life calculator to turn an isotope's decay constant into a concrete, usable answer.
N = N₀ × 0.5^(t ÷ t½)
Radioactive decay is a first-order process, meaning a fixed fraction of the remaining atoms decays in every equal interval rather than a fixed number. The half-life is the interval over which exactly half of whatever is present decays, so after each half-life the quantity is multiplied by one half again. Raising 0.5 to the power of the number of half-lives elapsed, t divided by t½, captures this repeated halving continuously, which is why the amount left falls along a smooth exponential curve instead of dropping in steps.
Source:Standard physics (exponential radioactive decay law)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter initial amount, half-life and elapsed time.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Amount remaining updates instantly as you type — no button to press.
Frequently asked questions
Do the half-life and elapsed time need the same units?
Yes, and this is the most common mistake. Both the half-life and the elapsed time must be expressed in the same unit of time, whether seconds, days, or years, because the formula only uses their ratio. If the half-life is 8 days, enter the elapsed time in days too. Mixing units, such as a half-life in years with a time in days, produces a wildly wrong result.
What unit is the remaining amount reported in?
The remaining amount keeps whatever unit you used for the initial amount, because the formula multiplies by a pure fraction. Enter grams and you get grams back; enter number of atoms or becquerels of activity and the answer stays in those units. The separate percentage output is unit-free and simply tells you what fraction of the original quantity still survives after the elapsed time.
Why does the substance never fully disappear?
Exponential decay halves the remaining amount in each half-life but never reaches exactly zero, because half of any positive quantity is still positive. In theory a trace always lingers. In practice, after roughly ten half-lives less than 0.1% remains, which is usually treated as effectively gone. This is why safe-storage guidance for radioactive waste is often quoted as about ten half-lives.
Can I use this calculator for drug dosing or medicine?
The same exponential model describes how many drugs clear from the bloodstream, so the biological half-life predicts how a concentration falls between doses. However, real pharmacology involves absorption, distribution, and individual metabolism that this simple calculator does not model. Use it to understand the concept, but always follow a clinician's dosing instructions and never adjust medication based on a general decay estimate.
How is half-life related to the decay constant?
The half-life and the decay constant λ are two ways of describing the same rate. They are linked by t½ = ln(2) ÷ λ, where ln(2) is about 0.693. A larger decay constant means faster decay and a shorter half-life. This calculator works directly from the half-life, which is usually the value quoted in reference tables, so you do not need the decay constant.