Four calculators, one panel.
Pick a mode below — mix and match units freely, everything recalculates live as you type, and every result explains itself.
Any consistent unit — grams, moles, activity, particle count, and so on.
How many half-lives have passed — doesn't need to be a whole number.
Must be greater than zero and less than the initial quantity.
Must be greater than 0% and less than 100%.
Must be greater than zero to solve for a half-life.
Must be greater than zero and no more than the initial quantity.
Must be greater than 0% and no more than 100%.
Must be greater than zero to solve for elapsed time.
Any time span converts the same way, whether it's a half-life or an elapsed time.
Two inputs to an answer.
No manual required — but here's the entire flow in four moves.
Pick a mode
Remaining amount for starting quantity + half-life → what's left. Solve half-life or Solve elapsed time for the two reverse cases. Unit converter for switching between time units on their own.
Enter what you know
Type a number and pick its unit from the dropdown right next to it — swap seconds for billions of years without touching the formula. Use the toggle to enter a percent remaining instead of two raw amounts. The example chips fill everything in with one tap.
Read the results
The main answer sits up top in large type. Related values in other units, the decay constant, and the number of half-lives elapsed sit below, with the exact formula and your numbers at the bottom.
Trust the checks
Impossible inputs — negative amounts, a remaining amount bigger than the starting one, or a zero half-life you're trying to divide by — get flagged with a plain-English reason instead of a wrong or broken answer. Copy any result set with one click.
One formula, three ways to use it.
Every mode above is the same equation, just solved for a different letter.
Remaining amount
Starting amount times one-half raised to the number of half-lives that have passed, t ÷ T.
Solving for half-life
Divide the elapsed time by how many half-lives it represents, worked out from the before-and-after ratio.
Solving for elapsed time
Multiply the half-life by the number of half-lives implied by the before-and-after ratio.
Questions people actually ask.
The short answers — with the long ones one tap away.
What is half-life?+
Half-life is the time it takes for exactly half of a decaying quantity — such as a radioactive isotope — to break down or reduce. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on, no matter how much you started with.
What is the formula for half-life decay?+
N(t) = N0 × (1/2)^(t ÷ T), where N0 is the starting amount, t is the elapsed time, and T is the half-life, both in the same time unit. The exponent t ÷ T is simply how many half-lives have passed.
How do I calculate the amount remaining after a given time?+
Enter the starting quantity, the half-life and its time unit, and either the elapsed time or the number of half-lives in the Remaining amount tab. The calculator applies N(t) = N0 × (1/2)^(t ÷ T) and also shows the percent remaining and the decay constant.
How do I find the half-life from a before-and-after amount?+
Rearrange the formula: T = t × ln(0.5) ÷ ln(N(t) ÷ N0). Enter the starting and remaining amounts — or just the percent remaining — plus the elapsed time in the Solve half-life tab, and the calculator returns the half-life in seconds, minutes, hours, days and years.
How do I find how much time has passed from a before-and-after amount?+
Rearrange the formula: t = T × ln(N(t) ÷ N0) ÷ ln(0.5). Enter the starting and remaining amounts — or the percent remaining — plus the known half-life in the Solve elapsed time tab to get the time passed.
How is the decay constant related to half-life?+
The decay constant λ and the half-life T are related by λ = ln(2) ÷ T. A shorter half-life means a larger decay constant, meaning the quantity shrinks faster.
Is this tool free, and where does my data go?+
It's completely free and runs entirely in your browser — nothing you type is uploaded, logged, or sent to any server. No account, no sign-up, no limits.