Half-Life Calculator – Calculate Decay Over Time
Find the half-life of a decaying quantity, or project how much remains after time.
About the Half Life Calculator
What is the Half Life Calculator?
A half life calculator works with the time it takes a decaying quantity to fall to half its value — either solving for the half-life or projecting a remaining amount.
Why use this calculator?
Radioactive decay, drug clearance and depreciation all follow exponential decay described by a half-life.
How to use it
- Choose to find the half-life or project the remaining amount.
- For half-life: give initial, remaining and elapsed time.
- For projection: give initial, half-life and elapsed time.
- Keep all times in the same unit.
Formula
Half-life = t × ln(2) ÷ ln(N₀/Nt); remaining = N₀ × 0.5^(t/HL).
The model assumes pure exponential decay for the whole period.
Frequently Asked Questions
What units should I use?
Any you like — hours, days, years — as long as the elapsed time and your answer\u2019s unit match.
Does doubling the amount double the half-life?
No. Half-life is a property of the decay process itself; it is independent of how much you start with.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.
How accurate are the results?
We use standard, widely accepted formulas and calculate in your browser using double-precision arithmetic. Results are rounded for readability, so treat them as reliable estimates rather than a guarantee. Real-world factors can vary the true figure.
Can I add this calculator to my own website?
Yes. Open this calculator page and use the "Add to your website" box in the sidebar to copy a ready-made iframe snippet, then paste it into any HTML page.
Does it work on a phone or tablet?
Yes. The layout is fully responsive, so it works on desktops, laptops, tablets and mobile phones, and every input adapts to touch screens.