Half-life calculator for amount, time and decay constant
Choose the unknown and enter the other three decay quantities. HitEquals returns the solution, number of elapsed half-lives, decay constant and a progression table.
Inputs used by this calculator
Half-Life Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Solve for | Remaining amount | Remaining amount · Elapsed time · Half-life · Initial amount | Chooses which Half-Life Calculator method or unknown the engine evaluates. |
| Initial amount | 100 | 1e-300 to 1e+300 | Supplies the initial amount quantity used by the published equation or result breakdown. |
| Remaining amount | 25 | 1e-300 to 1e+300 | Supplies the remaining amount quantity used by the published equation or result breakdown. |
| Elapsed time | 20 | 0 to 1e+300 | Supplies the elapsed time quantity used by the published equation or result breakdown. |
| Half-life | 10 | 1e-300 to 1e+300 | Supplies the half-life quantity used by the published equation or result breakdown. |
What half-life means
Half-life is the time required for an exponentially decaying quantity to reach half its current amount.
Exponential decay formula
The fraction remaining depends on elapsed time divided by half-life.
N=N₀(1/2)^(t/T½)λ=ln(2)/T½Solving inverse questions
Natural logarithms isolate elapsed time or half-life when both amounts are known.
t=T½·ln(N/N₀)/ln(1/2)Worked two-half-life example
After one half-life, 100 becomes 50. After the second, 50 becomes 25, so 20 years at a 10-year half-life leaves 25.
Decay constant
The positive decay constant λ equals ln(2) divided by half-life and appears in N=N₀e^(−λt).
Model limitations
A single half-life assumes one constant exponential process. Multi-compartment pharmacokinetics and changing environmental conditions need richer models.
Remaining fraction by half-lives
| Half-lives | Fraction | Percent remaining |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
Frequently asked questions
Does half-life depend on initial amount?
No, under a constant exponential-decay model.
Do time units matter?
Yes. Elapsed time and half-life must use the same unit.
Can the remaining amount reach zero?
The mathematical exponential approaches zero without reaching it.
What is the decay constant?
It is λ=ln(2)/T½.
Can I solve for the original amount?
Yes. Choose Initial amount.
Does this model drug dosing?
Only as simple one-phase decay; clinical pharmacokinetics may require more detail.
What to keep in mind
This is a constant-rate exponential model. Real biological clearance, chemical degradation and environmental processes may use multiple phases or changing rates. Time and half-life must use the same unit.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.