Which formula does the calculator use?

It uses first-order exponential decay: N(t) = N0 × (1/2)^(t/T1/2). It also uses λ = ln(2) / T1/2 and t = T1/2 × log2(N0/N).

Can I use units other than grams?

Yes. The amount can be grams, milligrams, moles, atoms, becquerels, or any consistent unit. Initial and remaining amounts must use the same unit.

When is this calculator not appropriate?

This tool assumes a constant half-life and first-order decay with no replenishment or multi-step kinetics. It is not suitable for non-exponential decay models or clinical dosing advice.

Half-Life Calculator

Solve exponential first-order decay for remaining amount, elapsed time, or half-life. Works for any consistent amount unit such as g, mg, mol, atoms, or Bq, and keeps all calculations in your browser.

Inputs & Options

Solve for

Amount label Display-only label. Initial and remaining amounts must use the same unit.

Initial amount (N₀)

Remaining amount (N)

Half-life (T½)

Elapsed time (t)

Choose a solve mode, enter the known values, then calculate.

Results

Ready.

This calculator assumes constant half-life and first-order exponential decay.

Primary result
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Fraction remaining

—

Percent remaining

—

Percent decayed

—

Elapsed half-lives

—

Decay constant λ

—

Decay Curve

Range: waiting for inputs Current point: not calculated

Half-Life Milestones

Half-lives	Elapsed time	Fraction remaining	Percent remaining	Amount remaining
0	—	1	100%	—

Formulas & Assumptions

Remaining amount: N(t) = N₀ × (1/2)^{t / T½}
Decay constant: λ = ln(2) / T½
Elapsed time: t = T½ × log₂(N₀ / N)
Half-life from data: T½ = t / log₂(N₀ / N)

These relations are valid for first-order exponential decay with a constant half-life. That model is standard for radioactive decay and many idealized first-order processes.

Initial amount must be greater than zero.
Remaining amount must be greater than zero and cannot exceed the initial amount.
Half-life and elapsed time must be positive when solving for finite decay.
If the remaining amount equals the initial amount after positive time, the implied half-life is infinite.

How to Use It

Select what you want to solve for.
Enter the known amount values using the same amount unit.
Enter the known time value and choose its unit.
Calculate to get the result, fraction remaining, and λ.
Use copy or download if you need a quick lab note or calculation record.

This tool is for educational and general scientific calculation use. It does not replace isotope-specific reference data, radiation safety procedures, or medical/pharmacokinetic advice.

FAQ

Can I use grams, moles, atoms, or becquerels?

Yes. The calculator treats amount as a generic quantity. Just keep the initial and remaining amounts in the same unit.

What if the amount becomes zero?

In a continuous exponential model, the amount approaches zero but never reaches an exact zero in finite time. If you enter zero, the elapsed-time and half-life formulas are undefined.

What if I know the decay constant instead of half-life?

You can convert using T½ = ln(2) / λ. This page reports λ automatically after each calculation.

Does this handle changing decay rates?

No. It assumes a single constant half-life. Multi-stage decay chains, growth terms, replenishment, and non-first-order kinetics need a different model.