A half-life is the time it takes for half of a quantity to decay or be eliminated. After one half-life, half remains; after two, a quarter; after three, an eighth, and so on, following the same fixed fractional rate.

Can I use any time units?

Yes, as long as the half-life and the elapsed time use the same unit. If the half-life is in hours, enter the time passed in hours; if it is in years, use years for both.

Does this apply to medication in the body?

Yes. Many drugs follow first-order elimination, so the same formula estimates how much of a dose remains after a given time using the drug's biological half-life. It is a simplified model and not medical advice.

Why does the quantity never reach exactly zero?

Exponential decay keeps halving the remaining amount, so mathematically a tiny fraction always persists. In practice the quantity becomes negligible after roughly ten half-lives, when less than 0.1 percent is left.

Half-Life Calculator

Initial Quantity

Half-Life

Time Passed

Remaining25.0000

Decayed75.0000

Percent Remaining25.00%

This half-life calculator models exponential decay, showing how much of a substance remains after a given time. Starting from an initial quantity, it applies the half-life law: every time one half-life elapses, the amount halves. It reports the remaining quantity, how much has decayed, and the percentage left. The same maths describes radioactive isotopes, drug elimination in the body, and any process with a constant fractional decay rate.

Formula

N = N₀ × (1/2)^(t ÷ t½)

N₀: Initial quantity at time zero
t: Time elapsed (same units as the half-life)
t½: Half-life: time for the quantity to halve (must be positive)
N: Quantity remaining after time t

How it works

Enter the initial quantity, the half-life of the substance, and the time that has passed (using the same time units for both).
The calculator raises one-half to the power of time divided by half-life and multiplies by the initial quantity to get the remaining amount.
It then reports the amount remaining, the amount decayed (initial minus remaining), and the percentage still present.

Worked example

A 100-gram sample of carbon-14, half-life 5,730 years, after 11,460 years have passed.

Number of half-lives: 11,460 ÷ 5,730 = 2.
Remaining fraction: (1/2)² = 0.25.
Remaining quantity: 100 × 0.25 = 25 g; decayed: 100 − 25 = 75 g.

25 g remain (25% of the original) and 75 g have decayed after two half-lives.

Frequently asked questions

What is a half-life?: A half-life is the time it takes for half of a quantity to decay or be eliminated. After one half-life, half remains; after two, a quarter; after three, an eighth, and so on, following the same fixed fractional rate.
Can I use any time units?: Yes, as long as the half-life and the elapsed time use the same unit. If the half-life is in hours, enter the time passed in hours; if it is in years, use years for both.
Does this apply to medication in the body?: Yes. Many drugs follow first-order elimination, so the same formula estimates how much of a dose remains after a given time using the drug's biological half-life. It is a simplified model and not medical advice.
Why does the quantity never reach exactly zero?: Exponential decay keeps halving the remaining amount, so mathematically a tiny fraction always persists. In practice the quantity becomes negligible after roughly ten half-lives, when less than 0.1 percent is left.

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