Half-Life Calculator
Solve exponential decay problems for remaining quantity, elapsed time, half-life, or initial amount. Includes the decay constant, mean lifetime, and a live decay curve chart.
25
REMAINING (NT)
25%
% REMAINING
2
HALF-LIVES (N)
Radioactive Decay Calculator
Remaining Quantity (Nt)
25
of 100 initial units
25% remaining
2
Half-Lives (n)
75%
Decayed
25
Remaining
2
Half-Lives
0.1386
λ (Decay Const)
7.21
Mean Lifetime τ
Exponential Decay Curve
Quantity remaining over time, N(t) = N₀ × (½)^(t/T½). The marker shows your current point.
Half-Life Reference Table
Percent of the initial quantity left after each half-life.
50%
1×T½
25%
2×T½
12.5%
3×T½
6.25%
4×T½
3.13%
5×T½
0.098%
10×T½
Understanding Half-Life and Exponential Decay
Half-life describes any process where a quantity shrinks by the same proportion in equal time intervals — radioactive isotopes are the textbook example, but the same math governs how quickly the body clears a medication from the bloodstream or how fast a charged capacitor discharges through a circuit. Because the decay rate depends on how much is left, the quantity never truly hits zero — it approaches it more and more slowly forever. Enter any three known values on the left and this calculator solves for whichever one is missing.
The Half-Life Formulas
Remaining quantity: Nt = N₀ × (½)^(t/T½) | equivalently Nt = N₀ × e^(−λt)Number of half-lives elapsed: n = t / T½Decay constant: λ = ln(2) / T½ ≈ 0.693 / T½Mean lifetime: τ = 1 / λ = T½ / ln(2) ≈ 1.4427 × T½Solve for time: t = T½ × log₂(N₀ / Nt) | Solve for half-life: T½ = t × log₂(N₀ / Nt)⁻¹Decay constant vs. half-life: λ and T½ describe the exact same process from two different angles. T½ tells you how long until half of a sample is gone; λ tells you the fraction decaying per unit time at any instant. They’re always related by λ = ln(2) / T½, so knowing either one gives you the other.
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Radioactive Decay
Carbon-14 (t½ ≈ 5,730 yrs) dates ancient organic material; iodine-131 (t½ ≈ 8 days) is used and tracked closely in medical treatment.
💊
Drug Elimination
A medication's elimination half-life determines how often it must be dosed to keep blood levels in a therapeutic range.
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Capacitor Discharge
The voltage across a discharging capacitor follows the same exponential curve, halving over equal time intervals.
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Never Reaches Zero
Because each interval only removes half of what remains, the curve approaches — but mathematically never touches — zero.
— FAQ