Calculator Tools

Half-Life Calculator

Calculate exponential decay, remaining quantity, time to reach a target, or half-life from observation, with drug and isotope presets.

Calculator mode

Start from an initial quantity and a half-life. The tool returns how much remains after the elapsed time, the fraction decayed, the number of half-lives passed, and the decay constant.

Formula: N(t) = N0 * (1/2)^(t/T)

Decimal places

Quantity unit

Initial quantity (N0)

Starting amount before any decay. Same unit as the result.

Half-life (T)

Unit

Elapsed time (t)

Unit

Result

Remaining quantity

32.99 mg

After 8 hours (1.6 half-lives), 32.99% of the original remains.

Remaining quantity
32.99 mg
Amount left after the elapsed time, on the exponential decay curve.
Amount decayed
67.01 mg
Initial minus remaining.
Fraction remaining
32.99%
Remaining divided by initial, as a percent.
Half-lives elapsed
1.6
Elapsed time divided by the half-life. 1 means exactly one half-life has passed.
Decay constant (lambda)
3.900000e-5 per s
ln(2) divided by the half-life in seconds.
Mean lifetime (tau)
7.213 h
1 / lambda. Average time before a single particle decays. About 1.443 times the half-life.
Time to drop to 1%
1.384 d
About 6.644 half-lives. Often used as a working definition of cleared.
Time to drop to 0.1%
2.076 d
About 9.966 half-lives. Useful for medication wash-out windows.

Equation

100 * (1/2)^(8 / 5) = 32.99

Calculations run entirely in your browser. Nothing is sent to a server.

Half-life presets

Tap any preset to load its half-life into the calculator. Pharmacology values are typical adult elimination half-lives; individual variation can be significant.

Pharmacology

Radioactive isotopes

Common

Half-lives elapsed and fraction remaining

For exponential decay, the fraction remaining depends only on the number of half-lives elapsed. 1 half-life leaves 50 percent, 2 leaves 25 percent, 10 leaves about 0.098 percent.

Half-lives elapsed (t / T)	Fraction remaining	Percent remaining
0	1	100%
0.5	0.707107	70.7107%
1	0.5	50%
1.5	0.353553	35.3553%
2	0.25	25%
3	0.125	12.5%
4	0.0625	6.25%
5	0.03125	3.125%
6.644	0.009999	0.9999%
7	0.007813	0.7813%
8	0.003906	0.3906%
9.966	0.001	0.1%
10	0.000977	0.0977%

How the math works

Exponential decay: the amount remaining follows N(t) = N0 * (1/2)^(t/T). After each half-life the quantity drops by 50 percent of whatever was left.
Decay constant: lambda equals ln(2) divided by the half-life. It is the instantaneous fractional decay rate.
Mean lifetime: tau equals 1 / lambda, about 1.443 times the half-life. It is the average time a single particle survives before decaying.
Cleared rules of thumb: about 5 half-lives reduce a substance to roughly 3 percent of the starting amount; 7 leaves about 0.78 percent; 10 leaves about 0.098 percent. Pharmacology commonly uses 5 half-lives as the wash-out point for therapeutic effect.

Where this applies

Radioactive isotopes: carbon-14 dating, medical tracers like Tc-99m and F-18, long-lived fallout isotopes like Sr-90 and Cs-137, and reactor fuels like U-235 and Pu-239.
Pharmacokinetics: most drugs follow first-order elimination in the therapeutic dose range, so the half-life predicts how long they stay in the bloodstream. Ethanol is a notable exception (zero order in the usual range).
RC circuits: the voltage across a discharging capacitor follows V(t) = V0 * exp(-t/RC) with a half-life of RC * ln(2).
Microbial growth and decay: the same math (with a sign flip) describes bacterial doubling time; the doubling time is the half-life of the reciprocal process.
Not medical advice: pharmacology results are estimates only. Real elimination depends on age, liver and kidney function, body composition, genetics, and other medications. Ask a clinician for clinical decisions.

How to use

Pick a calculator mode: Remaining after time, Time to reach quantity, or Half-life from observation.
Type the initial quantity, and the half-life or the observed remaining amount, depending on the mode.
Pick the time unit for each field (seconds through years) and the output unit for the answer.
Optionally tap a preset (caffeine, carbon-14, technetium-99m, uranium-238, and more) to seed a realistic half-life.
Read the result panel for the answer, the equation, the fraction remaining, the number of half-lives, the decay constant, and the mean lifetime.
Click Copy summary to grab a clean text block, or Reset to restore the default example.

About this tool

Half-Life Calculator handles the three classic questions around first-order exponential decay in one tool. Remaining after time mode takes an initial quantity, a half-life, and an elapsed time, and returns how much is left using N(t) = N0 * (1/2)^(t/T), plus the fraction decayed, the number of half-lives that have passed, the decay constant lambda, the mean lifetime tau, and how long it will take to reach 1 percent and 0.1 percent of the original. Time to reach quantity mode rearranges the equation to solve for elapsed time when you know an initial value, a target value below it, and the half-life; this is the calculation behind drug wash-out windows, medical isotope cool-down, and radiocarbon dating. Half-life from observation mode takes two data points (initial and remaining) plus the elapsed time and returns the half-life that explains the decay, which is how labs derive half-life numbers from real measurements. Every input accepts seconds, minutes, hours, days, weeks, months, or years; months use the average month length (30.4375 days) and years use the Julian year (365.25 days) that NIST and IAEA tables are based on. A preset menu seeds realistic numbers for the common cases: caffeine (5 h), ibuprofen (2 h), acetaminophen (2.5 h), Benadryl (8 h), Xanax (11 h), Valium (36 h), Prozac (4 d), THC single dose (1.3 d), nicotine (2 h); plus the classic isotopes carbon-14 (5730 y), iodine-131 (8.025 d), technetium-99m (6.01 h), fluorine-18 (109.77 min), cobalt-60 (5.27 y), tritium (12.32 y), strontium-90 (28.79 y), caesium-137 (30.17 y), radium-226 (1600 y), plutonium-239 (24,110 y), uranium-235 (704 million y), uranium-238 (4.468 billion y), and potassium-40 (1.251 billion y). The result panel reports the headline value, a plain English summary, and every derived quantity any chemistry, physics, pharmacology, or biology user might need next. Useful for chemistry students working through decay homework, biology students checking microbial growth curves, nurses and pharmacists checking medication wash-out windows, archaeologists sanity-checking radiocarbon ages, nuclear medicine technologists tracking tracer cool-down, electrical engineers modeling capacitor discharge, and anyone trying to understand 'how long does this stay around.' Pharmacology values are typical adult elimination half-lives; individual variation can be significant, and the tool is not medical advice. Everything runs locally in your browser; nothing is uploaded.

Free to use. Works in your browser. No signup, no login.

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