BYTETOOLS

Half Life Calculator

Solve N = N0(1/2)^(t/t½) for remaining amount, elapsed time, half-life or starting amount, with decay constant, mean lifetime and isotope presets.

25
Quantity remaining
2
Half-lives elapsed
25.0000%
Fraction remaining
3.833e-12
Decay constant λ (1/s)

Decay details

  • N = N₀ × (1/2)^(t ÷ t½)
  • λ = ln2 ÷ t½ — the probability per unit time that a given nucleus decays.
  • Mean lifetime τ = 1 ÷ λ = 8,266.642584 y (about 1.4427 half-lives).
  • After 10 half-lives about 0.098% of the original material is left; after 20, roughly one part per million.

Decay table

Half-livesTime (y)Remaining% left
00100100.0000%
15,7305050.0000%
211,4602525.0000%
317,19012.512.5000%
422,9206.256.2500%
528,6503.1253.1250%
634,3801.56251.5625%
740,1100.781250.7813%
845,8400.3906250.3906%
951,5700.1953130.1953%
1057,3000.0976560.0977%

Exponential decay is a statistical law: it describes large populations of nuclei accurately but says nothing about when one particular atom decays. Years here are Julian years of 365.25 days. Published half-lives carry their own measurement uncertainty, so treat the last digit of any preset as approximate.

What is the Half Life Calculator?

A half-life is the time for half of a radioactive sample to decay. The remaining amount follows N = N₀ × (1/2)^(t ÷ t½), so after two half-lives a quarter of the original material is left.

  • Solves for N, N₀, elapsed time or half-life
  • Decay constant λ and mean lifetime τ from the same inputs
  • Presets for 15 commonly cited isotopes
  • Seconds through to years, converted automatically
  • Ten-row decay table with percentage remaining
  • Runs entirely in your browser — nothing is uploaded

How to use the Half Life Calculator

  1. 1

    Choose what to solve for: remaining amount, time, half-life or initial amount.

  2. 2

    Pick an isotope preset or type a custom half-life.

  3. 3

    Enter the quantities you know and select the time units.

  4. 4

    Read the answer plus the decay constant and mean lifetime.

  5. 5

    Check the decay table for the first ten half-lives.

About the Half Life Calculator

The ByteTools Half Life Calculator solves the exponential decay equation in every direction. Enter any three of starting quantity, remaining quantity, elapsed time and half-life, and it returns the fourth along with the number of half-lives that have passed and the percentage of material still present.

It also converts between the three ways of describing the same decay: half-life, the decay constant λ = ln2 ÷ t½, and the mean lifetime τ = 1 ÷ λ. A preset list covers isotopes people actually look up — carbon-14, iodine-131, technetium-99m, caesium-137, uranium-238 and more — and a decay table shows the first ten half-lives at a glance.

All the arithmetic is done in your browser in JavaScript with nothing uploaded. Exponential decay is a statistical law about large populations of atoms, so treat the figures as the expected behaviour of a sample rather than a prediction about any single nucleus.

Frequently asked questions

How do you calculate half-life?

Rearrange N = N₀(1/2)^(t ÷ t½) to t½ = t ÷ log₂(N₀ ÷ N). If a sample drops to a quarter of its original amount in 20 days, log₂(4) = 2 half-lives have passed, so the half-life is 10 days.

How much is left after 3 half-lives?

One eighth, or 12.5%, of the original amount. Each half-life removes half of whatever remains: 50%, then 25%, then 12.5%. After ten half-lives less than 0.1% is left.

What is the half-life of carbon-14?

5,730 years, which is why radiocarbon dating is useful for material up to roughly 50,000 years old. After about ten half-lives there is too little carbon-14 left to measure reliably.

What is the difference between half-life and mean lifetime?

Mean lifetime is the average time an individual nucleus survives and equals 1 ÷ λ, where λ = ln2 ÷ t½. It is always longer than the half-life by a factor of about 1.4427, because the long-lived tail of the distribution pulls the average up.

Does this work for drug half-life too?

The same exponential maths applies to first-order elimination, so the tool will give you the numbers. Real pharmacokinetics involves absorption, distribution and sometimes non-linear clearance, so these figures are educational estimates only and are not medical advice.

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