Half-Life Calculator
Solve any half-life problem: remaining or initial amount, elapsed time or half-life itself, plus the decay constant and mean lifetime of exponential decay.
Amount remaining
70.711
70.711% of the original remains
Half-lives elapsed
0.5
Of 10 days each
Decay constant (λ)
0.069
λ = ln(2) ÷ half-life
Mean lifetime (τ)
14.427
τ = half-life ÷ ln(2), in days
Exponential decay follows N(t) = N(0) × 0.5^(t ÷ T). After each half-life the amount halves: 100% → 50% → 25% → 12.5%, so it never quite reaches zero. All time values must use the same unit.
Last updated: January 2026
How this calculator is verified
Checked by Rahim Virani on
- Decay constant derived as ln(2)/t-half and applied to remaining quantity
- Verified against a 500-year half-life sample decaying over 2000 years
- Elapsed time beyond several half-lives does not underflow to zero
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Use this calculator whenever you work with anything that decays exponentially: radioactivity in physics labs, drug clearance in pharmacy and medicine, pesticide breakdown in agriculture, and even capacitor discharge in electronics. In India it is especially handy for students preparing for Class 12 physics and chemistry, where half-life problems are a favourite exam question, and for pharmacists estimating how long a compounded preparation stays effective. Researchers measuring contamination after radiation treatment, and farmers timing how long a pesticide remains active before harvest, both use the same math. It is also a fine demonstration of exponential decay for anyone curious about why radioactive waste stays dangerous for such long periods — run the numbers and see how slowly the last few percent disappear.
How to Use This Calculator
- Step 1: Choose what to solve for — Remaining, Initial, Time or Half-life — in the segmented control.
- Step 2: Enter the values you know, keeping every time value in the same unit (seconds up to years).
- Step 3: Read the solved value, the percentage of the original remaining and the number of half-lives elapsed.
- Step 4: Check the decay constant λ and the mean lifetime τ, which describe how fast the substance decays.
Worked Example
Carbon dating relies on this exact math: a fossil sample containing 25% of its original carbon-14 (half-life 5,730 years) has been decaying for two half-lives, so it is 11,460 years old — the calculator returns 11,460 years with 2.00 half-lives elapsed. In the lab, a 2.5 kg sample measured down to 2.1 kg after 5 minutes gives a half-life of 19.88 minutes, and a 200 mg drug dose with an 8-hour half-life leaves exactly 25 mg after 24 hours, 12.5% of the original. The decay constant and mean lifetime are derived automatically: for carbon-14, λ = 0.000121 per year and τ = 8,266.6 years.
Tips and Common Mistakes
- •Use the same time unit for half-life and elapsed time, or the exponent will be wrong.
- •For practical purposes, plan on 10–12 half-lives for a substance to be effectively gone.
- •Remember that 50% remaining means half-life × 1; 25% means × 2; 12.5% means × 3 — a quick mental check.
- ✗Do not subtract half-lives from the amount as if it were linear — halving is not subtraction.
- ✗Do not mix units: entering half-life in hours and elapsed time in days silently breaks the answer.
Expert Note
The half-life formula N(t) = N₀ × (1/2)^(t/t½) applies to all first-order exponential decay processes, not just radioactivity. Drug elimination, carbon dating, and capacitor discharge all follow the same math. For carbon-14 dating, the half-life is 5,730 years — a fossil with 25% of original C-14 is exactly 2 half-lives old (11,460 years).
Sources and References
- •IUPAC Compendium of Chemical Terminology: Half-life
- •NIST: Radioactive Decay Data — National Nuclear Data Center
- •NCERT Class 12 Physics, Chapter 13: Nuclei
Official sources are linked so you can confirm the current rate yourself. Check the linked page for the latest notification before relying on these figures.
Frequently Asked Questions
What is half-life?
Half-life is the time it takes for half of a radioactive (or decaying) substance to break down. After one half-life 50% remains, after two 25%, after three 12.5% — the amount halves each period, never reaching zero.
How is half-life calculated?
Remaining = initial × 0.5^(elapsed ÷ half-life). For example, 500 mg of a substance with a 12-hour half-life leaves 62.5 mg after 36 hours (three half-lives). The exponent is the number of half-lives elapsed.
Is half-life only for radioactive material?
No. The same exponential-decay math applies to drug clearance from the body, chemical reactions, capacitor discharge and even carbon-14 dating. Any quantity that decays proportionally to what remains follows a half-life.
Does the amount ever reach zero?
Mathematically, no — decay is exponential, so a fraction always remains. In practice, quantities fall below measurable or biologically significant levels after 10–12 half-lives (about 0.1% of the original).
What units should I use?
Days, hours or years — both the half-life and elapsed time must use the same unit. For example, iodine-131 has a half-life of about 8 days; for carbon-14 it is about 5,730 years.
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