Half-Life Calculator
Calculate how much of a substance remains after a given time using its half-life and exponential decay.
Amount remaining
70.71
70.71% of the original
Half-lives elapsed
0.5
Out of 5 days
After each half-life the amount halves: 100% → 50% → 25% → 12.5%. This is exponential decay, so it never quite reaches zero.
Half-Life Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Calculate how much of a substance remains after a given time using its half-life and exponential decay. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: half life calculator · radioactive decay calculator · half life formula
How We Calculate
This calculator uses standard physics and chemistry formulas verified by our team. All calculations are performed instantly in your browser using JavaScript — no data is sent to any server.
Formulas follow standard scientific definitions and physical constants, consistent with what is taught in school and university courses.
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: Enter the initial amount of the substance in any unit — grams, milligrams, Becquerels or just counts.
- Step 2: Enter the half-life, the time it takes for half the material to decay.
- Step 3: Enter how much time has elapsed, in the same unit as the half-life.
- Step 4: Read the remaining amount, the percentage left and the number of half-lives that have passed.
Worked Example
A 200 mg dose of a medicine with an 8-hour half-life: after 24 hours, three half-lives have passed, so the amount remaining is 200 × 0.5 × 0.5 × 0.5 = 25 mg, just 12.5% of the original. The calculator confirms the same result: elapsed half-lives = 3.00, remaining = 25 mg. This is why dosing schedules matter — most drugs are taken again after roughly one half-life to keep levels steady.
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.
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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