Half-Life Calculator: Track Exponential Decay and Remaining Amounts

Whether you're studying nuclear physics, analyzing drug elimination in pharmacokinetics, dating ancient artifacts with carbon-14, or just curious about how substances decay over time, our free Half-Life Calculator makes it simple and accurate. Enter your initial amount, half-life value, and time elapsed — and instantly see how much remains, the decay constant (λ), percentage decayed, and number of half-lives passed.

This powerful exponential decay tool is mobile-friendly, ad-free, works offline after first load, and requires no sign-up. Perfect for students in Sahiwal or anywhere else preparing for exams, researchers modeling radioactive isotopes, or medical professionals tracking medication clearance. Try the half life calculator now and master exponential decay in seconds!

How to Use the LizoCalc Half-Life Tool

Entering Your Initial Amount and Decay Parameters

  1. Enter the initial amount (N₀) — this can be mass (grams, mg), number of atoms, activity (becquerels), or concentration. Any positive number works.
  2. Type the half-life value — the time it takes for half the substance to decay (e.g., 5730 years for carbon-14).
  3. Input the time elapsed (t) — how long the decay has been happening.
  4. Choose consistent time units for half-life and elapsed time (the tool auto-converts if needed).
  5. Hit Calculate — see remaining amount, decay constant λ, percent remaining/decayed, and half-lives elapsed instantly.
  6. Use Reset to clear fields and start a new calculation — great for comparing scenarios.

Pro tip: For very large or small numbers, the tool handles scientific notation automatically. No crashes, no ads — just clean results.

Selecting Time Units: From Seconds to Millennia

Decay happens across vastly different timescales. Our calculator supports:

  • Seconds — ideal for short-lived isotopes in labs
  • Minutes / Hours — pharmacokinetics and drug half-lives
  • Days / Weeks — biological and medical applications
  • Years / Centuries / Millennia — radioactive dating and nuclear waste

Need quick unit conversion? Check our Time Calculator or Date Calculator.

Reading the Results: Remaining Amount and Decay Constant (λ)

Results show:

  • Remaining amount — exact quantity left
  • Decay constant λ — rate of decay (larger λ = faster decay)
  • Percentage remaining / decayed
  • Number of half-lives elapsed
  • Interactive decay table and graph visualization

Understanding the Half-Life Formulas Used

The Exponential Decay Equation: N(t) = N₀ × 0.5^(t/t_0.5)

This is the most intuitive form — every half-life halves the amount:

N(t) = N₀ × (1/2)^(t / t_0.5)

Equivalent exponential form (using decay constant):

N(t) = N₀ × e^(-λt)

How to Calculate the Decay Constant (λ)

The decay constant shows how quickly decay occurs:

λ = ln(2) / t_0.5 ≈ 0.693 / t_0.5

Shorter half-life → larger λ → faster decay.

Determining Total Decay Percentage and Half-Lives Elapsed

Percentage remaining = (N(t) / N₀) × 100%
Percentage decayed = 100% − percentage remaining
Half-lives elapsed = t / t_0.5

For percentage help, try our Percentage Calculator.

Interactive Decay Table and Data Visualization

Tracking Substance Reduction Over Time Intervals

The tool generates a table showing remaining amount at regular intervals (e.g., every half-life or custom steps). Visualize the classic exponential curve — rapid early loss, then slower decline.

Why the Decay Table is Essential for Predictive Modeling

See patterns — predict storage times for nuclear waste, dosing schedules for medications, or when a sample becomes undetectable in carbon dating. Great for science fair projects or professional reports.

Practical Applications of Half-Life Calculation

Nuclear Physics: Calculating Isotope Stability

Determine safe handling times for isotopes like iodine-131 (8 days) or uranium-238 (4.5 billion years). Essential in reactors and waste management.

Pharmacokinetics: Managing Drug Clearance in Medicine

Many drugs have known half-lives (e.g., ibuprofen ~2 hours, morphine ~2–4 hours). Calculate how much remains in the body after dosing intervals to avoid overdose or underdose.

Archaeology: Carbon Dating and the Age of Samples

Carbon-14 (half-life 5730 years) dates organic remains up to ~50,000 years. Measure remaining ¹⁴C to estimate age — revolutionized archaeology and paleontology.

Step-by-Step Decay Calculation Examples

Example: How much of 100g remains after 3 half-lives?

N(t) = 100 × (1/2)^3 = 100 × 1/8 = 12.5 g

After 1 half-life: 50 g
After 2: 25 g
After 3: 12.5 g (87.5% decayed)

Solving for Time: How long until 10% of a substance remains?

0.10 = (1/2)^(t / t_0.5)
Take log: t / t_0.5 = log₂(1/0.10) = log₂(10) ≈ 3.322
t ≈ 3.322 × t_0.5

If half-life = 10 years → t ≈ 33.22 years until only 10% remains.

How do I convert minutes to years for half-life calculations?

Use conversion: 1 year ≈ 525,600 minutes.
For drug half-life of 120 minutes → in years: 120 / 525600 ≈ 0.000228 years.
Our Conversion Calculator or time tools handle this instantly.

Half-Lives ElapsedRemaining FractionExample (Start 100g)% Decayed
11/250g50%
21/425g75%
31/812.5g87.5%
41/166.25g93.75%
51/323.125g96.875%

More Math & Science Tools to Explore

Enhance your decay calculations with these free LizoCalc tools:

Exponential decay is everywhere — from atoms to medicine to history. Our Half-Life Calculator makes it accessible and accurate. Bookmark it, share it, and keep exploring the fascinating world of decay!

Frequently Asked Questions

Get instant answers to the most common questions. Can't find what you're looking for? Contact us

Half-life is the time required for a quantity to reduce to half of its initial value. In physics and chemistry, it describes how quickly unstable atoms undergo radioactive decay. The standard formula used in our calculator is: $N(t) = N_0(1/2)^{t/t_{1/2}}$, where $N(t)$ is the remaining quantity, $N_0$ is the initial quantity, $t$ is the elapsed time, and $t_{1/2}$ is the half-life period.

To find the half-life ($t_{1/2}$) when you know the initial and remaining amounts, use the formula: $t_{1/2} = (t cdot ln(2)) / ln(N_0 / N_t)$. For example, if 100g of a substance decays to 25g in 10 hours, it has gone through two half-lives (100 -> 50 -> 25), meaning the half-life is 5 hours. Our calculator automates this logarithmic math for instant results.

While both measure decay, they are inversely related. The decay constant ($lambda$) represents the fraction of atoms decaying per unit time, while half-life is the time it takes for 50% to disappear. They are linked by the equation: $t_{1/2} = ln(2) / lambda approx 0.693 / lambda$. High decay constants mean very short half-lives.

After each half-life, the remaining amount is reduced by 50%. After 1 half-life, 50% remains; after 2, 25% remains; and after 3 half-lives, exactly 12.5% (or 1/8th) of the original substance is left. You can calculate this easily by taking $(1/2)^n$, where $n$ is the number of half-lives elapsed.

Yes! While most common in nuclear physics, the concept of half-life is widely used in pharmacology (biological half-life) to determine how long a drug stays in your system, and in finance to calculate the 'half-life' of a debt or the depreciation of assets. Our calculator supports various time units to accommodate these different scientific and financial fields.

To find the remaining amount, identify the initial quantity, the elapsed time, and the half-life. Use the decay formula: $Remaining = Initial imes (0.5)^{(Time / Half ext{-}Life)}$. If you start with 80mg of an isotope with a 2-day half-life, after 6 days (which is 3 half-lives), the remaining amount is $80 imes (0.5)^3 = 10 ext{mg}$.