🧪 Half-Life Calculator – Calculate Radioactive Decay, Time, and Half-Life Instantly

The Half-Life Calculator is an interactive scientific tool that helps you understand and calculate radioactive decay and the half-life process.
With a clean interface and three calculation modes, it’s perfect for students, teachers, and researchers working in chemistry, physics, nuclear science, or archaeology.

What This Calculator Can Do

This online calculator allows you to compute any part of the half-life equation. It includes three functional tabs:

1. Calculate Remaining Amount

Determine how much of a substance remains after a certain time period.

• Enter the initial amount (N₀)

• Enter the half-life (T₁/₂) and choose the unit (seconds, minutes, hours, days, or years)

• Enter the time elapsed (t) in your preferred unit
  → The calculator outputs the remaining amount (Nₜ) based on the formula:

  $$N(t) = N₀ × (1/2)^{t/T}$$

2. Calculate Time Elapsed

Find out how long it took for a substance to decay from an initial to a remaining amount.

• Enter initial and remaining quantities

• Enter the half-life and unit
  → The tool calculates the elapsed time (t) using the formula:

$$t = T × \log_2(N₀ / N(t))$$

3. Calculate Half-Life

When you know the time and the decay ratio, this mode finds the half-life period (T₁/₂).

• Enter initial and remaining amounts

• Enter the elapsed time and unit
  → The result shows how long it takes for the quantity to reduce by half:

$$T = t / \log_2(N₀ / N(t))$$

Supported Units

You can freely switch between:

• Seconds

• Minutes

• Hours

• Days

• Years

All conversions are handled automatically, ensuring accurate results across any scale.

Example: Carbon-14 Dating

Carbon-14 has a half-life of 5730 years.
If an ancient sample now has 25% of its original Carbon-14, this means it has gone through two half-lives.
The calculator shows that approximately 11,460 years have passed — allowing scientists to date the artifact accurately.

The Science Behind Half-Life

Half-life is the time required for a quantity to decay to half of its initial value. It’s a key concept in:

• Radioactive decay (e.g., Uranium-238, Carbon-14)

• Pharmacokinetics (how drugs break down in the body)

• Chemical reactions and environmental science

The calculator also displays exponential decay formulas and relationships between constants such as:

$$t_{1/2} = \frac{\ln(2)}{λ} = τ × \ln(2)$$

$$λ = \frac{\ln(2)}{t_{1/2}}, \quad τ = \frac{t_{1/2}}{\ln(2)}$$

Why Use This Tool

✅ Accurate, science-based calculations
✅ Intuitive tab layout for easy navigation
✅ Multi-unit time conversion
✅ Clear explanations and examples for learners
✅ Works on both desktop and mobile devices

Whether you’re analyzing nuclear decay or studying the age of fossils, this Half-Life Calculator provides precise results instantly — no manual math needed.