Half-Life Calculator

Calculate remaining quantity, time elapsed, half-life, or initial amount | Radioactive Decay & Exponential Decay

Result
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📝 Step-by-step solution
Select a calculation type and enter values
💡 Formula: N(t) = N₀ × (1/2)^(t / t½)

📖 How to Use This Half-Life Calculator

1
Select what to calculate - Remaining Quantity, Time, Half-Life, or Initial Quantity.
2
Enter known values - Fill in the required fields for your calculation.
3
Click "Calculate" - Get step-by-step solution.

☢️ What is Half-Life?

Half-life (t½) is the time required for a quantity to reduce to half its initial value. Used in nuclear physics, carbon dating, and drug metabolism.

📊 Half-Life Formulas

Remaining: N(t) = N₀ × (1/2)^(t / t½)
Time: t = t½ × log₂(N₀ / N)
Half-Life: t½ = t × ln(2) / ln(N₀ / N)
Initial: N₀ = N / (1/2)^(t / t½)

🔬 Common Half-Life Examples

❓ Frequently Asked Questions

How many half-lives until a substance is gone?
After 1: 50%; 2: 25%; 3: 12.5%; 4: 6.25%; 5: 3.125%; 10: ~0.1%. Never reaches zero.
What is the decay constant (λ)?
λ = ln(2) / t½ ≈ 0.693 / t½. Used in: N(t) = N₀ × e^(-λt).
How accurate is carbon-14 dating?
Accurate up to 50,000-60,000 years with ±40-100 years error margin.