Half-Life Calculator

Calculate half-life, remaining quantity, or time elapsed with ease.

The Complete Guide to Half-Life Calculations

What is Half-Life?

Half-life (t½) is the time required for a substance to reduce to half its initial quantity due to decay. This concept is widely used in:

  • Radioactive decay analysis
  • Pharmacokinetics and drug elimination
  • Biological decay studies
  • Environmental science and pollutant breakdown

Half-Life Formula: t½ = ln(2)/λ
Decay Formula: N = N₀ × 2^(-t/t½)
Mean Lifetime: τ = t½ / ln(2)

Key Formulas for Half-Life Calculations

Half-Life Formula

t½ = ln(2)/λ

The half-life is inversely proportional to the decay constant (λ), representing the rate of decay.

Decay Formula

N = N₀ × 2^(-t/t½)

This formula calculates the remaining quantity (N) of a substance after time (t), given the initial quantity (N₀) and half-life (t½).

Mean Lifetime

τ = t½ / ln(2)

Mean lifetime (τ) represents the average lifetime of particles in a decaying system and is related to the decay constant.

How to Use the Half-Life Calculator: Step-by-Step

Step 1: Enter Known Values

  • Provide at least three of the following: N₀, N, t½, or t.
  • The calculator automatically computes the missing value.

Step 2: Interpret the Results

View precise values for the remaining quantity, time elapsed, or half-life, with results displayed to six decimal places for accuracy.

Step 3: Use Additional Insights

The calculator also provides:

  • Decay constant (λ)
  • Mean lifetime (τ)

Practical Tips for Half-Life Calculations

Accurate Input

  • Ensure input values are in consistent units (e.g., time in seconds or hours).
  • Use natural logarithms for precise calculations.

Interpretation of Results

  • Remember, half-life is independent of the initial quantity (N₀).
  • Decay constant (λ) reflects the speed of decay.

Half-Life FAQs

What does half-life tell us about a substance?

Half-life indicates the time required for a substance to decay to half its initial amount, helping determine decay rates and stability.

How does decay constant (λ) relate to half-life?

The decay constant (λ) is inversely proportional to half-life and reflects the rate of decay: t½ = ln(2)/λ.

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