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.