Half-Life Calculator

Calculated using standard mathematical and industry formulas.

Free online Half Life Calculator calculator and unit conversion tool for everyday, engineering, and home projects.

How to use this calculator?

1. Select what you want to find: remaining amount, half-life, or elapsed time.
2. Enter the known values in the visible fields.
3. Read the result along with the decay constant λ and number of half-lives elapsed.

Formula & calculation method

Exponential half-life decay formula

N(t) = N₀ × (½)^(t/t₁/₂) · t₁/₂ = t × ln(2) / ln(N₀/N(t)) · λ = ln(2) / t₁/₂

N₀ = initial amount, N(t) = remaining at time t, t₁/₂ = half-life, λ = decay constant.

Step-by-step calculation example

N₀ = 100, t₁/₂ = 5, t = 15 → 3 half-lives → N(15) = 100 × (1/2)³ = 12.5.

Key insights to remember

• After each half-life, exactly 50% of the substance remains: 100 → 50 → 25 → 12.5.
• The decay constant λ = ln(2) / t₁/₂ — it represents the probability of decay per unit time.
• Carbon-14 has a half-life of 5,730 years — the basis of radiocarbon dating.
• Pharmaceuticals use half-life to schedule dosing: a drug with t₁/₂ = 6 hours needs re-dosing every 6–12 hours.

How to interpret your results?

Exponential decay

N(t) = N₀ × (1/2)^(t/t₁/₂). After n half-lives, only N₀/2ⁿ remains.

Decay constant λ

λ = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂. Larger λ means faster decay.

Frequently asked questions

How do I use the Half Life Calculator calculator?

Enter your numerical input and select desired units to get instant accurate results.

How accurate are the conversions?

Conversions use official ISO conversion factors for maximum precision.

Does it convert metric and imperial units?

Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.

Is my data stored?

No, all calculations execute 100% locally in your browser with zero data logging.

Can I use this for DIY or engineering projects?

Yes, it provides reliable estimates for construction, crafting, science, and everyday math.

What if I enter invalid inputs?

The calculator will display a friendly error prompt if non-numeric values are entered.

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