Half-Life Calculator
Calculate radioactive decay and understand the science behind half-life
Half-Life Calculator
Half-Life Formula
Where:
- N(t) is the amount remaining after time t
- N₀ is the initial amount
- t is the time elapsed
- T is the half-life of the substance
About Half-Life
Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not.
One of the most well-known applications of half-life is carbon-14 dating. The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago.
Example: If an archaeologist found a fossil sample that contained 25% carbon-14 in comparison to a living sample, the time of the fossil sample's death could be determined as follows:
Using the formula: N(t) = N₀ × (1/2)t/T
0.25 = 1 × (1/2)t/5730
Solving for t gives approximately 11,460 years.
This means that the fossil is 11,460 years old.
Exponential Decay Formulas
Where:
- N₀ is the initial quantity
- N(t) is the remaining quantity after time, t
- t₁/₂ is the half-life
- τ is the mean lifetime
- λ is the decay constant
Relationship Between Half-Life Constants
| Constant | Relationship |
|---|---|
| Half-life (t₁/₂) | t₁/₂ = ln(2) / λ = τ × ln(2) |
| Decay constant (λ) | λ = ln(2) / t₁/₂ = 1 / τ |
| Mean lifetime (τ) | τ = 1 / λ = t₁/₂ / ln(2) |
The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere. It is incorporated into plants through photosynthesis, and then into animals when they consume plants. The carbon-14 undergoes radioactive decay once the plant or animal dies, and measuring the amount of carbon-14 in a sample conveys information about when the plant or animal died.
🧪 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.
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Enter the initial amount (N₀)
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Enter the half-life (T₁/₂) and choose the unit (seconds, minutes, hours, days, or years)
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Enter the time elapsed (t) in your preferred unit
→ The calculator outputs the remaining amount (Nₜ) based on the formula:
2. Calculate Time Elapsed
Find out how long it took for a substance to decay from an initial to a remaining amount.
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Enter initial and remaining quantities
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Enter the half-life and unit
→ The tool calculates the elapsed time (t) using the formula:
3. Calculate Half-Life
When you know the time and the decay ratio, this mode finds the half-life period (T₁/₂).
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Enter initial and remaining amounts
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Enter the elapsed time and unit
→ The result shows how long it takes for the quantity to reduce by half:
Supported Units
You can freely switch between:
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Seconds
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Minutes
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Hours
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Days
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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:
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Radioactive decay (e.g., Uranium-238, Carbon-14)
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Pharmacokinetics (how drugs break down in the body)
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Chemical reactions and environmental science
The calculator also displays exponential decay formulas and relationships between constants such as:
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.
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