☢️ Radioactive Decay Calculator
Calculate the remaining quantity of a radioactive substance after a given time using N = N₀ · e−λt. Enter the initial amount, half-life, and elapsed time to find the remaining activity, decay constant, and more. Supports multiple time units.
What Is Radioactive Decay?
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can happen spontaneously or as a result of nuclear reactions. The decay is a random process at the level of individual atoms, but for a large number of atoms, the rate follows a predictable exponential law.
The fundamental equation for radioactive decay is:
N(t) = N₀ · e−λt
where N(t) = remaining quantity at time t, N₀ = initial quantity, λ = decay constant, and t = elapsed time.
The half-life (T½) is the time required for half of the radioactive atoms to decay. It is related to the decay constant by:
T½ = ln(2) / λ ≈ 0.693 / λ
Radioactive decay is used in many applications, including:
- Radiocarbon dating — using carbon-14 to date organic remains.
- Medical imaging and therapy — using radioisotopes like technetium-99m and iodine-131.
- Nuclear power — energy generation from uranium and plutonium.
- Geology — dating rocks and minerals using uranium-lead and potassium-argon methods.
How to Calculate Radioactive Decay
The calculator uses the following steps:
- Convert half-life to the same unit as elapsed time for consistency.
- Calculate the decay constant λ using λ = ln(2) / T½.
- Calculate the remaining quantity N using N = N₀ · e−λt.
- Calculate the decayed amount as N₀ − N.
- Determine the number of half-lives as t / T½.
For example, if you start with 100 g of Carbon-14 (half-life = 5,730 years) and wait 10,000 years:
λ = ln(2) / 5730 ≈ 0.0001209 per year
N = 100 × e−0.0001209 × 10000 ≈ 29.8 g
Remaining: ≈ 29.8 g (≈ 29.8%)
Why Use This Calculator?
- Instant results: Get remaining quantity, decay constant, and half-lives in real-time.
- Flexible units: Supports seconds, minutes, hours, days, and years for both half-life and elapsed time.
- Step-by-step breakdown: See exactly how the calculation is done.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Radioactive Decay Calculator FAQ
What is the formula for radioactive decay?
The fundamental formula is N(t) = N₀ · e−λt, where N₀ is the initial quantity, λ is the decay constant, and t is the elapsed time.
What is half-life?
Half-life (T½) is the time required for half of the radioactive atoms in a sample to decay. It is related to the decay constant by T½ = ln(2) / λ.
What is the decay constant λ?
The decay constant λ is the probability per unit time that a given nucleus will decay. It is related to half-life by λ = ln(2) / T½.
What is the half-life of Carbon-14?
Carbon-14 has a half-life of approximately 5,730 years. It is used in radiocarbon dating of organic materials up to about 50,000 years old.
What is the half-life of Uranium-238?
Uranium-238 has a half-life of approximately 4.47 × 10⁹ years (4.47 billion years), making it one of the longest-lived radioactive isotopes.
How many half-lives until a substance is considered "safe"?
After 10 half-lives, only about 0.098% of the original substance remains. After 20 half-lives, it is less than one-millionth. However, "safe" depends on the specific isotope and its radiation type.
Does temperature affect radioactive decay?
No. Radioactive decay is a nuclear process and is not significantly affected by temperature, pressure, or chemical state. It is a random process governed by quantum mechanics.
How accurate is this calculator?
This calculator uses the exact standard formulas for radioactive decay. Accuracy depends on the precision of your input values. You can adjust the decimal precision in the results.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.
Can I use this for medical isotopes?
Yes. The calculator supports any time unit, making it suitable for medical isotopes with short half-lives like technetium-99m (6 hours) or iodine-131 (8 days).