Enter your initial amount N₀, elapsed time, and either the half-life t₁/₂ or decay constant λ — or pick a common isotope to autofill — and the Radioactive Decay Calculator gives you the remaining amount N(t), activity A(t), and fraction remaining, or solves for whichever variable you choose.
Result
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Half-life
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Decay constant
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Activity A(t)
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Fraction remaining
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Radioactive decay is the process by which unstable atomic nuclei spontaneously transform into more stable nuclei by emitting radiation. It follows first-order kinetics, meaning the rate of decay is proportional to the amount of radioactive material present.
Half-life (t₁/₂) and decay constant (λ) are inversely related by the formula λ = ln(2)/t₁/₂ ≈ 0.693/t₁/₂. The decay constant represents the probability of decay per unit time, while half-life is the time required for half the material to decay.
The fundamental decay formula is N(t) = N₀·e^(-λt), where N(t) is the remaining amount at time t, N₀ is the initial amount, λ is the decay constant, and t is elapsed time. This exponential function describes how radioactive material decreases over time.
You can use any consistent units for initial and remaining amounts (grams, moles, atoms, activity units like Bq or Ci). The key is using the same unit for both N₀ and N(t), as the calculation depends on their ratio.
Activity A(t) = λ·N(t), where λ is the decay constant and N(t) is the number of radioactive nuclei. Activity is measured in becquerels (Bq) when λ is in s⁻¹ and represents the number of decays per second.
Yes, the calculator works for any time period from seconds to billions of years. Just ensure your half-life and elapsed time use compatible units. The exponential decay law applies regardless of the time scale.
Common isotopes include Carbon-14 (5,730 years), used in dating; Uranium-238 (4.47 billion years); Radium-226 (1,600 years); Cobalt-60 (5.27 years); Cesium-137 (30.2 years); and Iodine-131 (8.02 days). The calculator includes quick picks for these common isotopes.
Radioactive decay calculations are highly accurate for large samples due to the statistical nature of decay. The exponential decay law is exact for the expected value, though individual atoms decay randomly. For practical purposes with macroscopic amounts, the calculations are extremely reliable.