Half-Life Calculator

Calculate radioactive decay using the half-life formula. Find remaining quantity, half-life, or elapsed time for any radioactive isotope. Includes reference table of common isotopes.

Remaining

88.6062

Half-Life

15.7 years

Elapsed

2.7 years

Half-Lives

0.17

Decay constant (λ) = 1.2097e-4 per day | Remaining: 88.61%

Understanding Radioactive Decay

Radioactive decay follows an exponential decay pattern described by N = N₀ × (½)^(t/t½). Each radioactive isotope has a characteristic half-life that is constant regardless of environmental conditions — temperature, pressure, or chemical bonding do not affect it. This predictability makes radioactive decay useful for dating archaeological artifacts, medical imaging, and nuclear power.

Common Radioactive Isotopes

IsotopeHalf-LifeApplication
Carbon-145,730 yearsArchaeological dating
Uranium-2384.47 billion yearsGeological dating, nuclear power
Iodine-1318.02 daysThyroid cancer treatment
Technetium-99m6.01 hoursMedical imaging (most common)
Cobalt-605.27 yearsCancer radiation therapy

Frequently Asked Questions

What is half-life?
Half-life is the time required for half of the radioactive atoms in a sample to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%; and so on. Each isotope has a unique half-life ranging from fractions of a second to billions of years. The formula is N = N₀ × (½)^(t/t½), where N₀ is the initial quantity, t is elapsed time, and t½ is the half-life.
How is carbon-14 dating used?
Carbon-14 has a half-life of 5,730 years. Living organisms maintain a constant ratio of C-14 to C-12. After death, C-14 decays without replenishment. By measuring the remaining C-14 ratio, scientists can determine how long ago the organism died. This method works for organic materials up to about 50,000 years old. Beyond that, too little C-14 remains for accurate measurement.
What is the decay constant?
The decay constant (λ) is the probability per unit time that a nucleus will decay. It is related to half-life by λ = ln(2) / t½. While half-life tells you how long until half decays, the decay constant tells you the rate of decay at any instant. The relationship N = N₀ × e^(-λt) is the exponential decay formula using the decay constant.

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