Half-Life Calculator

Calculate radioactive decay

Formula

N = N₀(1/2)^(t/T½) = N₀e^(-λt). λ = ln(2)/T½. Percent remaining = 100 × (1/2)^(t/T½).

Radioactive decay follows exponential decay. The half-life is constant for each isotope. The formula calculates how much remains after any time period.

How to Calculate Manually

1
Select what to calculate
2
Choose isotope or enter custom half-life
3
Enter known values
4
Calculator shows result + decay constant + % remaining

Reference Table

Isotope	Half-Life	Decay Constant (yr⁻¹)	Common Use
Carbon-14	5,730 yr	1.21×10⁻⁴	Archaeological dating
Uranium-238	4.47 Byr	1.55×10⁻¹⁰	Geological dating
Uranium-235	704 Myr	9.85×10⁻¹⁰	Geological dating
Potassium-40	1.25 Byr	5.55×10⁻¹⁰	Geological dating
Iodine-131	8.02 d	31.6 yr⁻¹	Medical therapy
Tc-99m	6.01 h	1010 yr⁻¹	Medical imaging
Cobalt-60	5.27 yr	0.131 yr⁻¹	Radiotherapy
Cesium-137	30.17 yr	0.0230 yr⁻¹	Industrial gauges
Tritium (H-3)	12.32 yr	0.0563 yr⁻¹	Tracers, lighting
Plutonium-239	24,110 yr	2.87×10⁻⁵ yr⁻¹	Nuclear weapons

Half-Life Calculator: Radioactive Decay and Isotope Dating

Half-life is the time required for half of the radioactive atoms in a sample to decay. It's one of the most important concepts in nuclear physics, with applications ranging from archaeological dating (carbon-14) to medical imaging (technetium-99m) to nuclear waste management...

Frequently Asked Questions

What is half-life? Half-life (T½) is the time required for half of the radioactive atoms in a sample to decay. It's constant for each isotope. After 1 half-life: 50% remains. After 2: 25%. After 3: 12.5%.: Half-life (T½) is the time required for half of the radioactive atoms in a sample to decay. It's constant for each isotope. After 1 half-life: 50% remains. After 2: 25%. After 3: 12.5%.
What's the decay formula? N = N₀ × (1/2)^(t/T½) = N₀ × e^(-λt). λ = ln(2)/T½. Activity A = λN.: N = N₀ × (1/2)^(t/T½) = N₀ × e^(-λt). λ = ln(2)/T½. Activity A = λN.
Common half-lives? C-14: 5,730 yr. U-238: 4.47 Byr. U-235: 704 Myr. K-40: 1.25 Byr. I-131: 8.02 d. Tc-99m: 6.01 h. Ra-226: 1,600 yr.: C-14: 5,730 yr. U-238: 4.47 Byr. U-235: 704 Myr. K-40: 1.25 Byr. I-131: 8.02 d. Tc-99m: 6.01 h. Ra-226: 1,600 yr.

Calculator

Formula

Formula

How to Calculate Manually

Reference Table

Half-Life Calculator: Radioactive Decay and Isotope Dating

Frequently Asked Questions

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