Half-Life & Radioactive Decay Calculator

Calculate half-life, remaining quantity, decay constant, elapsed time, and more.

Enter any two values to calculate the third. Supports various units and real-world scenarios.

Practical Examples

See how to use the half-life calculator in real-world scenarios.

Radium-226 Decay

Half-Life

Calculate the remaining amount of Radium-226 after 7,600 years, starting with 100 grams. Half-life is 1,600 years.

Initial Amount (N₀): 100

Remaining Amount (N): undefined

Half-Life (t₁/₂): 1600

Elapsed Time (t): 7600

Decay Constant (λ): undefined

Unit: g

Time Unit: y

Carbon-14 Dating

Half-Life

Find the age of a sample if 25% of Carbon-14 remains. Half-life is 5,730 years, initial amount is 1 mol.

Initial Amount (N₀): 1

Remaining Amount (N): 0.25

Half-Life (t₁/₂): 5730

Elapsed Time (t): undefined

Decay Constant (λ): undefined

Unit: mol

Time Unit: y

Iodine-131 Medical Use

Half-Life

How much Iodine-131 remains after 24 days if you start with 50 mg? Half-life is 8 days.

Initial Amount (N₀): 50

Remaining Amount (N): undefined

Half-Life (t₁/₂): 8

Elapsed Time (t): 24

Decay Constant (λ): undefined

Unit: g

Time Unit: d

Pharmaceutical Clearance

Half-Life

A drug has a half-life of 6 hours. How much remains after 18 hours if the initial dose is 200 mg?

Initial Amount (N₀): 200

Remaining Amount (N): undefined

Half-Life (t₁/₂): 6

Elapsed Time (t): 18

Decay Constant (λ): undefined

Unit: g

Time Unit: h

Other Titles
Understanding Half-Life & Radioactive Decay: A Comprehensive Guide
Master the science and math behind half-life calculations.

What is Half-Life?

  • Definition and Concept
  • Mathematical Representation
  • Physical Meaning
Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in nuclear physics, chemistry, and pharmacology.
Half-Life in Science

Famous Half-Lives

  • Radium-226 has a half-life of 1,600 years.
  • Carbon-14 dating uses half-life to estimate age.

Step-by-Step Guide to Using the Calculator

  • Input Selection
  • Calculation Process
  • Interpreting Results
Enter any two values (e.g., initial amount and elapsed time) to calculate the third (e.g., remaining amount). The calculator supports various units and scenarios.
Flexible Input System

How to Use

  • Calculate remaining amount after a given time.
  • Find elapsed time if you know initial and remaining amounts.

Real-World Applications of Half-Life

  • Radioactive Dating
  • Medical Treatments
  • Environmental Science
Half-life calculations are essential in radiometric dating, cancer treatment, and tracking environmental pollutants.
Applications in Everyday Life

Applications

  • Carbon-14 dating in archaeology.
  • Iodine-131 in thyroid treatment.

Common Misconceptions and Correct Methods

  • Half-Life vs. Total Decay
  • Exponential vs. Linear Decay
  • Unit Consistency
Half-life is not the time for complete decay. Decay is exponential, not linear. Always use consistent units for accurate results.
Avoiding Calculation Errors

Misconceptions

  • After two half-lives, 25% remains, not 0%.
  • Mixing units can lead to wrong answers.

Mathematical Derivation and Examples

  • Half-Life Formula
  • Decay Constant Calculation
  • Worked Examples
The half-life formula is N = N₀ × (1/2)^(t/t₁/₂). The decay constant λ = ln(2)/t₁/₂. Use logarithms to solve for time or half-life as needed.
Formulas in Action

Math Examples

  • If N₀ = 100g, t₁/₂ = 1600y, t = 4800y, then N = 100 × (1/2)^(4800/1600) = 12.5g.
  • If N₀ = 1mol, N = 0.25mol, t₁/₂ = 5730y, then t = t₁/₂ × log(N₀/N)/log(2) = 11460y.