Physics Tool

Half-Life Calculator

Calculate radioactive decay and remaining quantity.

Σ The Formula

N(t) = N\u2080 \u00d7 (1/2)^(t/t\u2081/\u2082)

Real World Examples

Radioactive Decay
100g, half-life 5 yrs, 10 yrs later = 25g
Carbon Dating
Finding age of a fossil based on C-14 decay
Medicine
Drug concentration in body after 6 hours
Time Elapsed
From 100% to 50% takes exactly one half-life

# About This Calculator

Half-Life is the time required for a quantity to reduce to half of its initial value. This concept is widely used in nuclear physics (radioactive decay), chemistry (reaction rates), and medicine (drug elimination).

The formula describes exponential decay. For example, if a substance has a half-life of 5 years, then after 5 years, 50% remains. After 10 years (2 half-lives), 25% remains. After 15 years, 12.5% remains, and so on.

This calculator solves for any variable:
• Remaining Amount: How much is left after time t?
• Time Elapsed: How long until it decays to amount N?
• Half-Life: Calculate the rate from two measurements.

Perfect for chemistry homework or understanding how long medications stay in your system.

How To Use

  1. Select what you want to calculate (Remaining Amount, Time, etc.).
  2. Enter the known values (Initial Quantity, etc.).
  3. Click Calculate.

Frequently Asked Questions

What does 'Half-Life' mean?+

It is the time it takes for half of the atoms of a radioactive substance to decay (change into another element). It is constant for a given isotope.

Does it ever reach zero?+

Theoretically, exponential decay approaches zero but never fully touches it. In reality, eventually, you reach the last atom!

Use in Carbon Dating?+

Carbon-14 is used to find the age of ancient organic materials. By measuring how much C-14 remains compared to stable C-12, and knowing C-14's half-life (5730 years), we can estimate age.

What is exponential decay?+

A process where quantity decreases at a rate proportional to its current value. The graph curves downward rapidly at first, then flattens out.

Is this used for finance?+

No, finance usually uses Compound Interest (Growth). Half-life is essentially 'Compound Decay' where the rate halves effectively.

Is Half-Life Calculator free to use?+

Yes, Half-Life Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Half-Life is the time required for a quantity to reduce to half of its initial value. This concept is widely used in nuclear physics (radioactive decay), chemistry (reaction rates), and medicine (drug elimination).

The formula describes exponential decay. For example, if a substance has a half-life of 5 years, then after 5 years, 50% remains. After 10 years (2 half-lives), 25% remains. After 15 years, 12.5% remains, and so on.

This calculator solves for any variable:
• Remaining Amount: How much is left after time t?
• Time Elapsed: How long until it decays to amount N?
• Half-Life: Calculate the rate from two measurements.

Perfect for chemistry homework or understanding how long medications stay in your system.

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