Half Life Calculator

Calculate radioactive decay, half-life periods, and remaining quantities. Essential for physics, chemistry, and medicine.

Half-Life Calculator

Calculate radioactive decay and half-life of substances using exponential decay formulas

Half-Life & Decay

Starting amount of substance

Time for half the substance to decay

Time that has passed

☢️ Common Examples

Remaining Amount

25

25.00% of original

Half-Lives Elapsed

2

Number of half-lives

Percent Decayed

75.00%

Amount lost

Step-by-Step Solution

1Given: N₀ = 100, t₁/₂ = 5730 years, t = 11460 years
2Formula: N(t) = N₀ × (1/2)^(t/t₁/₂)
3N(t) = 100 × (1/2)^(11460/5730)
4N(t) = 100 × (1/2)^2.0000
5N(t) = 100 × 0.250000
6N(t) = 25.000000

Decay Over Time

Time
Amount
%
Half-Lives
Chart
0
100
100%
0.0
5730
50
50%
1.0
11460
25
25%
2.0
17190
12.5
12.5%
3.0
22920
6.25
6.25%
4.0
28650
3.125
3.13%
5.0

1Mastering Half-Life Calculations

Calculate radioactive decay and half-life of substances. Whether you're a student, educator, or professional, understanding the mathematical principles behind half-life will enhance your problem-solving abilities. This guide breaks down complex concepts into understandable components and provides practical applications for real-world scenarios.

Mathematical Foundations

The underlying mathematics involves fundamental principles that have wide-ranging applications. Understanding these concepts helps you: • Verify calculator results manually • Apply knowledge to related problems • Develop mathematical intuition • Solve more complex variations • Teach others effectively

Step-by-Step Problem Solving

Approach problems systematically: 1. Identify what you're solving for 2. Gather all necessary information 3. Choose the appropriate formula 4. Perform calculations carefully 5. Verify results make sense 6. Consider alternative methods


2Real-World Applications

Mathematical concepts aren't just theoretical - they have practical applications in many fields.

Professional Applications

Professionals in various fields use these calculations: • Engineers for design and analysis • Scientists for research and experiments • Financial analysts for modeling • Architects for planning and construction • Data scientists for analysis and predictions

Educational Value

For students and educators: • Builds foundational math skills • Develops logical thinking • Prepares for advanced topics • Provides exam preparation • Enables peer tutoring and collaboration

This comprehensive guide is regularly updated to ensure accuracy. Last reviewed: 7/25/2025

Frequently Asked Questions

What is half-life?

Half-life is the time required for a quantity to reduce to half its initial value through exponential decay.

How do I calculate remaining amount after n half-lives?

Remaining = Initial × (1/2)^n, where n is the number of half-lives that have passed.

What substances have half-lives?

Radioactive isotopes, medications in the body, and any substance undergoing exponential decay have measurable half-lives.