The Half-Life Calculator helps you explore how substances decay over time. Half-life is a key concept in physics, chemistry, biology, geology, medicine, and environmental science because it describes how long it takes for a material to reduce to half its original amount.

This calculator lets you compute remaining quantity, initial quantity, time, or half-life itself. It also includes a conversion tool for half-life, mean lifetime, and decay constant, giving you a complete set of tools for analyzing exponential decay.

What half-life represents

Half-life describes the predictable rate at which something decreases. Most commonly, it applies to radioactive materials, but it is also used for:

• Drug metabolism and dosage planning
• Carbon dating and geological timelines
• Environmental breakdown of chemicals
• Population decay in mathematical models
• Physics and nuclear science

In any system where decay follows an exponential pattern, half-life provides a clear way to measure and compare rates of change.

The decay formula in simple terms

Exponential decay can be expressed using the standard formula:

Nt = N0 × (1/2)^(t / t½)

Where:

• Nt is the remaining quantity
• N0 is the initial quantity
• t is the time elapsed
• t½ is the half-life

This relationship makes it easy to predict how much of a substance remains after any amount of time.

What the calculator solves

The tool allows you to find one missing variable if the others are known. You can calculate:

• Remaining quantity after a specific time
• Initial quantity before decay
• Total time elapsed
• Half-life

Since each value is tied through the same exponential relationship, knowing any three lets you solve for the fourth.

Half-life, mean lifetime and decay constant

In physics and chemistry, decay is also described using the decay constant (λ) and mean lifetime (τ). These are linked:

• Mean lifetime equals 1 divided by the decay constant
• Half-life equals the natural log of 2 divided by the decay constant
• Half-life equals mean lifetime multiplied by ln(2)

The calculator includes a dedicated panel that converts between these three quantities. This is especially useful for scientific research and engineering work where different fields prefer different units.

Why half-life matters

Understanding half-life helps you predict how systems change. It allows you to:

• Estimate how long medication stays active
• Determine the age of fossils and archaeological samples
• Evaluate nuclear material safety and storage
• Predict environmental persistence of pollutants
• Analyze decay processes in physics experiments

Any time decay follows an exponential curve, half-life becomes one of the most useful reference points.

Try the Half-Life Calculator

Enter any combination of known values and the calculator will solve the rest.

It handles half-life equations automatically so you can focus on understanding the results rather than doing the math by hand.