Half-Life Calculator
Calculate exponential decay instantly ⚛️ Fast, accurate, and 100% free 🔬 Trusted results in seconds — try it now.
Calculate exponential decay instantly ⚛️ Fast, accurate, and 100% free 🔬 Trusted results in seconds — try it now.
A Half Life Calculator is a scientific tool used to determine how long it takes for a substance to reduce to half of its original amount. The concept of half-life is widely used in physics, chemistry, medicine, pharmacology, and nuclear science. It helps measure the decay of radioactive materials, the breakdown of drugs in the human body, and even chemical reactions over time.
In simple terms, if you start with 100 grams of a substance and its half-life is 5 years, after 5 years only 50 grams will remain. After another 5 years, 25 grams will remain, and so on. This calculator allows you to quickly determine remaining quantity, decay constant, elapsed time, or half-life value using standard exponential decay formulas. It eliminates manual calculation errors and provides instant, accurate results.
The calculator is based on the exponential decay formula used in science and engineering. The core formula is: N(t) = N₀ × (1/2)^(t / T½). In this formula, N(t) represents the remaining quantity after time t, N₀ is the initial quantity, and T½ is the half-life of the substance. This equation models how materials naturally decrease over time at a consistent decay rate.
Another important formula used is the decay constant formula: λ = ln(2) / T½. Here, λ (lambda) is the decay constant and ln(2) is the natural logarithm of 2, approximately 0.693. The decay constant connects half-life to the exponential decay equation: N(t) = N₀ × e^(−λt). These formulas allow the calculator to compute unknown values when you provide the known variables.
To use the calculator step by step: first enter the initial quantity of the substance. Next, input either the half-life value or the time elapsed. Then choose what you want to calculate, such as remaining amount or time required to reach a certain level. The system instantly processes the exponential decay calculation and displays precise results.
A Half Life Calculator is commonly used in radioactive decay calculations. For example, Carbon-14 dating uses half-life to determine the age of ancient fossils. Carbon-14 has a half-life of about 5,730 years. Scientists measure how much Carbon-14 remains in an artifact to estimate how old it is.
In medicine and pharmacology, half-life helps determine how long a drug stays active in the body. Suppose a medication has a half-life of 8 hours. If a patient takes 200 mg, after 8 hours only 100 mg remains in the bloodstream. After 16 hours, 50 mg remains. Doctors use this information to decide safe dosing intervals.
It is also useful in environmental science and chemistry. For example, if a chemical pollutant has a half-life of 10 days in water, environmental engineers can estimate how long it will take for contamination levels to drop to safe limits. Students use half-life calculations in physics and chemistry assignments to solve decay rate and exponential growth problems.
The logic behind half-life calculation follows exponential decay principles. Unlike linear reduction, exponential decay means the substance decreases by a percentage, not a fixed amount, during each equal time interval. Every half-life period reduces the current amount by 50 percent.
For example, assume an initial quantity of 80 grams with a half-life of 4 years. After the first 4 years, 40 grams remain. After 8 years, 20 grams remain. After 12 years, 10 grams remain. The calculation follows the pattern: Remaining Amount = Initial Amount × (1/2)^(Number of Half Lives). If 12 years have passed, that equals 3 half-lives, so 80 × (1/2)^3 = 80 × 1/8 = 10 grams.
If you need to calculate time instead of quantity, the formula can be rearranged using logarithms: t = (T½ × log(N₀ / N)) / log(2). This allows you to determine how long it takes for a substance to decay to a specific level. The calculator performs these logarithmic and exponential operations automatically, ensuring mathematical precision without manual steps.
Is the Half Life Calculator accurate?
Yes. The calculator applies verified exponential decay formulas and logarithmic equations to produce precise scientific results suitable for academic and practical use.
Can this calculator be used for drug half-life calculations?
Yes. It can estimate how much of a medication remains in the body over time, helping users understand dosing intervals and drug elimination rates.
Does it work only for radioactive materials?
No. The half-life formula applies to radioactive decay, chemical reactions, biological processes, and pharmacokinetics wherever exponential decay occurs.
What units should I use?
You can use any consistent unit such as grams, milligrams, years, days, or hours. Just make sure time and half-life are expressed in the same unit.
Is any personal data stored?
No. All calculations run instantly in your browser. No input values are stored, saved, or transmitted.