Initial amount
Remaining amount
Half-life
Time elapsed
Chemistry calculator
Half Life Calculator
Use the Half Life Calculator to solve for remaining amount, time, half-life, or decay constant with clear formulas, step-by-step results, and practical decay estimates.
Result
Half life calculator results
Your results will appear here
Enter your values and click Calculate to see the result.
Solved Value
Formula expression
Half-Lives Elapsed
Percent Remaining
Percent Decayed
Decay Constant
Step-by-step solution
Each step uses your entered values so the result reads like a worked solution instead of a black box.
This calculator applies the standard exponential decay formulas. Results depend on the values you enter and do not replace lab measurements or source-specific scientific data.
Calculator overview
Quick Half Life Calculator Overview
Use this half life calculator to solve decay time, remaining amount, initial amount, half-life, or decay constant from the values you know. It is built for chemistry and physics problems where you need clean exponential-decay steps instead of only a final number.
Enter the known decay values above to calculate the missing variable and review the step-by-step half-life work.
Guide
Half Life Calculator Guide
Use this guide to understand how half-life problems are solved, when to use the decay-constant form, and how to read the output from the calculator as a practical worked solution.
What This Half Life Calculator Does
This half life calculator solves common exponential decay problems involving remaining amount, initial amount, time elapsed, half-life, and decay constant. It is designed for chemistry questions, radioactive decay examples, algebra 2 exponential decay practice, and general half-life formula math.
Instead of forcing you to rearrange the formula manually each time, the calculator lets you choose the value you want to solve, enter the known values, and then review a concise step-by-step solution. It also derives useful supporting values such as percent remaining, percent decayed, half-lives elapsed, and the decay constant when enough information is available.
Half-Life Formula
The standard half-life relationship expresses exponential decay in powers of one-half. The equivalent decay constant form uses the natural exponential function.
Half-life decay form
N(t) = N0 x (1/2)^(t / T1/2) Decay-constant form
N(t) = N0 x e^(-lambda x t) N(t)Remaining amount after time has passed
N0Initial amount before decay starts
tElapsed time
T1/2Half-life
lambdaDecay constant, where lambda = ln(2) / T1/2
The two versions describe the same process. The half-life form is often easier for homework and isotope questions, while the decay-constant form is useful when the problem gives lambda directly or asks you to calculate it.
Example Calculation
Suppose a Carbon-14 style problem starts with 100 grams and asks how much remains after 11,460 years. Using the Carbon-14 half-life of 5,730 years, two half-lives pass over that time span.
Initial amount 100 grams Half-life 5,730 years Time elapsed 11,460 years Half-lives elapsed 2 half-lives
Example result summary
25 grams 25% remains, which means 75% has decayed.Because two half-lives pass, the starting amount is halved twice: 100 to 50, then 50 to 25.
How to Use the Calculator
- 1Choose a solve mode
Select whether you want to solve for remaining amount, initial amount, time elapsed, half-life, or decay constant.
- 2Enter the known values
Fill only the fields needed for that mode. The calculator uses those values as the basis for the solution.
- 3Add plain-language labels
Use labels such as years, days, grams, atoms, or moles so the result reads like your actual problem.
- 4Click Calculate
The solved value, derived outputs, and step-by-step breakdown appear only after you run the calculation.
- 5Review the solution
Check the formula used, the substituted values, and whether the time units and half-life units match.
Half-Life vs Decay Constant
Half-life tells you how long it takes for a quantity to fall to half of its current value. The decay constant tells you the continuous exponential rate of decay. They describe the same process from different angles.
It works well when a problem is described in “how long until half remains” language.
It fits the natural exponential form N(t) = N0 x e^(-lambda x t).
Use lambda = ln(2) / T1/2 and T1/2 = ln(2) / lambda to convert between them.
Tips / Notes
Half-life assumes exponential decay
The model works when the substance decays proportionally over time rather than by a fixed amount each step.
Match the time units
If half-life is in years, elapsed time should also be entered in years unless you convert first.
Use the same amount unit throughout
Grams, milligrams, atoms, or moles all work as long as the initial and remaining amounts use the same unit.
Carbon-14 is only one example
The same half-life formula works for many radioactive and chemical decay problems, not just carbon dating.
Results depend on the values entered
This is a clean formula-based solver, so incorrect units or assumptions will change the output.
FAQ
Frequently Asked Questions
Quick answers about half-life formulas, Carbon-14, decay constants, units, and worked-solution behavior.
What is the half-life formula?
The standard half-life formula is N(t) = N0 x (1/2)^(t / T1/2), where N0 is the starting amount, N(t) is the remaining amount, t is elapsed time, and T1/2 is the half-life.
How do I calculate remaining amount after several half-lives?
Count how many half-lives have passed by dividing time by the half-life, then multiply the initial amount by one-half raised to that count. After two half-lives, 25% remains. After three half-lives, 12.5% remains.
Can I use this for Carbon-14?
Yes. The calculator includes a light Carbon-14 preset that fills the common 5,730-year half-life. You can still edit the inputs if your problem uses a different context or unit style.
What is the decay constant?
The decay constant, often written as lambda, is the exponential rate in N(t) = N0 x e^(-lambda x t). It is directly related to half-life by lambda = ln(2) / T1/2.
Is this calculator good for algebra and chemistry homework?
Yes. It is designed for practical half-life and exponential decay problems, including algebra 2-style exponential decay questions, chemistry homework, and radioactive isotope examples.
Why do time units need to match half-life units?
Because the formula compares elapsed time to half-life as a ratio. If half-life is in years and time is in days, the numbers need to be converted first or the result will be wrong.
Does this show the steps?
Yes. After you click Calculate, the result panel includes a concise step-by-step solution showing the formula used, value substitution, and final answer.