Decay Time Calculator
Estimate how long it takes for a quantity to decay from an initial amount to a final amount using either half-life or decay constant.
What is a decay time calculator?
A decay time calculator tells you how long it takes for something to decrease from one amount to another when it follows an exponential decay pattern. This is common in radioactive isotopes, drug concentration in the body, chemical breakdown, and even charge loss in some systems.
Instead of guessing, you can use measured values and a known half-life (or decay constant) to compute a realistic time estimate in seconds, minutes, hours, days, or years.
The decay equations behind the calculator
1) Using half-life
Exponential decay with half-life is commonly written as:
N(t) = N₀ × (1/2)t / T½
Solving for time gives:
t = (T½ / ln 2) × ln(N₀ / N)
2) Using decay constant
An equivalent form uses decay constant λ:
N(t) = N₀ × e-λt
Solving for time:
t = ln(N₀ / N) / λ
- N₀ = initial amount
- N = final amount
- T½ = half-life
- λ = decay constant
- t = elapsed decay time
How to use this calculator
Step-by-step
- Choose whether you know half-life or decay constant.
- Enter your initial amount and final amount.
- Enter either half-life or λ based on your method.
- Set the output unit label (for readability only).
- Click Calculate Decay Time.
The result includes elapsed time, percentage remaining, and equivalent half-lives passed.
Example calculations
Example 1: Carbon-14 dating
If a sample dropped from 100 units to 25 units and Carbon-14 has a half-life of 5,730 years:
- 25 is one-quarter of 100.
- That is 2 half-lives.
- Time = 2 × 5,730 = 11,460 years.
Example 2: Drug concentration in blood
A medication concentration drops from 80 mg/L to 20 mg/L with a 6-hour half-life. Since 20 is one-quarter of 80, that is also 2 half-lives:
Time = 12 hours.
Where decay time calculations are useful
- Radiometric dating and isotope analysis
- Nuclear medicine and health physics
- Pharmacokinetics and dosing schedules
- Chemical decomposition and stability studies
- Battery self-discharge approximations
Common mistakes to avoid
- Using mismatched units (e.g., half-life in days but reporting in years).
- Entering final amount greater than initial amount for a decay-only model.
- Using percentage values inconsistently (e.g., 25 instead of 0.25 when mixing formats).
- Confusing decay constant λ with half-life T½.
Quick FAQ
Can I use percentages?
Yes. You can set N₀ = 100 and N = percentage remaining, or use decimals consistently. Ratios are what matter.
What if final amount equals initial amount?
The elapsed decay time is zero.
What if final amount is larger than initial amount?
That indicates growth, not decay, under this model. The calculator will warn you.
Final note
This tool is ideal for clean exponential decay scenarios. Real-world systems can include multiple phases, background noise, and measurement uncertainty, so treat outputs as model-based estimates unless validated experimentally.