What this rad decay calculator does
This calculator estimates how much radioactive material remains after a given amount of time. It uses the standard half-life decay model, which is the same model used in physics, chemistry, geology, and nuclear medicine for first-pass decay estimates.
Enter an initial amount, the half-life, and elapsed time, and you get:
- Remaining amount
- Amount decayed
- Percent remaining and percent decayed
- Decay constant and number of half-lives passed
- Optional: time needed to reach a target amount
Radioactive decay formula used
Core equation:
N(t) = N₀ × (1/2)t / T1/2
Equivalent exponential form: N(t) = N₀ × e-λt, where λ = ln(2) / T1/2
Where:
- N₀ = initial quantity
- N(t) = remaining quantity after time t
- T1/2 = half-life
- λ = decay constant
How to use the calculator
Step-by-step
- Type the starting amount of material.
- Type the half-life in your chosen time units.
- Type elapsed time in the same units.
- (Optional) Add a target remaining amount.
- Click Calculate decay.
Important: If half-life is in years, elapsed time and target-time output are in years too. Unit consistency is everything in decay calculations.
Worked examples
Example 1: Carbon-14 dating style estimate
Suppose N₀ = 100 units, half-life = 5730 years, and elapsed time = 11,460 years. That is two half-lives, so remaining material is about 25 units.
Example 2: Iodine-131 medical context
If N₀ = 80, half-life ≈ 8 days, and t = 24 days, then about three half-lives have passed. Remaining amount is near 10 units (12.5% of initial), assuming ideal decay conditions.
Common isotope half-lives (quick reference)
- Radon-222: ~3.82 days
- Iodine-131: ~8.02 days
- Cobalt-60: ~5.27 years
- Cesium-137: ~30.17 years
- Carbon-14: ~5730 years
- Uranium-238: ~4.47 billion years
Practical notes and limitations
This tool assumes a simple closed system with ideal first-order decay. In real settings, measured activity can also be affected by shielding, detector efficiency, environmental loss, daughter-product behavior, and sampling error.
Use this calculator for planning, learning, and quick checks. For regulated health, lab, environmental, or engineering decisions, rely on certified instrumentation and qualified experts.