Half-Life Calculator

Half-Life is evaluated from Initial Quantity, Half-Life and Elapsed Time. The calculation reports Remaining Quantity, Amount Decayed and Percent Remaining.

Results

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About the Half-Life Calculator

Half-Life is treated here as a quantitative relation between Initial Quantity, Half-Life and Elapsed Time and Remaining Quantity, Amount Decayed, Percent Remaining and Number of Half-Lives.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Each half-life reduces remaining quantity by 50%. After t/t½ half-lives: N = N₀ x (½)^(t/t½). Decay constant λ = ln(2)/t½.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Each half-life reduces remaining quantity by 50%. After t/t½ half-lives: N = N₀ x (½)^(t/t½). Decay constant λ = ln(2)/t½.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Carbon-14 dating (t½ = 5,730 years, 11,460 years elapsed)

Inputs

initial_quantity: 100 half_life: 5730 elapsed_time: 11460
Remaining Quantity: 25. Amount Decayed: 75. Percent Remaining: 25%. Number of Half-Lives: 2. Decay Constant: 0.00012097 per unit time

With Initial Quantity = 100, Half-Life = 5,730 and Elapsed Time = 11,460 as the stated inputs, the result is Remaining Quantity = 25, Amount Decayed = 75 and Percent Remaining = 25%. Each value corresponds to the declared output fields.

Example 2: Iodine-131 medical use (t½ = 8.02 days, 24 days elapsed)

Inputs

initial_quantity: 200 half_life: 8.02 elapsed_time: 24
Remaining Quantity: 25.129978. Amount Decayed: 174.870022. Percent Remaining: 12.565%. Number of Half-Lives: 2.9925. Decay Constant: 0.08642733 per unit time

With Initial Quantity = 200, Half-Life = 8.02 and Elapsed Time = 24 as the stated inputs, the result is Remaining Quantity = 25.129978, Amount Decayed = 174.870022 and Percent Remaining = 12.565%. Each value corresponds to the declared output fields.

Example 3: Uranium-238 (t½ = 4.47 billion years, 1 billion years elapsed)

Inputs

initial_quantity: 1000 half_life: 4470000000 elapsed_time: 1000000000
Remaining Quantity: 856.358242. Amount Decayed: 143.641758. Percent Remaining: 85.6358%. Number of Half-Lives: 0.2237. Decay Constant: 0 per unit time

With Initial Quantity = 1,000, Half-Life = 4,470,000,000 and Elapsed Time = 1,000,000,000 as the stated inputs, the result is Remaining Quantity = 856.358242, Amount Decayed = 143.641758 and Percent Remaining = 85.6358%. Each value corresponds to the declared output fields.

Example 4: Cs-137 Chernobyl fallout (t½ = 30.17 years, 38 years elapsed)

Inputs

initial_quantity: 500 half_life: 30.17 elapsed_time: 38
Remaining Quantity: 208.840101. Amount Decayed: 291.159899. Percent Remaining: 41.768%. Number of Half-Lives: 1.2595. Decay Constant: 0.02297472 per unit time

With Initial Quantity = 500, Half-Life = 30.17 and Elapsed Time = 38 as the stated inputs, the result is Remaining Quantity = 208.840101, Amount Decayed = 291.159899 and Percent Remaining = 41.768%. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate remaining radioactive material after N half-lives
  • Find elapsed time to reach a remaining percentage
  • Chemistry and nuclear physics homework