03 // Bidirectional STEM Calculators // PHYSICSN = N₀ × (0.5)^(t / t_½)

Radioactive Half-Life Exponential Decay Calculator

Exponential half-life decay determines the remaining quantity N of an unstable isotope, drug concentration, or decaying signal after elapsed time t given characteristic half-life t_½.

N = N₀ × (0.5)^(t / t_½)

Pick which value you want to calculate (or type into any field):Solving for: N(t) — Remaining Quantity

Remaining QuantityCalculated

Amount of substance remaining at time t

0.0011,000,000.00

Initial Quantity

Starting amount at t = 0

0.011,000,000.00

Elapsed Time

Total decay duration (same time unit as half-life)

0.01100,000.00

unit

Half-Life Period

Time required for quantity to reduce by 50%

0.01100,000.00

unit

Calculated Result · Remaining Quantity (N(t))

12.5kg

Converted units:

Step-by-Step Calculation

01Canonical Law: N = N₀ × (0.5)^(t / t_½)

02Given Inputs (Base Units): N₀ = 100 kg, t = 24, t_½ = 8

03Solve for N(t) (Remaining Quantity): N(t) = 12.5 kg

Exponential half-life decay determines the remaining quantity N of an unstable isotope, drug concentration, or decaying signal after elapsed time t given characteristic half-life t_½.

Real-World Reference Values

Carbon-14 Radiometric Datingt_½ = 5,730 Years

Organic archaeological dating standard

Iodine-131 Medical Isotopet_½ = 8.02 Days

After 3 half-lives (24 days), 12.5% remains

5 Half-Lives Rule of Thumb(0.5)⁵ = 3.125% Remaining

96.875% clearance threshold in pharmacokinetics

20-Row Comparison Table

Remaining Quantity (N(t)) · Initial Quantity (N₀)

Compare across:

Radioactive Half-Life Exponential Decay Calculator — Initial Quantity → Remaining Quantity
#	Initial Quantity (kg)	Remaining Quantity (kg)	Δ %
01	100 kgCurrent	12.5 kg	0.00%
02	7,242.11 kg	905.2643 kg	+7142.11%
03	14,484.22 kg	1,810.53 kg	+14384.22%
04	21,726.32 kg	2,715.79 kg	+21626.32%
05	28,968.43 kg	3,621.05 kg	+28868.43%
06	36,210.53 kg	4,526.32 kg	+36110.53%
07	43,452.64 kg	5,431.58 kg	+43352.64%
08	50,694.74 kg	6,336.84 kg	+50594.74%
09	57,936.85 kg	7,242.11 kg	+57836.85%
10	65,178.95 kg	8,147.37 kg	+65078.95%
11	72,421.06 kg	9,052.63 kg	+72321.06%
12	79,663.16 kg	9,957.90 kg	+79563.16%
13	86,905.27 kg	10,863.16 kg	+86805.27%
14	94,147.37 kg	11,768.42 kg	+94047.37%
15	101,389.48 kg	12,673.68 kg	+101289.48%
16	108,631.58 kg	13,578.95 kg	+108531.58%
17	115,873.68 kg	14,484.21 kg	+115773.68%
18	123,115.79 kg	15,389.47 kg	+123015.79%
19	130,357.89 kg	16,294.74 kg	+130257.89%
20	137,600.00 kg	17,200.00 kg	+137500.00%

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Frequently Asked Questions

How do I calculate the age of a sample from its remaining fraction?+

Click SOLVE FOR on t (Elapsed Time), set N₀ = 100 and N(t) to the remaining percentage, and enter the isotope's half-life t_½.

How is the decay constant λ related to half-life?+

The exponential decay constant equals λ = ln(2) / t_½ ≈ 0.693147 / t_½.

Does this equation apply to pharmacology drug clearance?+

Yes. First-order pharmacokinetic elimination in blood plasma follows the exact same half-life equation.