Radioactive Decay (N = N₀ e^(−kt))
Quantity remaining after time t given decay constant k or half-life.
Result
N(t) remaining
250.0000
2.000 half-lives elapsed.
- N₀1000
- Decay constant k1.2097e-4
- Half-life5,730.0000
- Elapsed t11460
- Half-lives elapsed2.0000
- Fraction remaining0.250000
- N(t)250.000000
- Decayed amount750.0000
Step-by-step
- N(t) = N₀ × e^(−kt) = 1000 × e^(−1.386294) = 250.0000.
- Half-lives elapsed = t / t½ = 2.0000.
How to use this calculator
- Enter N₀ and decay parameter (t½ or k).
- Enter elapsed time.
- Read remaining N(t).
About this calculator
First-order radioactive decay: N(t) = N₀ × e^(−kt). After n half-lives, N/N₀ = (½)ⁿ. Each radioactive nucleus has constant decay probability per unit time — independent of past. Bulk decay is exponential because of large numbers. Same math applies to many other first-order processes: drug elimination, RC capacitor discharge, exponential cooling.
Frequently asked
dN/dt = −kN (rate proportional to amount). Solution: N = N₀e^(−kt).
Related calculators
Half-Life ↔ Decay Constant
t½ = ln(2) / k. Convert between half-life and decay constant; predict remaining fraction.
Atomic Mass from Isotopes Calculator
Σ (isotope mass × abundance fraction). Periodic-table atomic mass from isotope mix.
Ideal Gas Law (PV = nRT)
Solve for any of P, V, n, T given the other three. R = 8.314 J/(mol·K).
Henderson-Hasselbalch (Buffer pH)
pH = pKa + log([A⁻]/[HA]). Predict buffer pH from acid + conjugate base concentrations.
Wavelength ↔ Frequency Calculator
c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.
Logarithm Calculator
log_b(x) for any base b > 0, b ≠ 1, x > 0. Common bases shown side-by-side.