Exponential Distribution Calculator

Exponential Distribution Formula

Worked Example

Rate λ = 0.5 per hour, probability of an event within 3 hours:

1. F(x) = 1 − e^(−λx) with λ = 0.5
2. = 1 − e^(−1.5) = 0.7768698399
3. Memoryless: P(X > s + t | X > s) = P(X > t)

Density f(x) = λe^(−λx): 0.1115650801 · Mean 1/λ: 2 · Variance 1/λ²: 4 · Median ln2/λ: 1.386294361

GATE tip

Reliability questions often give the mean time to failure; λ = 1/MTTF, and the reliability at time t is e^(−t/MTTF).

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• De Moivre’s Theorem Calculator

  [r(cos θ + i sin θ)]ⁿ = rⁿ(cos nθ + i sin nθ)

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  Example: z = 1 + i with n = 3: zⁿ = z^3 = -2 + 2i.

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Frequently asked questions

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.