Exponential Distribution Calculator
PDF, CDF and survival probability from rate λ.
Enter your values
Enter the rate λ in per unit.
Enter the value x you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- P(X ≤ x)
- 77.687%
- P(X > x)
- 22.313%
- Density f(x)
- 0.111565
- Mean
- 2
- Median
- 1.3863
- Standard deviation
- 2
Quick answer
The exponential distribution models waiting time between random events; P(X ≤ x) = 1 − e^(−λx) with mean 1/λ.
P(X ≤ x) = 1 − e^(−λx)
At a glance
| What it does | PDF, CDF and survival probability from rate λ. |
|---|---|
| Category | Statistics |
| Inputs needed | Rate λ, Value x |
| Main output | P(X ≤ x) |
| Formula | P(X ≤ x) = 1 − e^(−λx) |
| Cost | Free — no sign-up, no download |
How to use the Exponential Distribution Calculator
- 1Enter the rate λ — events per unit of time.
- 2Enter the value x you are testing.
- 3Read the cumulative and survival probabilities.
Inputs explained
- Rate λ(per unit)
- Enter the rate λ in per unit.
- Value x
- Enter the value x you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Rate λ0.5 per unit
- Value x3
Results
- P(X ≤ x)77.687%
- P(X > x)22.313%
- Density f(x)0.111565
- Mean2
- Median1.3863
- Standard deviation2
Frequently asked questions
What is λ in the exponential distribution?
The average number of events per unit time; if events arrive every 4 minutes, λ = 0.25 per minute.
Is the exponential distribution memoryless?
Yes — the chance of waiting another 5 minutes is the same no matter how long you already waited.
What do I need to enter into the Exponential Distribution Calculator?
Just 2 values: rate λ, value x. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Exponential Distribution Calculator work out the answer?
The exponential distribution models waiting time between random events; P(X ≤ x) = 1 − e^(−λx) with mean 1/λ. It applies the formula P(X ≤ x) = 1 − e^(−λx) and shows the working so you can check each step by hand.
Is the Exponential Distribution Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.