When to use this calculator
Use matching time units for the rate and waiting time. This is a model probability rather than an empirical guarantee.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Independent Events Probability Calculator: Find the probability that two independent events both occur.
PUTTING IT INTO PRACTICE
Exponential Survival Probability: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Event rate per time unit | 1 |
| Waiting time | 0 |
| Result | 100 % |
- Check the input labels and enter the example values above.
- Apply the relationship: Survival probability (%) = exp(−rate × time) × 100.
- The result is 100 %, rounded for display.
How to interpret your result
Assumes a constant event rate and the memoryless exponential waiting-time model.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
When is the exponential survival probability calculator useful?
Use matching time units for the rate and waiting time. This is a model probability rather than an empirical guarantee.
How do I use the exponential survival probability calculator?
Enter event rate per time unit, waiting time. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Survival probability (%) = exp(−rate × time) × 100.
What should I check before using the result?
Assumes a constant event rate and the memoryless exponential waiting-time model.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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