Calculate failure rate, MTBF, and reliability R(t) from observed failures, operating time, mission time, and MTBF in hours, days, or years.

Failure Rate Calculator

Pick what you want to find, enter the numbers, press Calculate.

Failure Rate & MTBF
Reliability R(t)
Enter a non-negative number.
Enter a time greater than zero.
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How this is calculated
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Enter an MTBF greater than zero.
Enter a mission time ≥ 0.
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How this is calculated
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Related Calculators

Failure Rate Formula

The following formula is used to calculate the (average) failure rate over an observation period.

\lambda = \frac{n}{t}

Variables:

  • λ is the failure rate (failures per unit time)
  • n is the number of failures
  • t is the time period

To calculate the failure rate, divide the number of failures by the time period. The result has units of “failures per time” (for example, failures per hour or failures per year).

What is Failure Rate?

Failure rate is a measure of how frequently a system or component fails over time, commonly used in reliability engineering. It is not a probability by itself because it has units (1/time). If you need a failure probability over a time interval and can assume a constant failure rate (exponential/Poisson model), a common model is:

P(\text{at least one failure in }T)=1-e^{-\lambda T}

How to Calculate Failure Rate?

The following steps outline how to calculate the failure rate.

  1. First, determine the number of failures (n) that have occurred.
  2. Next, determine the time period (t) over which the failures were observed.
  3. Next, gather the formula from above = λ = n / t.
  4. Finally, calculate the failure rate (λ) in failures per unit time.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

number of failures (n) = 5

time period (t) = 1 year

failure rate (λ) = n / t = 5 / 1 = 5 failures/year