MTBF Calculator
Work out the mean time between failures from observed operating time.
In short
Formula: MTBF = Total operating time / Number of failures
What this calculator does
The mean time between failures defined in the NIST/SEMATECH handbook, with its reciprocal shown as the observed failure rate.
Use it to turn Total operating time, Failures in that time into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
Inputs and what they mean
- Total operating time
- — Hours the service or system was in operation..
- Failures in that time
- — Number of failures observed..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
MTBF = Total operating time / Number of failures.
Inputs used: Total operating time, Failures in that time.
Edge handling: Total operating time is required.; Total operating time cannot be negative.; Total operating time must be no more than 1000000000000.; Failures in that time is required.; Failures in that time cannot be negative..
Worked example
5,040 operating hours with 7 failures
- Start with Total operating time: 5040, Failures in that time: 7.
- Apply the method: MTBF = Total operating time / Number of failures.
- A mean over the time you observed; it says nothing about future failures.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this mtbf calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: National Institute of Standards and Technology — Reliability measures: MTBF, MTTR and availability
Last reviewed:
Common questions
Where does this formula come from?
Section 8.1.2.4 — mean time between failures is operating time divided by the number of failures; mean time to repair is total repair time divided by the number of repairs; inherent availability is MTBF / (MTBF + MTTR). See the source link on this page.
What kind of calculation is this?
Observed operating time divided by the failures seen in that time. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
Arithmetic over the figures entered — it cannot tell whether the underlying monitoring, incident records or change records are complete. A mean over a short period, or over few events, is a weak description of behaviour. Observed over one period; it is not a prediction of time to the next failure.
How do I use the MTBF Calculator?
Enter the required values for Total operating time, Failures in that time. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the MTBF Calculator use?
MTBF = Total operating time / Number of failures The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the MTBF Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Formula, source and verification
Observed operating time divided by the failures seen in that time.
The question it answers: What availability, uptime, mean time between failures and mean time to repair does our own data show?
The formula
MTBF = Total operating time / Number of failures
- T — Operating time
- (h). Hours the service or system was in operation.
- f — Failures
- (count). Failures observed in that time.
Units: Hours in, hours and days out; failure rate in failures per hour.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
The mean time between failures defined in the NIST/SEMATECH handbook, with its reciprocal shown as the observed failure rate.
Assumptions built into the result
- Mathematical: The figures entered all cover the same measurement period.
- Mathematical: Incidents, changes and requests are counted consistently with the definition the team has written down.
- Mathematical: Operating time counts only the time the system was actually running.
Figures this calculator will never guess for you
- No target, benchmark, industry average or performance band is supplied for any figure.
- A definition is never presented as a goal: the availability formula is not an availability target, and the change failure rate formula is not an acceptable failure rate.
- No failure distribution is fitted and no prediction is made.
Limitations
- Arithmetic over the figures entered — it cannot tell whether the underlying monitoring, incident records or change records are complete.
- A mean over a short period, or over few events, is a weak description of behaviour.
- Observed over one period; it is not a prediction of time to the next failure.
Source and version
- Standard or reference
- NIST/SEMATECH e-Handbook of Statistical Methods — NIST (Section 8.1.2.4 — mean time between failures is operating time divided by the number of failures; mean time to repair is total repair time divided by the number of repairs; inherent availability is MTBF / (MTBF + MTTR).)
- Published source
- National Institute of Standards and Technology — Section 1.4
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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