Calculation reviewed: 4 October 2026 · Engineering Desk Tools
How to use the Weibull reliability calculator
Calculate reliability, failure probability, hazard rate, MTTF and B10 life from Weibull parameters. Start with measurements or documented values for the equipment and reporting period you actually want to assess. The calculator does not fill in a typical installation for you. Its blank fields help keep a demonstration value from being mistaken for your own operating data.
Choose the required options, enter the values in the labelled units and select Calculate. If a field is rejected, check its range and unit before changing it. The result is accompanied by the equation and assumptions so you can decide whether it answers your engineering question.
Inputs and measurement basis
- Shape parameter β. Shape from a Weibull fit of your own failure data: below 1 early failures, about 1 random, above 1 wear-out. The value must be greater than zero.
- Scale parameter η, characteristic life (hours). Scale: the time by which about 63.2 percent of units have failed, in hours. The value must be greater than zero.
- Operating time t (hours). The operating time at which you want the reliability, in hours.
Record the measurement source and operating condition. Retain unrounded values for verification.
Method and interpretation
The Weibull distribution describes time to failure with a shape parameter β and a scale parameter η. Reliability at time t is the probability of surviving to t. The shape shows the failure pattern: below 1 the failure rate falls with age, near 1 failures are random, and above 1 the rate rises with wear. B10 life is the time by which 10 percent of units have failed, and is often used for replacement planning.
R(t) = exp(−(t / η)^β). Failure probability F(t) = 1 − R(t). Hazard rate h(t) = (β / η) × (t / η)^(β − 1). MTTF = η × Γ(1 + 1 / β). B10 life = η × (−ln 0.9)^(1 / β).
The parameters must come from a Weibull analysis of your own failure data. β below 1 suggests early-life failures, about 1 suggests random failures and above 1 suggests wear-out. η is the time by which 63.2 percent of units have failed. This tool takes the parameters as given and does not fit data. Suspended (non-failed) units must be handled in the fit, and a small sample gives wide uncertainty.
Worked example
This example does not populate the form. Enter your own installation data.
Calculated result: 77.8801 % reliability at time t. β is above 1: the failure rate rises with time, which suggests wear-out. Planned replacement before the B10 life may be worthwhile.
Check the arithmetic independently using the displayed equation. Retain intermediate precision and compare the final value with your equipment documentation.
Quick-reference table
These are illustrative values, not certified ratings or manufacturer data. Use the form for your own conditions.
Common mistakes
Entering parameters estimated from too few failures; mixing operating hours with calendar hours; ignoring suspended (still running) units when fitting; treating η as the average life; mixing different failure modes in one fit. Before relying on the output, check the decimal format, unit scale and source of each value. Recheck unusual results against the formula.
Frequently asked questions
Are the example values used automatically?
No. Inputs remain blank when the tool opens or when you clear them. The worked example and table are reading material below the calculator. Enter the actual values you want to check each time, and label saved reports so their context is not lost.
What does the result mean?
The results give the chance that a unit survives to the entered time, the failure rate at that time, the mean life and the B10 life. The shape parameter shows whether failures are early, random or wear-out.
Can I use a zero or a negative value?
The allowed range follows the meaning of each input. A divisor needs a positive value; other fields may allow zero. Check the form labels and error message rather than forcing an invalid value. A rejected input must be corrected before a result can be shown.
Is this a final design or equipment approval?
No. The parameters must come from a Weibull analysis of your own failure data. β below 1 suggests early-life failures, about 1 suggests random failures and above 1 suggests wear-out. η is the time by which 63.2 percent of units have failed. This tool takes the parameters as given and does not fit data. Suspended (non-failed) units must be handled in the fit, and a small sample gives wide uncertainty. Use the calculation as support for a checked decision, and review equipment documentation and applicable requirements before changing an installation or operating setting.
How can I save or share a calculation?
Calculate first, then use Copy result or Print report. Some maintenance tools also provide a CSV summary. Reports contain your own entered data, so review them before sharing. You can share the public page URL without including plant records or confidential measurements.
How do I report an unexpected result?
Use the Contact page and include the tool URL, input values, units, expected output and the reference you used. Explain the measurement basis. Exclude confidential information.
Related tools and records
Use related calculations with consistent units, periods and equipment scope.
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