WEIBULL.DIST in Excel: Separate Shape, Scale, Density and Survival

=WEIBULL.DIST(x, alpha, beta, cumulative)

All four arguments are required. x is the nonnegative evaluation point, alpha positive shape and beta positive scale. TRUE selects the cumulative distribution and FALSE the density, as illustrated by Microsoft’s equations and examples.

The cumulative equation is 1-EXP(-((x/beta)^alpha)). Scale beta has the same units as x. It is not a rate and is not generally the mean or median. Shape alpha has no units and changes the form of the distribution.

The function can be used in duration or reliability models when their assumptions are justified. Entering chosen parameters does not establish a fit, estimate uncertainty or verify an actual device’s behavior.

Put 0, 2.5, 5, 7.5 and 10 in A2:A6. Enter =WEIBULL.DIST(A2,3,5,TRUE) in B2 and fill down. Independent targets are approximately 0, 0.1175030974, 0.6321205588, 0.9657818817 and 0.9996645374.

In C2 enter =1-EXP(-((A2/5)^3)) and fill down as an independent expression check. At x=beta, the exponent’s power is one, so the cumulative probability is always 1−EXP(−1) for any positive shape.

This makes beta a useful 63.2121% scale checkpoint. It does not make beta the 50th-percentile value or an arithmetic average.

=WEIBULL.DIST(5,3,5,FALSE) has independent density 0.2207276647 per unit of x. It is not the probability of exactly five under the continuous model.

The survival probability beyond five is =1-WEIBULL.DIST(5,3,5,TRUE), independently 0.3678794412. For the interval 2.5 through 7.5, subtract the two cumulative results to obtain 0.8482787843.

Use event labels such as “at or below,” “beyond,” and “between.” Changing TRUE to FALSE does not select the opposite tail; it changes the mathematical kind of output.

For an interior probability p, solve the CDF equation to obtain beta*(-LN(1-p))^(1/alpha). With shape three and scale five, the independent median is 4.4249852225 and the 95th percentile 7.2078267140.

Put p=0.95 in F2 and enter =5*(-LN(1-F2))^(1/3) in F3. Passing the full F3 value into =WEIBULL.DIST(F3,3,5,TRUE) mathematically recovers 0.95.

Do not round the quantile before checking it. This algebraic reference does not establish Excel’s numerical behavior for probabilities extremely close to one.

At alpha=1, the model becomes exponential with rate 1/beta. =WEIBULL.DIST(3,1,2,TRUE) has independent target 0.7768698399, the same mathematical value as an exponential calculation with rate 0.5.

The official exponential-equivalence image confirms that reciprocal relationship. Supplying a rate directly as beta without inversion changes the distribution. Units should make the distinction visible: beta is a duration, while a rate is per duration.

Microsoft uses x=105, alpha=20, beta=100. Independent results are cumulative probability 0.9295813901 and density 0.0355888640, matching the source’s displayed 0.929581 and 0.035589.

A high shape value makes the distribution relatively concentrated near its scale, but the function does not explain how those parameters were estimated. Preserve the stated parameters when reproducing a reference example.

Microsoft documents #VALUE! for nonnumeric x, alpha or beta, and #NUM! for x<0 or nonpositive alpha or beta. At zero, density has different mathematical limits depending on shape; the shape-three example’s zero density does not certify all native endpoint behavior.

Check swapped shape/scale inputs, incompatible units and a FALSE density flag in a probability calculation. Native error displays, extreme-tail precision and all coercion rules were not executed here. The official equation images were freshly inspected, while the numerical results are independent mathematical expectations.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks WEIBULL.DIST as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft WEIBULL.DIST reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.