BETA.DIST in Excel: Calculate Probabilities on a Bounded Interval

=BETA.DIST(x, alpha, beta, cumulative, [A], [B])

x, alpha, beta and cumulative are required. The two shape parameters must be positive. TRUE selects the cumulative distribution; FALSE selects density. Optional A and B set the lower and upper bounds. Microsoft specifies defaults A=0 and B=1 when both are omitted.

Use increasing bounds and an evaluation point within them. With general bounds, the standardized position is y=(x−A)/(B−A). The shapes control the distribution on that interval; they are not its lower and upper endpoints.

Density is a curve height per unit of x. It may exceed one without implying a probability above 100%. Probabilities are areas, found here from cumulative values or their differences.

Put 0.25, 0.5 and 0.75 in A2:A4. In B2 enter =BETA.DIST(A2,2,3,TRUE,0,1) and fill down. Independent cumulative targets are 0.26171875, 0.6875 and 0.94921875.

For these particular shapes, the cumulative function is 6*y^2-8*y^3+3*y^4. Enter =6*A2^2-8*A2^3+3*A2^4 in C2 and fill down as an independent algebraic check.

The mean of this standard beta model is alpha/(alpha+beta)=0.4. The cumulative value at the midpoint 0.5 exceeds one half because the model is not symmetric. The midpoint of the bounds is not necessarily the median; symmetry requires equal shape parameters.

=BETA.DIST(0.5,2,3,FALSE,0,1) targets density 1.5, from the polynomial 12*y*(1-y)^2. That value is not a 150% chance of exactly 0.5 in a continuous model.

For the interval from 0.25 through 0.75, use =BETA.DIST(0.75,2,3,TRUE)-BETA.DIST(0.25,2,3,TRUE). Its independent target is 0.6875. Subtracting density heights would not produce that area.

The upper tail above 0.75 is independently 0.05078125, obtained by subtracting the cumulative result there from one. Inclusive versus exclusive endpoints have the same probability for this continuous model.

Map the standard interval onto 10 through 20. The original midpoint 0.5 becomes 15, and =BETA.DIST(15,2,3,TRUE,10,20) still targets 0.6875.

Density changes with the horizontal scale. =BETA.DIST(15,2,3,FALSE,10,20) targets 0.15, one tenth of the standard-scale density because the interval is ten times wider. Keep the evaluation point and both bounds in matching units.

This rescaling does not estimate shape parameters or establish a suitable model for observed data. A bounded variable is not automatically beta-distributed merely because the function accepts its range.

The dedicated reference uses x=2, alpha=8, beta=10, A=1 and B=3. =BETA.DIST(2,8,10,TRUE,1,3) independently targets 0.6854705811. Switching TRUE to FALSE gives 1.4837646484.

These are the more detailed values behind the displayed 0.6854706 and 1.4837646. The cumulative example’s prose says “cumulative … density,” but the TRUE argument selects a cumulative probability, as the syntax explicitly states.

Microsoft documents #NUM! for nonpositive shapes, x below A, x above B or A=B. It documents #VALUE! for nonnumeric arguments; use the explicit logical cumulative flag shown in its syntax rather than interpreting that broad wording as disallowing TRUE or FALSE.

Require A<B as a model validation rule. Endpoint density can be zero, finite or singular depending on the shapes, and native treatment of all such boundaries was not tested. The polynomial examples use shapes whose ordinary endpoint limits are finite.

Check whether alpha and beta were mistaken for bounds, whether FALSE was used for a probability request, and whether all units were transformed consistently. No native Excel error or extreme-tail precision is inferred from these independent calculations.

• 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 BETA.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 BETA.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.