Zoho Sheet BETADIST Function: Beta Probabilities and Density Examples
Use BETADIST in Zoho Sheet for cumulative beta probabilities, scaled intervals, probability density, and bounded-rate examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: Use =BETADIST(0.5;2;3) to obtain the cumulative probability at 0.5 for a beta distribution with shape parameters 2 and 3. The independently calculated expected answer is 0.6875: under that model, 68.75% of outcomes are at or below 0.5. For a density rather than a cumulative probability, use =BETADIST(0.5;2;3;0;1;FALSE), whose expected result is 1.5. A density of 1.5 is not a probability of 150%.
The beta family models a continuous quantity confined to a finite interval, such as a proportion between 0 and 1, when its shape is adequately described by two positive parameters. It cannot, without additional modelling, predict discrete numbers of defective units, and its shape parameters should not be mistaken for observed percentages. The official Zoho BETADIST reference explicitly documents both cumulative and density modes. [Z1, checked 2026-10-12]
Availability and version history
- Introduced: The original introduction version and date are not established by the checked sources.
- Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
- Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
- Checked: October 14, 2026, against the official BETADIST reference. Documentation check; not a new native test.
Exact documented syntax and argument order
BETADIST(x; α; β; [a]; [b]; [cumulative])
| Argument | Required? | Expected type and purpose | Default, when documented |
|---|---|---|---|
x |
Yes | Numeric observation at which to evaluate the model; between lower and upper limits | None |
α (alpha) |
Yes | Positive numeric first beta shape parameter | None |
β (beta) |
Yes | Positive numeric second beta shape parameter | None |
a |
No | Numeric lower limit of the modeled interval | 0 |
b |
No | Numeric upper limit of the modeled interval | 1 |
cumulative |
No | Logical TRUE for the cumulative distribution or FALSE for density |
TRUE() |
Zoho-specific ordering matters: the cumulative flag comes after both optional bounds, not before them. The semicolons above are copied from Zoho’s English reference rather than assumed from another spreadsheet. Square brackets identify optional parameters and are not characters to enter. This guide does not claim that every workbook locale has identical separators; Zoho’s locale settings help documents workbook-level numeric and locale choices. [Z1, Z4; checked 2026-10-12]
To use density mode without depending on how omitted arguments in the middle of a formula are parsed, provide both interval bounds explicitly: =BETADIST(x;alpha;beta;0;1;FALSE).
Worked example 1: a fraction between zero and one
Create a new test area using this specific cell layout (literal numbers, no percentage-formatted text):
| Cell | Value | Meaning |
|---|---|---|
| A2 | 0.5 |
Point of interest, x |
| B2 | 2 |
First shape parameter, alpha |
| C2 | 3 |
Second shape parameter, beta |
| D2 | 0 |
Lower bound |
| E2 | 1 |
Upper bound |
Enter these formulas in separate result cells:
| Formula | Expected result (independent calculation) | Interpretation |
|---|---|---|
=BETADIST(A2;B2;C2) |
0.6875 |
Probability at or below 0.5, using all documented defaults |
=BETADIST(A2;B2;C2;D2;E2;TRUE) |
0.6875 |
Explicit cumulative version of the same calculation |
=BETADIST(A2;B2;C2;D2;E2;FALSE) |
1.5 |
Probability density at 0.5 |
=1-BETADIST(A2;B2;C2) |
0.3125 |
Probability strictly above 0.5 for a continuous variable |
How the first result is calculated: when alpha = 2 and beta = 3 over [0, 1], the density simplifies to 12*x*(1-x)^2. Integrating from 0 through 0.5 yields 11/16 = 0.6875. This is an independent mathematical derivation, not a native Zoho execution. A density can be greater than one because probabilities concern areas under the density curve, not the height at a single point.
Worked example 2: measure probabilities across a real interval
Suppose the bounded quantity is a hypothetical completion time between 10 and 30 minutes. Set shape parameters 2 and 3. Scaling changes the units of the input and of the density.
| Cell | Value |
|---|---|
| A5 | 15 |
| A6 | 25 |
| B5 | 2 |
| C5 | 3 |
| D5 | 10 |
| E5 | 30 |
Calculate the probability of the interval from 15 to 25 minutes:
=BETADIST(A6;B5;C5;D5;E5;TRUE)-BETADIST(A5;B5;C5;D5;E5;TRUE)
Expected output: 0.6875, because the model gives CDF(25)=0.94921875 and CDF(15)=0.26171875. It is mathematically correct to subtract the two cumulative values for this continuous model; do not add two densities instead. The scaled density at 20 minutes is =BETADIST(20;2;3;10;30;FALSE), expected 0.075 per minute, rather than the unit-interval value 1.5. The normalizing interval width (20) accounts for this difference.
Advanced use: compare threshold risk across scenarios
For a bounded performance rate, store the model parameters once (for example alpha in $B$2, beta in $C$2) and make a threshold column F2:F6 containing 0.10, 0.25, 0.40, 0.50 and 0.75. In G2, enter:
=BETADIST(F2;$B$2;$C$2)
Copy it down. With alpha 2 and beta 3, the independent expected cumulative probabilities at those thresholds are approximately 0.0523, 0.26171875, 0.5248, 0.6875, 0.94921875 respectively. The output is a modeled distribution, not the proportion of observed rows satisfying each threshold. For empirical fractions, count actual observations and divide by the sample size instead. Use different alpha and beta parameters only when a justified statistical model supports them.
For a modeled 95% threshold, the companion Zoho function BETAINV provides the inverse calculation; that function is documented in Zoho’s BETAINV help. [Z2]
Edge cases, errors, and troubleshooting
| Symptom | Likely cause or check | What to do |
|---|---|---|
#NUM! |
Zoho documents alpha or beta at/below 0 | Use strictly positive shape parameters. |
#NUM! |
Zoho documents x outside the specified interval, or equal bounds | Ensure x falls between a and b, and choose different limits. |
#VALUE! |
Argument has an invalid type | Check that numeric cells contain numbers, not number-like text; use logical TRUE/FALSE for the flag. |
#NAME! |
Misspelled function or unrecognized name | Enter BETADIST, not BETA_DIST, and check formula delimiters. |
#REF! |
Referenced cell/range was removed | Restore the original address or revise the formula. |
| Result greater than 1 | Usually density mode FALSE, not cumulative mode |
A density can exceed 1. Choose TRUE when you want a cumulative probability. |
| Formula returns a different value after switching workbooks | Bound/shape/locale/cumulative argument moved | Verify all six argument positions and the number format. |
| Extreme edge cases | Docs do not specify all endpoint, inverted-bound, or precision rules | Flag a native Zoho Sheet test; do not guess the exact error. |
Zoho’s published error table also displays generic #N/A! guidance borrowed from lookup examples. This is not evidence that valid beta inputs generate #N/A!. Nor does the reference establish how a > b is handled independently of the documented a = b error. [Z1]
Excel and Google Sheets compatibility: do not copy a formula blindly
| Product/function | Documented signature/availability note | Practical consequence |
|---|---|---|
Zoho Sheet BETADIST |
BETADIST(x; α; β; [a]; [b]; [cumulative]); flag defaults TRUE |
FALSE is sixth, after both bounds. [Z1] |
Excel BETA.DIST |
BETA.DIST(x,alpha,beta,cumulative,[A],[B]) |
The cumulative flag is fourth and required in that documented signature. [M1] |
Excel legacy BETADIST |
Cumulative beta calculation, legacy backward-compatibility function | The Excel legacy function name does not guarantee Zoho’s optional density argument. [M2] |
| Google Sheets | Its function index lists BETADIST(value,alpha,beta,lower_bound,upper_bound) and BETA.DIST(value,alpha,beta,cumulative,lower_bound,upper_bound) |
The listed alternatives likewise must be checked for argument positions. [G1] |
Exact historical first-support versions, account-tier restrictions, native mobile evaluation and distribution-tail precision were not established by the consulted Zoho material. Zoho’s 2026 what’s-new page lists several recent features but does not establish a BETADIST first-release date. Avoid describing this function as newly introduced or promising identical platform behaviour. [Z5]
Related learning and checked references
For general averages in existing site content, see Zoho AVERAGE; it summarizes observations instead of returning probabilities from a parameterized model. For error-handling patterns, see Zoho IFERROR, but do not hide an invalid shape parameter without logging the cause.
- [Z1] Zoho Sheet, BETADIST official reference — syntax, defaults, modes and documented errors; checked 2026-10-12.
- [Z2] Zoho Sheet, BETAINV official reference — inverse function identity; checked 2026-10-12.
- [Z4] Zoho Sheet, spreadsheet locale settings — workbook locale options; checked 2026-10-12.
- [Z5] Zoho Sheet, What’s new — release-note scope check, not a version guarantee; checked 2026-10-12.
- [M1] Microsoft, Excel BETA.DIST — argument order and documented Excel-specific errors; checked 2026-10-12.
- [M2] Microsoft, Excel legacy BETADIST — backward compatibility notes; checked 2026-10-12.
- [G1] Google, Sheets function list — BETADIST/BETA.DIST argument listing; checked 2026-10-12.
Validation boundary: documentation claims above were source-checked; expected numbers were independently calculated using Python/SciPy and a simple polynomial check. No native Zoho Sheet formulas, screenshots, beta error cases, account editions or mobile versions were tested.