GAMMADIST in Zoho Sheet: Gamma Density and Cumulative Probability

• 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 GAMMADIST reference. Documentation check; not a new native test.

GAMMADIST evaluates a gamma probability distribution at a nonnegative numeric value. Zoho’s official GAMMADIST help provides the exact English-reference syntax GAMMADIST(x; α; β; mode). Here α (alpha) is the shape, β (beta) is the scale, and the fourth argument deliberately chooses either the probability density (0/FALSE) or the cumulative probability (1/TRUE). A density describes height of a continuous distribution’s curve and is not itself the probability of getting that exact value. A cumulative probability is the probability that a modelled observation is at or below x. Z1

For example, an independent gamma-distribution calculation predicts that =GAMMADIST(4;3;2;TRUE) yields approximately 0.323323583817—a modelled 32.33% chance of a value at or below 4, given gamma shape 3 and scale 2. The companion density-mode result =GAMMADIST(4;3;2;FALSE) is approximately 0.135335283237 in reciprocal units of x. These example results were calculated independently, not copied from or executed in Zoho Sheet.

Evidence scope: The Zoho English help supports the function signature, interpretation of its four arguments and listed errors. It does not establish a universal first-supported release, uniform mobile behavior, numeric precision limits or specific behaviour for every invalid/blank input. Such claims need actual native tests.

GAMMADIST(x; α; β; mode)

All four parameters appear without optional square brackets in Zoho’s help. There is no officially documented default when mode is omitted, so specify it explicitly rather than relying on another spreadsheet’s rule. Square-bracket notation is not part of this documented signature. The examples use ; as the delimiter because that is the exact punctuation in the English Zoho reference; input separators and decimal notation should be verified for the actual workbook locale. Do not reverse shape and scale or substitute a gamma rate directly for the documented scale. Z1

For a continuous gamma variable, the independently evaluated density is f(x)=x^(α−1) exp(−x/β)/(Γ(α) β^α) for x>0; the cumulative probability is F(x)=P(X≤x)=∫₀ˣ f(t)dt. Γ is the mathematical gamma function, and the distribution’s modelled mean and variance are αβ and αβ². These are standard distribution identities used to check example arithmetic; they are not proof of Zoho’s undocumented boundary-handling or numerical algorithm.

Suppose hypothetical completion times (in minutes) are modelled with shape 3, scale 2, giving a modelled mean of 3×2=6 minutes and standard deviation √(3×2²)=√12≈3.4641 minutes. This is an assumed probabilistic model, not a fitted model estimated from the four example rows. Create the following worksheet (leave D and F unused as visual spacers):

Enter A1–C5, place the formula in E2 and G2, and either copy it down or enter each shown row’s formula. Columns E and G deliberately differ; D and F may be used for plain-language headings if you do not want adjacent formulas.

Expected values are independent SciPy gamma-distribution predictions, rounded to 12 decimals; they are not native Zoho output. In the documented cumulative mode, values should rise (or stay the same) as the threshold grows. Density can rise and then fall; it does not have to be increasing or bounded by 1 in general.

An exact cross-check for integer shape

For α=3, β=2 and x=4, the standard gamma CDF simplifies to:

F(4) = 1 − exp(−4/2) × (1 + 4/2 + (4/2)^2/2)
     = 1 − exp(−2) × 5
     = 0.323323583817

A proposed independent spreadsheet cross-check is =1-EXP(-4/2)*(1+4/2+(4/2)^2/2). Verify local formula parsing and outputs in Zoho before publishing it as a native test. The check is useful because it does not call GAMMADIST and therefore can reveal a mistaken mode, parameter order or scale.

A typical question is: “What proportion of these modelled service completions take more than 4 but no more than 10 minutes?” For a continuous distribution the independent result is F(10)−F(4):

=GAMMADIST(10;3;2;TRUE)-GAMMADIST(4;3;2;TRUE)

Predicted result: 0.875347980517 − 0.323323583817 = 0.552024396700, or roughly 55.20%. Entering FALSE for either term would subtract a density from a probability, producing a result with no correct interval-probability interpretation. The distribution is continuous: including or excluding a single endpoint does not change its theoretical probability, but rounding/measurement rules matter in real systems.

For “more than 10 minutes,” use the complement of the CDF, =1-GAMMADIST(10;3;2;TRUE); independently predicted result 0.124652019483 (12.47%). Do not misread this as 12.47% of a particular observed sample without validating the fit of the underlying gamma model.

Scenario comparisons. Put shape and scale in dedicated cells such as K2=3, K3=2. Use absolute references:

=GAMMADIST(A2;$K$2;$K$3;TRUE)

Copy down across several candidate thresholds. You can then compare a second model with shape 5 and scale 2. For example, =GAMMADIST(10;5;2;TRUE) independently predicts 0.559506714935, noticeably less than the shape-3 model’s 0.87535. This comparison isolates a shape change only when both models use the same scale. If parameters came from sample estimates, reflect that uncertainty separately: GAMMADIST computes under parameters, it does not fit them.

Exponential special case. With α=1, a gamma distribution reduces to an exponential distribution of scale β. Therefore =GAMMADIST(4;1;4;TRUE) is independently expected to equal 1−EXP(−1) ≈ 0.632120558829. This is a useful algebraic check, not a native Zoho compatibility test of EXPONDIST.

Chi-square relationship. For a theoretical chi-square random variable with ν degrees of freedom, the gamma representation is shape ν/2, scale 2. For example, theoretical chi-square CDF at 6 for ν=6 corresponds to GAMMADIST(6;3;2;TRUE) ≈ 0.576809918873. Zoho separately documents CHISQDIST; the algebraic relationship does not prove exact floating-point parity or boundary behavior between its implementations.

Inverse thresholds. To find a percentile instead of evaluating a given threshold, use Zoho’s separately documented GAMMAINV. For example, =GAMMAINV(0.9;3;2) is independently expected to be approximately 10.644640675668, whose mathematical gamma CDF is 0.9. This cross-link is evidence-based; GAMMAINV is not a different interpretation of the GAMMADIST mode argument.

Zoho specifically lists #NUM! when x<0 or α≤0 or β≤0; these are documented invalid domains. It also lists general #VALUE! for unsuitable types, #NAME! for bad function/name spelling and #REF! for invalid references. The help page includes generic #N/A! guidance mostly about lookup functions—do not infer that a valid GAMMADIST necessarily produces that error. Z1

Unknown until native verification: Behaviour when mode is omitted, mode is 2/text/blank, x=0 for shape below 1, extremely large parameters, loss of precision in tails, text-numbers accepted/coerced, or formula punctuation in a particular non-English locale. Likewise, Zoho’s public reference does not state a maximum number of rows, a first supported version, a plan restriction or separate desktop/mobile feature parity for this function. Do not invent error strings for these cases.

The Zoho English reference explicitly names GAMMADIST with four arguments and semicolons. Microsoft’s separate Excel documentation names the newer GAMMA.DIST(x,alpha,beta,cumulative) and likewise describes a shape/scale model, but Excel syntax and error behavior are not Zoho evidence. Spreadsheet imports may rewrite names and delimiters; verify the actual displayed formula and both TRUE/FALSE modes after migration. Google Sheets’ function catalogue mentions related gamma names, but that does not establish Zoho accepting an Excel-style dotted alias. Do not invent a first-supported Zoho version or assure operation on every paid/free plan or mobile app without an official version matrix. Z1 M1 G1

• Z1 Zoho GAMMADIST, official description, syntax, parameter order, mode and errors, checked 2026-10-13: Zoho GAMMADIST.
• Z2 Zoho GAMMAINV, official inverse cumulative description and shape/scale arguments, checked 2026-10-13: Zoho GAMMAINV.
• Z3 Zoho CHISQDIST, independently related chi-square statistical function, checked 2026-10-13: Zoho CHISQDIST.
• M1 Microsoft Excel GAMMA.DIST, product-specific syntax reference only, checked 2026-10-13: Microsoft GAMMA.DIST.
• G1 Google Sheets function list, other-product naming reference only, checked 2026-10-13: Google Sheets list.

Testing boundaries: Mathematical values were generated independently with SciPy and additional closed-form/monotonicity checks. No execution, screenshot, account login or error reproduction occurred in Zoho Sheet. For native validation, test cloud app, formula separators/locale, example cells, all documented invalid domains, explicit/omitted mode, and extreme values, recording actual app date and outputs.