Zoho Sheet CHISQDIST: Chi-Square CDF and PDF

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

This tutorial follows Zoho Sheet’s English online help reference checked on 2026-10-13. The examples use the help article’s semicolon argument separator and decimal point. In a workbook with another locale, inspect File → Spreadsheet Settings → Locale (language, decimal separator, grouping and regional formats are configurable); use the syntax accepted by your actual spreadsheet rather than guessing from a different product. Zoho locale settings.

These probability calculations assume the mathematical chi-square distribution with the specified positive integer degrees of freedom. A chi-square statistic is generally nonnegative; it is not a raw percentage or a test score. For hypothesis tests, the statistic, degrees of freedom and sampling assumptions must be justified before obtaining a tail probability or cutoff. A low p-value under a model is not the probability that a hypothesis is true, and statistical significance is not an effect size.

Zoho’s current public help article does not identify the function’s earliest-supported product release or establish exact parity across browser, mobile, desktop/offline, editions or account plans. Accordingly, no first-version claim or unsupported platform guarantee is made. No formula was executed in a signed-in Zoho Sheet instance. The values below are independently calculated using a standard chi-square model (SciPy 1.17.0), not screenshots, Zoho output or vendor certification.

=CHISQDIST(x; k; [cumulative])

Zoho’s CHISQDIST reference explicitly says cumulative defaults to FALSE if omitted. That is a material difference from reading “distribution” as necessarily cumulative. The function is documented as left-tailed when cumulative is TRUE; it is not the right-tail CHIDIST and it has no upper-tail boolean mode in the referenced article. There are no further optional parameters.

Mathematically, for X ~ χ²(k), CHISQDIST(x;k;TRUE) represents F(x) = P(X ≤ x). The density at x is f(x), with the distribution shape determined by k. Density is an ordinate on a curve, not an event probability at a point; adding density values across a few x values is not generally a probability. An accumulated area, not one ordinate, gives an interval probability.

Create a blank Zoho Sheet and enter the following table beginning at A1. A and B/C below are plain values; the reference probabilities in D:F were calculated independently for checking and are not outputs of Zoho Sheet:

Format probability cells with 9–12 decimal places when inspecting a calculation. Formatting alone can make two close values look identical; rounding also affects round-trip inverse checks. Formulas belong in a new column G or farther right so you do not overwrite the comparison data. A PDF (probability density) is not the probability that a continuously distributed statistic equals a single exact number: for a continuous variable that point probability is zero.

1. In G1 enter Left-tail probability; in H1, Density at x.
2. In G2 use =CHISQDIST(B2;C2;TRUE). With B2=14 and C2=5, independently expect 0.984390583900.
3. In H2 enter =CHISQDIST(B2;C2;FALSE); independently expect 0.006352131663.
4. In I2 enter =CHISQDIST(B2;C2). As documented, omitted cumulative defaults FALSE; independently expect the same density as H2, not the value in G2.
5. Fill G2:I2 down through row 5. CDF values should increase when x increases with k fixed. The density may rise then fall, so do not expect it to behave like a cumulative percentage.

This sample shows how a small density can coexist with a very large cumulative probability: most of the left-tail area can lie before x=14 even though the instantaneous curve height at x=14 is about 0.00635. Conflating these gives bad thresholds and misleading charts.

For k=5, suppose you need the modeled probability that a chi-square variable is between x=4 and x=10. The appropriate cumulative difference is:

=CHISQDIST(10;5;TRUE)-CHISQDIST(4;5;TRUE)

The independently expected result is 0.474180705206, obtained by subtracting the chi-square CDF at x=4 from the CDF at x=10 (k=5). Never subtract the PDF at two endpoints as if it represented interval area. You can put 4 in J2, 10 in K2, and 5 in L2, then use =CHISQDIST(K2;L2;TRUE)-CHISQDIST(J2;L2;TRUE) in M2. The formula requires lower bound ≤ upper bound; if reversed it produces a negative difference, which is a sign that your input interval has been reversed, not a “negative probability.”

For another verification use =1-CHISQDIST(14;5;TRUE): independently 0.015609416100, the corresponding right-tail result for =CHIDIST(14;5). Near the far upper tail, subtracting a CDF close to 1 can lose numerical precision; where available, a dedicated right-tail function is preferable for extreme p-values.

An upper 95th percentile for k=5 is given by =CHISQINV(0.95;5) (independently 11.070497694). Feeding it to =CHISQDIST(CHISQINV(0.95;5);5;TRUE) mathematically returns 0.95 up to rounding. This illustrates the proper left-tail inverse pair.

A frequently encountered chi-square statistic is a sum of nonnegative contributions from deviations between observed and expected category counts. For five categories with observed counts 18,22,20,25,15 and expected counts 20 each, the independently calculated statistic is 2.9 with four degrees of freedom under standard goodness-of-fit assumptions. =CHISQDIST(2.9;4;TRUE) has independent expected left-tail value 0.425302794170; its complement 0.574697205830, not 0.4253, is the right-tail goodness-of-fit p-value. Use CHIDIST for that common right-tail question.

The density mode is useful when visualizing a continuous theoretical distribution: enter x values 0, 1, 2, … in column B, fixed k in C, and =CHISQDIST(B2;C2;FALSE) in a separate column. Plot the curve. If you want an area across a range, integrate or difference CDF values; merely summing a finite set of densities without accounting for step size is not a valid probability calculation.

Zoho expressly lists #NUM for x < 0 or k < 1 / k > 10^10. The k argument is a degree-of-freedom count; supply a positive integer consistent with the analysis. The article does not explicitly specify fractional-k coercion, boolean-as-numeric conversion, precise behavior at x=0 for every k, or the treatment of blank cumulative cells. Do not substitute Microsoft documentation for those Zoho facts. If the optional flag is omitted, the reference does specify the default: FALSE.

The function-specific help page lists generic errors alongside specific #NUM conditions. A generic entry does not mean every such error necessarily occurs for every input. Neither floating-point accuracy guarantees nor boundary outcomes not explicitly documented by Zoho are asserted here. Large degrees of freedom, noninteger degrees of freedom, probability endpoints, blank inputs, logical values and high-precision tails remain native validation cases; do not infer their treatment from Excel or another calculator.

A density can be greater than one for some continuous distributions and parameter choices without violating probability laws; it is not constrained to be a probability of a point event. In this particular chi-square example, the density is small, but that alone tells you nothing about the tail area without considering the shape.

Zoho’s help article supplies the behavior described in the syntax section. Modern Excel separately documents CHISQ.DIST(x,deg_freedom,cumulative) where its third argument is required, whereas the Zoho CHISQDIST help page documents an optional flag that defaults to FALSE. Microsoft’s Excel documentation is evidence for Excel only; it does not prove that Zoho has identical numeric coercions, aliases, error names or version availability. Legacy CHI... names in Excel or Google Sheets should be mapped by tail and function type rather than by visual similarity alone.

For porting a model, explicitly specify tails and cumulative modes, preserve degrees of freedom, and test representative cases in the target spreadsheet. A right-tail probability and a left-tail probability are complements for a continuous chi-square statistic, but the corresponding inverse functions receive different probability inputs for the same cutoff.

• Zoho Sheet CHIDIST tutorial
• Zoho Sheet CHIINV tutorial
• Zoho Sheet CHISQDIST tutorial
• Zoho Sheet CHISQINV tutorial

Official Zoho sources, opened and checked on 2026-10-13 (each item supports the stated syntax, direction, related function or the locale setting; none establishes first release):

• Zoho Sheet — this function reference
• CHIDIST in Zoho Sheet
• CHIINV in Zoho Sheet
• CHISQDIST in Zoho Sheet
• CHISQINV in Zoho Sheet
• CHITEST in Zoho Sheet
• Zoho Sheet — spreadsheet locale settings
• Microsoft Excel — CHISQ.DIST behavior (Excel comparison only)

Validation: Official documentation checked on 2026-10-13; worked numbers independently recalculated. Native Zoho executions: 0. Screenshots: 0. Runtime edge cases remain unverified.