CHISQ.DIST.RT in Google Sheets: Right-Tail Probabilities

=CHISQ.DIST.RT(x, degrees_freedom)

Both arguments are required. Google’s function-specific reference specifies:

• numeric, positive x;
• numeric degrees_freedom from 1 through 10^10;
• integer truncation when degrees of freedom is fractional;
• CHIDIST as a synonymous name.

There is no cumulative switch. This function always evaluates the right-tail probability. The related CHISQ.DIST has a separate Boolean for left-tail cumulative probability or density and must not be substituted without reviewing that difference.

In mathematical terms, the result is P(X ≥ x). The probability of a single exact point is zero for this continuous distribution, so writing P(X > x) gives the same area.

Enter this table in A1:B3:

In D2 enter:

=CHISQ.DIST.RT(B2,B3)

Expected result: 0.04978706836786394, or about 4.97871%. This is just below 5%; the conclusion of an actual test still depends on its prespecified significance rule and valid statistical assumptions.

For the documented legacy spelling, enter in D3:

=CHIDIST(B2,B3)

The documented mathematical expectation is the same right-tail value. This alias mapping comes from Google, not from a different spreadsheet application.

With exactly two degrees of freedom, the chi-square survival probability is exp(−x/2). An independent check is:

=EXP(-B2/2)

Expected result: 0.0497870684. This special-case expression is not valid for every degree count.

For comparison, Google’s CHISQ.DIST reference distinguishes these two calls:

=CHISQ.DIST(6,2,TRUE)
=CHISQ.DIST(6,2,FALSE)

Expected outputs are 0.9502129316 for the left tail and 0.0248935342 for density. Only the first complements the right-tail probability to 1. Subtracting density from 1 would have no useful interpretation as the other tail.

Suppose a prespecified model assigns equal probabilities to three categories. A sample of 60 produces counts 30, 20 and 10, so the expected counts are 20 each. Enter:

In I2 enter =(G2-H2)^2/H2 and fill down through I4. Expected contributions: 5, 0, 5. In I6 enter =SUM(I2:I4), expected 10.

The standard Pearson goodness-of-fit model has two degrees of freedom here: three categories minus one, with no category probabilities estimated from these observations. Then:

=CHISQ.DIST.RT(I6,2)

Expected result: 0.006737946999085467, about 0.67379%. The NIST goodness-of-fit discussion explains the statistic and the degrees-of-freedom adjustment when parameters are fitted.

The p-value describes the right-tail extremeness of the statistic under the null model. It is not the probability that the null model itself is true. Categories must be mutually exclusive, observations appropriately independent, and expected counts adequate for the approximation.

For two degrees of freedom, the area between 2 and 6 is:

=CHISQ.DIST.RT(2,2)-CHISQ.DIST.RT(6,2)

Expected result: 0.3180923728035784. Right-tail probabilities decrease as the cutoff increases, so subtract the tail at the higher cutoff from the tail at the lower cutoff. Reversing this order would give a negative number.

When a desired right tail is very small, calculate it directly. Subtracting a displayed left-tail value rounded to 1 would produce zero even when the true tail is positive.

A degree value of 2.9 is documented to be truncated to 2; with x = 6 its expected result is still 0.0497870684. If the statistical method requires a different degree treatment, do not quietly rely on truncation.

If a formula fails, verify both inputs are numbers, x is positive, and the degree count is within Google’s documented range. The function help does not list exact native error tokens for every bad value; zero, negative and text inputs have not been tested here.

If the answer looks wrong without an error, check whether you supplied raw counts instead of an already calculated statistic, used sample size instead of degrees of freedom, or accidentally read a density as a p-value. Keep unrounded inputs when comparing a result to a threshold close to it.

CHISQ.DIST.RT and CHIDIST are documented in Google’s rolling Sheets service. An original launch date and last functioning numbered release were not established. This worksheet reference is not evidence of identical import/export behavior in other spreadsheet products.

NOT_TESTED_IN_GOOGLE_SHEETS. Google help and relevant mathematical references were inspected on October 17, 2026, including indexed official text where direct retrieval failed. All outputs were calculated independently. No native Sheets test or screenshot is claimed.

Related published guides: COUNTIF for category counts, SUM for contributions and EXP for the two-degree cross-check.