# Google Sheets CHISQ.DIST.RT Function: Syntax, Examples & Tips

- URL: https://betteranalyst.com/google-sheets/chisqdistrt-function
- Author: Better Analyst

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Returns the right-tailed chi-square probability, commonly used as a test p-value.

```
=CHISQ.DIST.RT(x, degrees_freedom)
```

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## Parameters

| Parameter | Required | Description |
| - | - | - |
| **x** | Yes | The value at which to evaluate the distribution. Must be 0 or greater. |
| **degrees\_freedom** | Yes | The number of degrees of freedom. Decimals are truncated; must be at least 1. |

## What Is CHISQ.DIST.RT?

CHISQ.DIST.RT returns the probability that a chi-square random variable is **greater than** a given value. In hypothesis testing, this right-tail area is the **p-value** for a chi-square statistic: the chance of seeing a result at least as extreme as yours if the null hypothesis were true.

The chi-square distribution describes the sum of squares of independent standard normal variables. It only takes non-negative values, is skewed to the right, and has one parameter: **degrees of freedom**. With few degrees of freedom the curve is bunched near zero with a long right tail; as degrees of freedom grow, it shifts right and becomes more symmetric. Its mean equals the degrees of freedom.

In practice you meet it most often in hypothesis tests: goodness-of-fit tests (does observed data match an expected pattern?), tests of independence in contingency tables (are two categories related?), and tests about a variance.

CHISQ.DIST.RT is the modern replacement for [CHIDIST](https://betteranalyst.com/google-sheets/chidist-function). Both take the same two arguments and return the same result.

## How CHISQ.DIST.RT Works

You pass the test statistic **x** and its **degrees of freedom**. The function returns the area under the curve to the right of **x**. Larger statistics produce smaller probabilities. It is equivalent to `1 - CHISQ.DIST(x, degrees_freedom, TRUE)`.

## Basic Examples

### p-value for a statistic

```
=CHISQ.DIST.RT(3.841, 1)
```

Returns about 0.05.

### An exact check

```
=CHISQ.DIST.RT(4, 2)
```

Returns about 0.1353. With 2 degrees of freedom the right tail equals e^(−x/2), so this is e^(−2).

### From a statistic you computed

```
=CHISQ.DIST.RT(F10, (ROWS(B2:D4)-1)*(COLUMNS(B2:D4)-1))
```

If F10 holds the chi-square statistic for a 3×3 contingency table, this computes degrees of freedom as (rows − 1) × (columns − 1) and returns the p-value.

### Make a decision

```
=IF(CHISQ.DIST.RT(F10, 4) < 0.05, "Significant", "Not significant")
```

## Computing the Statistic Yourself

If you have observed counts in B2:B6 and expected counts in C2:C6, the goodness-of-fit statistic is:

```
=SUMPRODUCT((B2:B6-C2:C6)^2/C2:C6)
```

Pass it to CHISQ.DIST.RT with 4 degrees of freedom (categories − 1). If you only need the p-value, [CHISQ.TEST](https://betteranalyst.com/google-sheets/chisqtest-function) skips this step.

## Reference Critical Values

| Degrees of freedom | Critical value at 5% (right tail) | Critical value at 1% |
| - | - | - |
| 1 | 3.841 | 6.635 |
| 2 | 5.991 | 9.210 |
| 3 | 7.815 | 11.345 |
| 4 | 9.488 | 13.277 |
| 5 | 11.070 | 15.086 |

A statistic above the 5% critical value gives a p-value below 0.05.

## Common Use Cases

- **Goodness-of-fit**: do website visits split evenly across weekdays?
- **Independence tests**: is product preference related to age group?
- **Survey analysis**: do response patterns differ between regions?
- **Model checks**: likelihood-ratio statistics compared against chi-square

## Common Errors

- **#NUM!**: **x** is negative or **degrees\_freedom** is below 1.
- **#VALUE!**: An argument is text.
- **Wrong degrees of freedom**: Goodness-of-fit uses categories − 1; independence tests use (rows − 1) × (columns − 1). A wrong value changes the p-value substantially.
- **Small expected counts**: The chi-square approximation is unreliable when expected counts are small (a common rule of thumb is below 5).

## Tips and Best Practices

- Report the statistic, degrees of freedom, and p-value together.
- Use [CHISQ.INV.RT](https://betteranalyst.com/google-sheets/chisqinvrt-function) to get the critical value for a chosen significance level.
- Round p-values with ROUND or display them with a fixed number of decimals.

## Related Functions

- [CHISQ.DIST](https://betteranalyst.com/google-sheets/chisqdist-function): left-tailed probability or density
- [CHISQ.INV.RT](https://betteranalyst.com/google-sheets/chisqinvrt-function): critical value from a right-tail probability
- [CHISQ.TEST](https://betteranalyst.com/google-sheets/chisqtest-function): p-value of a test from observed and expected tables
- [CHIDIST](https://betteranalyst.com/google-sheets/chidist-function): legacy right-tailed probability
- [IF](https://betteranalyst.com/google-sheets/if-function): turn a p-value into a decision

## Example use case

A marketer counts sign-ups by weekday and computes a chi-square statistic of 14.2 against an even split. =CHISQ.DIST.RT(14.2, 6) returns a p-value of about 0.03, suggesting sign-ups really do vary by day.

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