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

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

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Returns the value at which the right-tailed chi-square probability equals a given probability, i.e. a critical value.

```
=CHISQ.INV.RT(probability, degrees_freedom)
```

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## Parameters

| Parameter | Required | Description |
| - | - | - |
| **probability** | Yes | The right-tail probability (often the significance level), between 0 and 1. |
| **degrees\_freedom** | Yes | The number of degrees of freedom. Decimals are truncated; must be at least 1. |

## What Is CHISQ.INV.RT?

CHISQ.INV.RT returns the chi-square **critical value** for a right-tail probability. If you plan to reject a null hypothesis at the 5% level, `CHISQ.INV.RT(0.05, df)` tells you how large the test statistic must be. Any statistic above that number is significant.

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.INV.RT replaces the legacy [CHIINV](https://betteranalyst.com/google-sheets/chiinv-function); the two take the same arguments and return the same value.

## How CHISQ.INV.RT Works

It is the inverse of [CHISQ.DIST.RT](https://betteranalyst.com/google-sheets/chisqdist-function). If `CHISQ.DIST.RT(x, df)` returns *p*, then `CHISQ.INV.RT(p, df)` returns *x*. Smaller probabilities give larger critical values, because you are cutting off a thinner slice of the right tail.

It is also linked to the left-tailed inverse: `CHISQ.INV.RT(p, df)` = `CHISQ.INV(1 - p, df)`.

## Basic Examples

### Critical value at 5% with 1 degree of freedom

```
=CHISQ.INV.RT(0.05, 1)
```

Returns about 3.841.

### Critical value for a 3 × 3 table

```
=CHISQ.INV.RT(0.05, 4)
```

Returns about 9.488. A 3 × 3 table has (3 − 1) × (3 − 1) = 4 degrees of freedom.

### Exact check with 2 degrees of freedom

```
=CHISQ.INV.RT(0.05, 2)
```

Returns about 5.991, which is 2 × ln 20.

### Compare a statistic with the critical value

```
=IF(F10 > CHISQ.INV.RT(0.05, F11), "Reject H0", "Fail to reject H0")
```

## Reference 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 |

All of these can be reproduced with CHISQ.INV.RT, so you never need a printed table.

## Common Use Cases

- **Hypothesis testing**: decide significance by comparing a statistic with a critical value
- **Dashboards**: show the threshold a metric must pass, alongside the current statistic
- **Teaching**: build your own chi-square table for any significance levels
- **Process control**: alarm limits for variance-based control charts

## Common Errors

- **#NUM!**: **probability** is outside 0 to 1, or **degrees\_freedom** is below 1.
- **#VALUE!**: An argument is text.
- **Passing the confidence level**: Use the significance level (0.05), not the confidence level (0.95). `CHISQ.INV.RT(0.95, 1)` returns a tiny number near 0.004.
- **Wrong degrees of freedom**: Goodness-of-fit uses categories − 1; independence tests use (rows − 1) × (columns − 1).

## Tips and Best Practices

- Store α in a named cell so all tests in the sheet use the same level.
- Report both the statistic and the critical value; readers can see how close the result was.
- If you just need a p-value, use CHISQ.DIST.RT or [CHISQ.TEST](https://betteranalyst.com/google-sheets/chisqtest-function) instead.

## Related Functions

- [CHISQ.DIST.RT](https://betteranalyst.com/google-sheets/chisqdistrt-function): right-tailed probability (p-value)
- [CHISQ.INV](https://betteranalyst.com/google-sheets/chisqinv-function): inverse of the left-tailed distribution
- [CHIINV](https://betteranalyst.com/google-sheets/chiinv-function): legacy inverse right-tailed function
- [CHISQ.TEST](https://betteranalyst.com/google-sheets/chisqtest-function): p-value of a test from observed and expected tables
- [IF](https://betteranalyst.com/google-sheets/if-function): turn a p-value into a decision

## Example use case

A researcher testing whether customer segment and preferred plan are related has a 4 × 3 table, giving 6 degrees of freedom. =CHISQ.INV.RT(0.05, 6) returns 12.592, so any test statistic above that value is significant at the 5% level.

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