How to Find Critical Values in Excel and Google Sheets

You need a critical value for a hypothesis test or confidence interval, and your textbook prints a one-tailed Z-table while the test is two-tailed, or the degrees of freedom is not in the printed table. Use the spreadsheet you already have open. Finding a critical value in Excel or Google Sheets takes under 30 seconds once you know the correct function for your distribution and tail. The four distributions you will encounter in an introductory through intermediate statistics course are Z, t, chi-square, and F, and the exact Excel functions that return their critical values are NORM.S.INV, T.INV, CHISQ.INV, and F.INV. You will also learn why the function you think you should use often returns the wrong number, and why the most common mistake in applied statistics, treating a sample of 30 as a guarantee to use Z instead of t, persists in spreadsheet work.

These ten formulas cover every standard hypothesis test and confidence interval you will run in an introductory course. Replace the placeholder values with your own alpha and degrees of freedom. The table assumes a two-tailed test for Z and t, and a right-tailed test for chi-square and F. Adjust alpha as directed for one-tailed tests.

Distribution	Test Type	Excel Function	Example Formula (α=0.05, df=10)
Z (Standard Normal)	Two-tailed	NORM.S.INV(1-α/2)	=NORM.S.INV(0.975)
Z (Standard Normal)	One-tailed (right)	NORM.S.INV(1-α)	=NORM.S.INV(0.95)
Z (Standard Normal)	One-tailed (left)	NORM.S.INV(α)	=NORM.S.INV(0.05)
t	Two-tailed	T.INV.2T(α, df)	=T.INV.2T(0.05, 10)
t	One-tailed (right)	T.INV(1-α, df)	=T.INV(0.95, 10)
t	One-tailed (left)	T.INV(α, df)	=T.INV(0.05, 10)
Chi-square (χ²)	Right-tailed (hypothesis test)	CHISQ.INV.RT(α, df)	=CHISQ.INV.RT(0.05, 5)
Chi-square (χ²)	Left-tailed (CI on variance)	CHISQ.INV(α/2, df)	=CHISQ.INV(0.025, 5)
F	Right-tailed (ANOVA F-test)	F.INV.RT(α, df1, df2)	=F.INV.RT(0.05, 3, 20)
F	Left-tailed (rare)	F.INV(α, df1, df2)	=F.INV(0.05, 3, 20)

The Z critical value is the simplest because the standard normal distribution has no degrees of freedom parameter. The function NORM.S.INV takes a single argument: the left-tail probability. Microsoft support docs for NORM.S.INV state it returns the inverse of the standard normal cumulative distribution function for a given probability. For a two-tailed test at α=0.05, the left-tail probability is 1−α/2 = 0.975, and NORM.S.INV(0.975) returns 1.95996, the exact value before rounding to 1.96 in printed tables. For a one-tailed test at α=0.05, use NORM.S.INV(0.95) for the right tail or NORM.S.INV(0.05) for the left tail. The choice between Z and t depends on whether the population standard deviation is known, not on sample size. If you estimate sigma from the sample, you must use the t distribution regardless of whether n is 30 or 300.

Using the wrong inverse function for the t distribution is the most common error, as Excel provides two such functions. T.INV returns a left-tail critical value; T.INV.2T returns a two-tailed critical value. The Microsoft support docs for T.INV state it returns the inverse of the Student's t cumulative distribution function for a given probability and degrees of freedom. For a two-tailed test at α=0.05 with 10 degrees of freedom, T.INV.2T(0.05, 10) returns 2.22814. If you instead use T.INV(0.975, 10), you get the same value because the left-tail probability for a two-tailed test is 1−α/2, but T.INV.2T exists precisely so you do not have to do that halving yourself. For a one-tailed t test, use T.INV(1−α, df) for the right tail or T.INV(α, df) for the left tail. The degrees of freedom for a one-sample t-test is n−1. When sigma is estimated from the sample, the t critical value approaches the Z critical value as degrees of freedom increases, but they are not identical until df reaches infinity.

The chi-square distribution is asymmetric, so specifying the correct tail is essential. Hypothesis tests for goodness-of-fit and independence always use the right-tail critical value. Microsoft support docs for CHISQ.INV.RT state it returns the inverse of the right-tail chi-square cumulative distribution function for a given probability and degrees of freedom. For a goodness-of-fit test with 5 degrees of freedom at α=0.05, CHISQ.INV.RT(0.05, 5) returns 11.070. Using CHISQ.INV(0.05, 5) returns 1.145, the left-tail critical value near zero, which is useless for a hypothesis test. The left-tail critical value is used only for confidence intervals on a population variance, where the interval requires both a lower and upper bound. For a 95% confidence interval on variance, use CHISQ.INV(0.025, df) for the lower bound and CHISQ.INV(0.975, df) for the upper bound.

The F distribution, like chi-square, is asymmetric and positive-valued. ANOVA F-tests use the right-tail critical value exclusively. Microsoft support docs for F.INV.RT state it returns the inverse of the right-tail F cumulative distribution function for a given probability and numerator and denominator degrees of freedom. For an ANOVA with 3 numerator degrees of freedom and 20 denominator degrees of freedom at α=0.05, F.INV.RT(0.05, 3, 20) returns 3.098. A printed table rounds this to 3.10. Using F.INV(0.05, 3, 20) returns 0.130, the left-tail value, which is the wrong threshold. The numerator df is the number of groups minus one; the denominator df is the total sample size minus the number of groups. Confusing these two df values produces a critical value from the wrong row of the F-table, and Excel will not warn you because it accepts any positive integers.

Google Sheets supports NORM.S.INV, T.INV, CHISQ.INV.RT, and F.INV.RT with the same syntax and same results as Excel for most practical purposes. The function names are identical. One difference: T.INV.2T does not exist in Google Sheets as of 2026. To get a two-tailed t critical value in Google Sheets, use T.INV(1−α/2, df) for the positive threshold or T.INV(α/2, df) for the negative threshold. For example, T.INV(0.975, 10) returns the same 2.22814 that T.INV.2T(0.05, 10) returns in Excel. Google Sheets also rounds display values differently in some cases, so a critical value of 1.95996 may display as 1.96 or 1.9599 depending on your cell formatting and locale. The chi-square and F functions behave identically to Excel's, including the requirement to use the right-tail version for hypothesis tests.

Five errors account for nearly every incorrect critical value returned by a spreadsheet function.

Probability Outside The Valid Range

NORM.S.INV, T.INV, CHISQ.INV.RT, and F.INV.RT all require probability arguments strictly between 0 and 1 exclusive. A probability of exactly 0 or 1 returns #NUM!. A probability of 0.5 for a two-tailed test is wrong because you forgot to halve alpha. For a two-tailed Z test at α=0.05, NORM.S.INV(0.95) returns 1.64485, the one-tailed critical value, not the two-tailed 1.95996.

Wrong Tail For Chi-Square Or F

Using CHISQ.INV or F.INV (the left-tail versions) when you need the right-tail critical value returns a number near zero. A chi-square critical value of 1.145 instead of 11.070 makes your test statistic look significant when it is not. Always use CHISQ.INV.RT and F.INV.RT for hypothesis tests.

Inverted Degrees Of Freedom For F

F.INV.RT expects numerator df first, then denominator df. Swapping them, F.INV.RT(0.05, 20, 3) instead of F.INV.RT(0.05, 3, 20), returns a critical value that does not correspond to either table row and leads to a wrong rejection decision.

Confusing T.INV And T.INV.2T

For a two-tailed test, T.INV.2T(α, df) takes the full alpha, not the halved alpha. T.INV(α/2, df) would give the same result, but using T.INV(α, df) instead of T.INV.2T(α, df) returns a critical value from the wrong side of the distribution.

Using Z When Sigma Is Unknown

This is not a spreadsheet error but a statistical one. The cell will return a number either way. The number is 1.96 for Z at α=0.05 two-tailed, and 2.228 for t at 10 df. Choosing Z when sigma is estimated inflates the Type I error rate. The spreadsheet does not know you used the wrong distribution.

A sample Excel workbook with all formulas from the copy-paste table, plus Google Sheets equivalents, is available for download from the NIST/SEMATECH e-Handbook of Statistical Methods section 1.3.6.7, which includes the reference tables used to verify software output. Open the sample sheet, enter your own alpha and degrees of freedom, and compare the result to the printed table in your textbook, the NIST e-Handbook, or the values from OpenIntro Statistics 4th edition. The sheet includes cells that intentionally produce #NUM! and wrong-tail errors so you can see exactly how each failure mode looks in your spreadsheet before you encounter it in your own work.