What is the critical value for a 95% confidence level?

Choose Confidence level, enter 95%, choose z and Two-tailed. The normal cutoffs are ±1.959964, corresponding to alpha 0.05 and 0.025 in each tail. With t, also enter the degrees of freedom: the two-tailed cutoff at 95% is ±2.228139 for df 10, ±2.063899 for df 24 and ±1.959988 for df 100,000. The calculator finds distribution cutoffs, not interval endpoints from sample data.

What is the difference between a one-tailed and a two-tailed critical value?

Where alpha goes. Two-tailed splits it, so alpha 0.05 leaves 0.025 at each end and the normal cutoff is 1.959964. One-tailed spends all of it on a single side, so the same alpha leaves 0.05 in one tail and the cutoff is 1.644854. Those are different numbers for the same alpha, which is why the tail count is printed next to the cutoff here and why the table underneath runs both columns. At alpha 0.01 the same pair is 2.575829 and 2.326348.

How do I find the critical value for a t test?

Choose t, enter the degrees of freedom and alpha, then choose Two-tailed, Right tail or Left tail. For df 10 at alpha 0.05, the two-tailed cutoffs are ±2.228139; the right-tail cutoff is 1.812461 and the left-tail cutoff is -1.812461. Fractional degrees of freedom, such as a Welch value you already have, are accepted without rounding. The calculator does not derive degrees of freedom from sample sizes or variances.

How do I use this as a critical value table or rejection-region calculator?

Set the distribution, degrees of freedom, significance level and tails. The table shows one-tail and two-tail cutoffs at common alphas; Use applies a row to the calculator. For a right tail the region is above the upper cutoff, for a left tail below the lower cutoff, and for two tails beyond both cutoffs. The shaded curve illustrates those regions. This page does not compute a test statistic or make a study decision.

What is the chi-square critical value at 0.05?

It depends on the degrees of freedom and, unlike the normal and t, on which end you mean, because the chi-square curve is not symmetric and its two cutoffs are different distances from the middle. On 3 degrees of freedom the upper-tail cutoff at alpha 0.05 is 7.814728. On 10 degrees of freedom, splitting the same alpha across both ends gives 3.246973 below and 20.483177 above, and this page prints both rather than a single plus or minus. For a Kruskal-Wallis asymptotic cutoff, choose Chi-square and use the supplied degrees of freedom and alpha in the right tail. This does not compute an exact rank-test cutoff.

How do I read an F critical value?

F takes two degrees of freedom: df1 from the variance on top of the ratio and df2 from the one underneath, and the order changes the answer. For df1 3 and df2 12 at alpha 0.05 the upper-tail cutoff is 3.490295. The lower cutoff is the reciprocal of the upper one with the two degrees of freedom swapped, which is why printed tables list only the upper end. This page computes either, and both at once when alpha is split. For an ANOVA cutoff, use the numerator and denominator degrees of freedom in F mode; this page computes the cutoff rather than an ANOVA from observations.

Why is the usual two-tailed t cutoff wider than z?

The t distribution has heavier tails. At alpha 0.05 two-tailed, its cutoff is 2.228139 for df 10, 2.063899 for df 24 and 1.959988 for df 100,000. These approach the normal cutoff of 1.959964 as df rises.

What significance levels does this take?

Alpha can be from 1e-10 to 0.9999999999, entered as a decimal such as 0.05 or a percentage such as 5%. Confidence level accepts the same range as a decimal or percentage and uses alpha = 1 - confidence level. Type a percentage sign when you mean a percentage; a bare 5 is rejected rather than treated as 5%. Exactly 0 and 1 are refused.

How are the critical values and graph displayed?

Cutoffs are numerical approximations displayed to six decimal places, or in scientific notation for very small or large values. The curve illustrates the distribution and shades the requested tail regions; its visible window can clip extreme cutoffs. Only the visible portions of the tails are shaded; a tail entirely outside the window has no visible fill. Read the numeric cutoff and labelled tail area for the value, rather than estimating it from the drawing.

Does this tell me whether my result is significant?

No. It reports a number and the geometry behind it: the cutoff, the distribution, the degrees of freedom and how much of the curve lies beyond it. What that means for a particular study depends on the design, the assumptions behind the test and what was decided before the data was collected, none of which this page knows.

Critical Value Calculator

Find critical values for z, t, chi-square or F with the degrees of freedom and tail count kept beside the cutoff. Enter alpha or confidence and select one or two tails. A curve and table of common significance levels label the area in each tail.

Critical value±2.228139Student t · df 10 · two-tailed · alpha 0.05, split 0.025 each side

Distribution

Degrees of freedom

Alpha

Tails

The Student t cutoff for supplied degrees of freedom, including a fractional Welch value.

Cutoff

±2.228139

Distribution

Student t, df 10

Alpha

0.05

Tails

Two, 0.025 each side

Two-tailed: alpha 0.05 is split, 0.025 in each tail. The number above is t such that P(T > t) = 0.025 on 10 degrees of freedom, taken either side of zero.

Normal, two-tailed, alpha 0.05z
±1.959964
t with df 10, two-tailed, alpha 0.05t
±2.228139
Normal, one-tailed, alpha 0.05z
1.644854

The same distribution at the usual alphas

One tail and two tails side by side, for Student t, df 10. Choose Use to apply a row's alpha to the calculator.

Alpha	One tail	Two tails
0.1	1.372184	±1.812461
0.05	1.812461	±2.228139
0.025	2.228139	±2.633767
0.01	2.763769	±3.169273
0.001	4.143700	±4.586894

Accuracy. Numerical cutoffs target twelve significant figures before display rounding. Values are shown to six decimal places or in scientific notation, with the distribution, degrees of freedom and tail area labelled. Alpha must be from 1e-10 to 0.9999999999 and degrees of freedom from 1 to 100,000. These are informational distribution cutoffs.

Common questions

What is the critical value for a 95% confidence level?: Choose Confidence level, enter 95%, choose z and Two-tailed. The normal cutoffs are ±1.959964, corresponding to alpha 0.05 and 0.025 in each tail. With t, also enter the degrees of freedom: the two-tailed cutoff at 95% is ±2.228139 for df 10, ±2.063899 for df 24 and ±1.959988 for df 100,000. The calculator finds distribution cutoffs, not interval endpoints from sample data.
What is the difference between a one-tailed and a two-tailed critical value?: Where alpha goes. Two-tailed splits it, so alpha 0.05 leaves 0.025 at each end and the normal cutoff is 1.959964. One-tailed spends all of it on a single side, so the same alpha leaves 0.05 in one tail and the cutoff is 1.644854. Those are different numbers for the same alpha, which is why the tail count is printed next to the cutoff here and why the table underneath runs both columns. At alpha 0.01 the same pair is 2.575829 and 2.326348.
How do I find the critical value for a t test?: Choose t, enter the degrees of freedom and alpha, then choose Two-tailed, Right tail or Left tail. For df 10 at alpha 0.05, the two-tailed cutoffs are ±2.228139; the right-tail cutoff is 1.812461 and the left-tail cutoff is -1.812461. Fractional degrees of freedom, such as a Welch value you already have, are accepted without rounding. The calculator does not derive degrees of freedom from sample sizes or variances.
How do I use this as a critical value table or rejection-region calculator?: Set the distribution, degrees of freedom, significance level and tails. The table shows one-tail and two-tail cutoffs at common alphas; Use applies a row to the calculator. For a right tail the region is above the upper cutoff, for a left tail below the lower cutoff, and for two tails beyond both cutoffs. The shaded curve illustrates those regions. This page does not compute a test statistic or make a study decision.
What is the chi-square critical value at 0.05?: It depends on the degrees of freedom and, unlike the normal and t, on which end you mean, because the chi-square curve is not symmetric and its two cutoffs are different distances from the middle. On 3 degrees of freedom the upper-tail cutoff at alpha 0.05 is 7.814728. On 10 degrees of freedom, splitting the same alpha across both ends gives 3.246973 below and 20.483177 above, and this page prints both rather than a single plus or minus. For a Kruskal-Wallis asymptotic cutoff, choose Chi-square and use the supplied degrees of freedom and alpha in the right tail. This does not compute an exact rank-test cutoff.
How do I read an F critical value?: F takes two degrees of freedom: df1 from the variance on top of the ratio and df2 from the one underneath, and the order changes the answer. For df1 3 and df2 12 at alpha 0.05 the upper-tail cutoff is 3.490295. The lower cutoff is the reciprocal of the upper one with the two degrees of freedom swapped, which is why printed tables list only the upper end. This page computes either, and both at once when alpha is split. For an ANOVA cutoff, use the numerator and denominator degrees of freedom in F mode; this page computes the cutoff rather than an ANOVA from observations.
Why is the usual two-tailed t cutoff wider than z?: The t distribution has heavier tails. At alpha 0.05 two-tailed, its cutoff is 2.228139 for df 10, 2.063899 for df 24 and 1.959988 for df 100,000. These approach the normal cutoff of 1.959964 as df rises.
What significance levels does this take?: Alpha can be from 1e-10 to 0.9999999999, entered as a decimal such as 0.05 or a percentage such as 5%. Confidence level accepts the same range as a decimal or percentage and uses alpha = 1 - confidence level. Type a percentage sign when you mean a percentage; a bare 5 is rejected rather than treated as 5%. Exactly 0 and 1 are refused.
How are the critical values and graph displayed?: Cutoffs are numerical approximations displayed to six decimal places, or in scientific notation for very small or large values. The curve illustrates the distribution and shades the requested tail regions; its visible window can clip extreme cutoffs. Only the visible portions of the tails are shaded; a tail entirely outside the window has no visible fill. Read the numeric cutoff and labelled tail area for the value, rather than estimating it from the drawing.
Does this tell me whether my result is significant?: No. It reports a number and the geometry behind it: the cutoff, the distribution, the degrees of freedom and how much of the curve lies beyond it. What that means for a particular study depends on the design, the assumptions behind the test and what was decided before the data was collected, none of which this page knows.

Numerical cutoffs target twelve significant figures before display rounding. Values are shown to six decimal places or in scientific notation, with the distribution, degrees of freedom and tail area labelled. Alpha must be from 1e-10 to 0.9999999999 and degrees of freedom from 1 to 100,000. These are informational distribution cutoffs.