Critical Value for Confidence Level Calculator

Common confidence levels
Confidence	α	z*	t* (df 24)
80%	0.2	1.282	1.318
90%	0.1	1.645	1.711
95%	0.05	1.96	2.064
98%	0.02	2.326	2.492
99%	0.01	2.576	2.797
99.9%	0.001	3.291	3.745

90%1.6449

95%1.9600

99%2.5758

What Is Critical Value for Confidence Level?

The critical value for a confidence level is the multiplier that sets the width of a confidence interval. It marks off the middle part of the distribution that holds the confidence level and leaves the rest in the two tails.

Enter the confidence level, such as 95, and the calculator works out α, splits it between the tails, and finds the z score. Add degrees of freedom and it gives the t value too.

A table of common levels, from 80 to 99.9 percent, is shown for reference.

How to Use the Critical Value for Confidence Level Calculator

Enter the confidence level.
Add degrees of freedom if you need the t value.
Use the value in estimate ± critical value × standard error.

Critical Value for Confidence Level Formula

Tail area

\alpha=1-\frac{C}{100},\quad z^*=z_{1-\alpha/2}

Confidence interval

\text{estimate}\pm z^*\times SE

Critical Value for Confidence Level Variables Explained

Symbol	Meaning	Notes
C	Confidence level
α	1 − C/100, the total tail area
z*	Critical value from the normal distribution	Leaves α/2 in each tail
t*	Critical value from the t distribution	Needs degrees of freedom

Critical Value for Confidence Level Worked Example

With the example values loaded in the calculator above, the steps are:

Confidence level 95% means α = 1 − 0.95 = 0.05. Split it in two tails: 0.025 each.
z* is the z score with 0.975 of the area to its left: z* = 1.96.
t* uses the same area with 24 degrees of freedom: t* = 2.0639.
Use the critical value in: estimate ± critical value × standard error.

Result: z critical value (±) = ± 1.96; t critical value (±), df = 24 = ± 2.0639.

Worked example: 95% confidence

Here α = 0.05, so each tail holds 0.025 and the z score with 0.975 to its left is z* = 1.96.

With 24 degrees of freedom the t critical value is 2.0639, a little larger because the t distribution has heavier tails.

z or t?

Use z* when the population standard deviation is known or the sample is large. Use t* when you only have the sample standard deviation.

Where Critical Value for Confidence Level Is Used

Building confidence intervals

Get the multiplier for estimate ± critical value × SE.

Replacing tables

Find z or t for any confidence level, not just table rows.

Comparing levels

See how the critical value grows as confidence rises.

Common Critical Value for Confidence Level Mistakes to Avoid

Higher confidence gives a larger critical value and a wider interval.
Round critical values to at least 3 decimals.

Critical Value for Confidence Level Terms and Definitions

Critical value: The multiplier from a distribution that sets the interval width.
Confidence level: The long-run share of intervals that capture the true value.

Critical Value for Confidence Level FAQs

What is the critical value for 95% confidence?

1.96 for z. For t it depends on the degrees of freedom.

What is the z value for 99% confidence?

2.576.

How do I find the critical value from a confidence level?

Compute α = 1 − confidence, then find the z or t value that leaves α/2 in each tail.

Why does t differ from z?

The t distribution accounts for the extra uncertainty of estimating σ, so it is wider, especially for small samples.