Critical value calculator with confidence level and sample size

Critical Value Formula

t = [x – μ] / [s / √ (n)]
In this equation:

μ is the population mean,

x is the mean of the sample,

s is the standard deviation of the sample, and

n is the size of the sample.


Critical value calculator finds the critical values of t distribution according to the probabilities of two alpha values and the degrees of freedom.

T-Distribution table refers to a type of probability distribution that is theoretical and resembles a normal distribution. The higher the degrees of freedom, the closer that distribution will resemble a standard normal distribution with a mean of 0, and a standard deviation of 1.

It is symmetrical, bell-shaped, and similar to the standard normal curve. The T distribution is also known as the "student t distribution".

T critical value calculator is used to calculate the critical value of t using a degree of freedom and significance level alpha. The table given below works as a critical t value calculator. In this post, we will discuss how to calculate t critical value using the below t distribution table (chart) and the critical value formula as well.

You can use t table calculator to calculate these values conveniently. If you need to perform a t test, use our T-Test calculator. 


How to find the critical value of t?

Example :

Let’s calculate the value of t without using t & z value calculator.

Follow these steps to calculate t value using t value table:

Step 1: Identify the size of the sample. Assume we have six samples.
 n = 6
Step 2: Calculate degrees of freedom. Subtract 1 from the sample size.
 df = n – 1 = 6 – 1 = 5
Step 3: Identify the value of the alpha level. Assume this value as 0.05 for now.
 α = 0.05
Step 4: In the table given below, search the value of df and its corresponding alpha level value. In this case, we will get:
 t = 2.015

Verify the values using our critical value of t calculator.

T Table

A T distribution differs from the normal distribution by its degrees of freedom. A distribution used to test a hypothesis about a population mean when the population standard deviation is not known, the sample size is small, and the normal distribution is assumed for the sample mean. 

Use following t critical value table (t score table) for calculating t value using t table.

α (1 tail) 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
α (2 tail) 0.1 0.05 0.02 0.01 0.005 0.002 0.001
df  
1 6.3138 12.7065 31.8193 63.6551 127.3447 318.4930 636.0450
2 2.9200 4.3026 6.9646 9.9247 14.0887 22.3276 31.5989
3 2.3534 3.1824 4.5407 5.8408 7.4534 10.2145 12.9242
4 2.1319 2.7764 3.7470 4.6041 5.5976 7.1732 8.6103
5 2.0150 2.5706 3.3650 4.0322 4.7734 5.8934 6.8688
6 1.9432 2.4469 3.1426 3.7074 4.3168 5.2076 5.9589
7 1.8946 2.3646 2.9980 3.4995 4.0294 4.7852 5.4079
8 1.8595 2.3060 2.8965 3.3554 3.8325 4.5008 5.0414
9 1.8331 2.2621 2.8214 3.2498 3.6896 4.2969 4.7809
10 1.8124 2.2282 2.7638 3.1693 3.5814 4.1437 4.5869
11 1.7959 2.2010 2.7181 3.1058 3.4966 4.0247 4.4369
12 1.7823 2.1788 2.6810 3.0545 3.4284 3.9296 4.3178
13 1.7709 2.1604 2.6503 3.0123 3.3725 3.8520 4.2208
14 1.7613 2.1448 2.6245 2.9768 3.3257 3.7874 4.1404
15 1.7530 2.1314 2.6025 2.9467 3.2860 3.7328 4.0728
16 1.7459 2.1199 2.5835 2.9208 3.2520 3.6861 4.0150
17 1.7396 2.1098 2.5669 2.8983 3.2224 3.6458 3.9651
18 1.7341 2.1009 2.5524 2.8784 3.1966 3.6105 3.9216
19 1.7291 2.0930 2.5395 2.8609 3.1737 3.5794 3.8834
20 1.7247 2.0860 2.5280 2.8454 3.1534 3.5518 3.8495
21 1.7207 2.0796 2.5176 2.8314 3.1352 3.5272 3.8193
22 1.7172 2.0739 2.5083 2.8188 3.1188 3.5050 3.7921
23 1.7139 2.0686 2.4998 2.8073 3.1040 3.4850 3.7676
24 1.7109 2.0639 2.4922 2.7970 3.0905 3.4668 3.7454
25 1.7081 2.0596 2.4851 2.7874 3.0782 3.4502 3.7251
26 1.7056 2.0555 2.4786 2.7787 3.0669 3.4350 3.7067
27 1.7033 2.0518 2.4727 2.7707 3.0565 3.4211 3.6896
28 1.7011 2.0484 2.4671 2.7633 3.0469 3.4082 3.6739
29 1.6991 2.0452 2.4620 2.7564 3.0380 3.3962 3.6594
30 1.6973 2.0423 2.4572 2.7500 3.0298 3.3852 3.6459
31 1.6955 2.0395 2.4528 2.7440 3.0221 3.3749 3.6334
32 1.6939 2.0369 2.4487 2.7385 3.0150 3.3653 3.6218
33 1.6924 2.0345 2.4448 2.7333 3.0082 3.3563 3.6109
34 1.6909 2.0322 2.4411 2.7284 3.0019 3.3479 3.6008
35 1.6896 2.0301 2.4377 2.7238 2.9961 3.3400 3.5912
36 1.6883 2.0281 2.4345 2.7195 2.9905 3.3326 3.5822
37 1.6871 2.0262 2.4315 2.7154 2.9853 3.3256 3.5737
38 1.6859 2.0244 2.4286 2.7115 2.9803 3.3190 3.5657
39 1.6849 2.0227 2.4258 2.7079 2.9756 3.3128 3.5581
40 1.6839 2.0211 2.4233 2.7045 2.9712 3.3069 3.5510
41 1.6829 2.0196 2.4208 2.7012 2.9670 3.3013 3.5442
42 1.6820 2.0181 2.4185 2.6981 2.9630 3.2959 3.5378
43 1.6811 2.0167 2.4162 2.6951 2.9591 3.2909 3.5316
44 1.6802 2.0154 2.4142 2.6923 2.9555 3.2861 3.5258
45 1.6794 2.0141 2.4121 2.6896 2.9521 3.2815 3.5202
46 1.6787 2.0129 2.4102 2.6870 2.9488 3.2771 3.5149
47 1.6779 2.0117 2.4083 2.6846 2.9456 3.2729 3.5099
48 1.6772 2.0106 2.4066 2.6822 2.9426 3.2689 3.5051
49 1.6766 2.0096 2.4049 2.6800 2.9397 3.2651 3.5004
50 1.6759 2.0086 2.4033 2.6778 2.9370 3.2614 3.4960
51 1.6753 2.0076 2.4017 2.6757 2.9343 3.2579 3.4917
52 1.6747 2.0066 2.4002 2.6737 2.9318 3.2545 3.4877
53 1.6741 2.0057 2.3988 2.6718 2.9293 3.2513 3.4838
54 1.6736 2.0049 2.3974 2.6700 2.9270 3.2482 3.4800
55 1.6730 2.0041 2.3961 2.6682 2.9247 3.2451 3.4764
56 1.6725 2.0032 2.3948 2.6665 2.9225 3.2423 3.4730
57 1.6720 2.0025 2.3936 2.6649 2.9204 3.2394 3.4696
58 1.6715 2.0017 2.3924 2.6633 2.9184 3.2368 3.4663
59 1.6711 2.0010 2.3912 2.6618 2.9164 3.2342 3.4632
60 1.6706 2.0003 2.3901 2.6603 2.9146 3.2317 3.4602
61 1.6702 1.9996 2.3890 2.6589 2.9127 3.2293 3.4573
62 1.6698 1.9990 2.3880 2.6575 2.9110 3.2269 3.4545
63 1.6694 1.9983 2.3870 2.6561 2.9092 3.2247 3.4518
64 1.6690 1.9977 2.3860 2.6549 2.9076 3.2225 3.4491
65 1.6686 1.9971 2.3851 2.6536 2.9060 3.2204 3.4466
66 1.6683 1.9966 2.3842 2.6524 2.9045 3.2184 3.4441
67 1.6679 1.9960 2.3833 2.6512 2.9030 3.2164 3.4417
68 1.6676 1.9955 2.3824 2.6501 2.9015 3.2144 3.4395
69 1.6673 1.9950 2.3816 2.6490 2.9001 3.2126 3.4372
70 1.6669 1.9944 2.3808 2.6479 2.8987 3.2108 3.4350
71 1.6666 1.9939 2.3800 2.6468 2.8974 3.2090 3.4329
72 1.6663 1.9935 2.3793 2.6459 2.8961 3.2073 3.4308
73 1.6660 1.9930 2.3785 2.6449 2.8948 3.2056 3.4288
74 1.6657 1.9925 2.3778 2.6439 2.8936 3.2040 3.4269
75 1.6654 1.9921 2.3771 2.6430 2.8925 3.2025 3.4250
76 1.6652 1.9917 2.3764 2.6421 2.8913 3.2010 3.4232
77 1.6649 1.9913 2.3758 2.6412 2.8902 3.1995 3.4214
78 1.6646 1.9909 2.3751 2.6404 2.8891 3.1980 3.4197
79 1.6644 1.9904 2.3745 2.6395 2.8880 3.1966 3.4180
80 1.6641 1.9901 2.3739 2.6387 2.8870 3.1953 3.4164
81 1.6639 1.9897 2.3733 2.6379 2.8859 3.1939 3.4147
82 1.6636 1.9893 2.3727 2.6371 2.8850 3.1926 3.4132
83 1.6634 1.9889 2.3721 2.6364 2.8840 3.1913 3.4117
84 1.6632 1.9886 2.3716 2.6356 2.8831 3.1901 3.4101
85 1.6630 1.9883 2.3710 2.6349 2.8821 3.1889 3.4087
86 1.6628 1.9879 2.3705 2.6342 2.8813 3.1877 3.4073
87 1.6626 1.9876 2.3700 2.6335 2.8804 3.1866 3.4059
88 1.6623 1.9873 2.3695 2.6328 2.8795 3.1854 3.4046
89 1.6622 1.9870 2.3690 2.6322 2.8787 3.1844 3.4032
90 1.6620 1.9867 2.3685 2.6316 2.8779 3.1833 3.4020
91 1.6618 1.9864 2.3680 2.6309 2.8771 3.1822 3.4006
92 1.6616 1.9861 2.3676 2.6303 2.8763 3.1812 3.3995
93 1.6614 1.9858 2.3671 2.6297 2.8755 3.1802 3.3982
94 1.6612 1.9855 2.3667 2.6292 2.8748 3.1792 3.3970
95 1.6610 1.9852 2.3662 2.6286 2.8741 3.1782 3.3959
96 1.6609 1.9850 2.3658 2.6280 2.8734 3.1773 3.3947
97 1.6607 1.9847 2.3654 2.6275 2.8727 3.1764 3.3936
98 1.6606 1.9845 2.3650 2.6269 2.8720 3.1755 3.3926
99 1.6604 1.9842 2.3646 2.6264 2.8713 3.1746 3.3915
100 1.6602 1.9840 2.3642 2.6259 2.8706 3.1738 3.3905
101 1.6601 1.9837 2.3638 2.6254 2.8700 3.1729 3.3894
102 1.6599 1.9835 2.3635 2.6249 2.8694 3.1720 3.3885
103 1.6598 1.9833 2.3631 2.6244 2.8687 3.1712 3.3875
104 1.6596 1.9830 2.3627 2.6240 2.8682 3.1704 3.3866
105 1.6595 1.9828 2.3624 2.6235 2.8675 3.1697 3.3856
106 1.6593 1.9826 2.3620 2.6230 2.8670 3.1689 3.3847
107 1.6592 1.9824 2.3617 2.6225 2.8664 3.1681 3.3838
108 1.6591 1.9822 2.3614 2.6221 2.8658 3.1674 3.3829
109 1.6589 1.9820 2.3611 2.6217 2.8653 3.1667 3.3820
110 1.6588 1.9818 2.3607 2.6212 2.8647 3.1660 3.3812
111 1.6587 1.9816 2.3604 2.6208 2.8642 3.1653 3.3803
112 1.6586 1.9814 2.3601 2.6204 2.8637 3.1646 3.3795
113 1.6585 1.9812 2.3598 2.6200 2.8632 3.1640 3.3787
114 1.6583 1.9810 2.3595 2.6196 2.8627 3.1633 3.3779
115 1.6582 1.9808 2.3592 2.6192 2.8622 3.1626 3.3771
116 1.6581 1.9806 2.3589 2.6189 2.8617 3.1620 3.3764
117 1.6580 1.9805 2.3586 2.6185 2.8612 3.1614 3.3756
118 1.6579 1.9803 2.3583 2.6181 2.8608 3.1607 3.3749
119 1.6578 1.9801 2.3581 2.6178 2.8603 3.1601 3.3741
120 1.6577 1.9799 2.3578 2.6174 2.8599 3.1595 3.3735
121 1.6575 1.9798 2.3576 2.6171 2.8594 3.1589 3.3727
122 1.6574 1.9796 2.3573 2.6168 2.8590 3.1584 3.3721
123 1.6573 1.9794 2.3571 2.6164 2.8585 3.1578 3.3714
124 1.6572 1.9793 2.3568 2.6161 2.8582 3.1573 3.3707
125 1.6571 1.9791 2.3565 2.6158 2.8577 3.1567 3.3700
126 1.6570 1.9790 2.3563 2.6154 2.8573 3.1562 3.3694
127 1.6570 1.9788 2.3561 2.6151 2.8569 3.1556 3.3688
128 1.6568 1.9787 2.3559 2.6148 2.8565 3.1551 3.3682
129 1.6568 1.9785 2.3556 2.6145 2.8561 3.1546 3.3676
130 1.6567 1.9784 2.3554 2.6142 2.8557 3.1541 3.3669
131 1.6566 1.9782 2.3552 2.6139 2.8554 3.1536 3.3663
132 1.6565 1.9781 2.3549 2.6136 2.8550 3.1531 3.3658
133 1.6564 1.9779 2.3547 2.6133 2.8546 3.1526 3.3652
134 1.6563 1.9778 2.3545 2.6130 2.8542 3.1522 3.3646
135 1.6562 1.9777 2.3543 2.6127 2.8539 3.1517 3.3641
136 1.6561 1.9776 2.3541 2.6125 2.8536 3.1512 3.3635
137 1.6561 1.9774 2.3539 2.6122 2.8532 3.1508 3.3630
138 1.6560 1.9773 2.3537 2.6119 2.8529 3.1503 3.3624
139 1.6559 1.9772 2.3535 2.6117 2.8525 3.1499 3.3619
140 1.6558 1.9771 2.3533 2.6114 2.8522 3.1495 3.3614
141 1.6557 1.9769 2.3531 2.6112 2.8519 3.1491 3.3609
142 1.6557 1.9768 2.3529 2.6109 2.8516 3.1486 3.3604
143 1.6556 1.9767 2.3527 2.6106 2.8512 3.1482 3.3599
144 1.6555 1.9766 2.3525 2.6104 2.8510 3.1478 3.3594
145 1.6554 1.9765 2.3523 2.6102 2.8506 3.1474 3.3589
146 1.6554 1.9764 2.3522 2.6099 2.8503 3.1470 3.3584
147 1.6553 1.9762 2.3520 2.6097 2.8500 3.1466 3.3579
148 1.6552 1.9761 2.3518 2.6094 2.8497 3.1462 3.3575
149 1.6551 1.9760 2.3516 2.6092 2.8494 3.1458 3.3570
150 1.6551 1.9759 2.3515 2.6090 2.8491 3.1455 3.3565
151 1.6550 1.9758 2.3513 2.6088 2.8489 3.1451 3.3561
152 1.6549 1.9757 2.3511 2.6085 2.8486 3.1447 3.3557
153 1.6549 1.9756 2.3510 2.6083 2.8483 3.1443 3.3552
154 1.6548 1.9755 2.3508 2.6081 2.8481 3.1440 3.3548
155 1.6547 1.9754 2.3507 2.6079 2.8478 3.1436 3.3544
156 1.6547 1.9753 2.3505 2.6077 2.8475 3.1433 3.3540
157 1.6546 1.9752 2.3503 2.6075 2.8472 3.1430 3.3536
158 1.6546 1.9751 2.3502 2.6073 2.8470 3.1426 3.3531
159 1.6545 1.9750 2.3500 2.6071 2.8467 3.1423 3.3528
160 1.6544 1.9749 2.3499 2.6069 2.8465 3.1419 3.3523
161 1.6544 1.9748 2.3497 2.6067 2.8463 3.1417 3.3520
162 1.6543 1.9747 2.3496 2.6065 2.8460 3.1413 3.3516
163 1.6543 1.9746 2.3495 2.6063 2.8458 3.1410 3.3512
164 1.6542 1.9745 2.3493 2.6062 2.8455 3.1407 3.3508
165 1.6542 1.9744 2.3492 2.6060 2.8452 3.1403 3.3505
166 1.6541 1.9744 2.3490 2.6058 2.8450 3.1400 3.3501
167 1.6540 1.9743 2.3489 2.6056 2.8448 3.1398 3.3497
168 1.6540 1.9742 2.3487 2.6054 2.8446 3.1394 3.3494
169 1.6539 1.9741 2.3486 2.6052 2.8443 3.1392 3.3490
170 1.6539 1.9740 2.3485 2.6051 2.8441 3.1388 3.3487
171 1.6538 1.9739 2.3484 2.6049 2.8439 3.1386 3.3483
172 1.6537 1.9739 2.3482 2.6047 2.8437 3.1383 3.3480
173 1.6537 1.9738 2.3481 2.6046 2.8435 3.1380 3.3477
174 1.6537 1.9737 2.3480 2.6044 2.8433 3.1377 3.3473
175 1.6536 1.9736 2.3478 2.6042 2.8430 3.1375 3.3470
176 1.6536 1.9735 2.3477 2.6041 2.8429 3.1372 3.3466
177 1.6535 1.9735 2.3476 2.6039 2.8427 3.1369 3.3464
178 1.6535 1.9734 2.3475 2.6037 2.8424 3.1366 3.3460
179 1.6534 1.9733 2.3474 2.6036 2.8423 3.1364 3.3457
180 1.6534 1.9732 2.3472 2.6034 2.8420 3.1361 3.3454
181 1.6533 1.9731 2.3471 2.6033 2.8419 3.1358 3.3451
182 1.6533 1.9731 2.3470 2.6031 2.8416 3.1356 3.3448
183 1.6532 1.9730 2.3469 2.6030 2.8415 3.1354 3.3445
184 1.6532 1.9729 2.3468 2.6028 2.8413 3.1351 3.3442
185 1.6531 1.9729 2.3467 2.6027 2.8411 3.1349 3.3439
186 1.6531 1.9728 2.3466 2.6025 2.8409 3.1346 3.3436
187 1.6531 1.9727 2.3465 2.6024 2.8407 3.1344 3.3433
188 1.6530 1.9727 2.3463 2.6022 2.8406 3.1341 3.3430
189 1.6529 1.9726 2.3463 2.6021 2.8403 3.1339 3.3428
190 1.6529 1.9725 2.3461 2.6019 2.8402 3.1337 3.3425
191 1.6529 1.9725 2.3460 2.6018 2.8400 3.1334 3.3422
192 1.6528 1.9724 2.3459 2.6017 2.8398 3.1332 3.3419
193 1.6528 1.9723 2.3458 2.6015 2.8397 3.1330 3.3417
194 1.6528 1.9723 2.3457 2.6014 2.8395 3.1328 3.3414
195 1.6527 1.9722 2.3456 2.6013 2.8393 3.1326 3.3411
196 1.6527 1.9721 2.3455 2.6012 2.8392 3.1323 3.3409
197 1.6526 1.9721 2.3454 2.6010 2.8390 3.1321 3.3406
198 1.6526 1.9720 2.3453 2.6009 2.8388 3.1319 3.3403
199 1.6525 1.9720 2.3452 2.6008 2.8387 3.1317 3.3401
200 1.6525 1.9719 2.3451 2.6007 2.8385 3.1315 3.3398

How do you find the critical value of the confidence level and sample size?

critical value: The critical t -value for a given confidence level c and sample size n is obtained by computing the quantity tα/2 t α / 2 for a t -distribution with n−1 degrees of freedom.

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

Determine the critical value for a 95% level of confidence (p<0.05). The critical value for a 95% two-tailed test is ± 1.96.

How do you find the critical value of a sample size?

To find the critical value for an f test the steps are as follows:.
Find the alpha level..
Determine the degrees of freedom for both samples by subtracting 1 from each sample size..
Find the corresponding value from a one-tailed or two-tailed f distribution at the given alpha level..
This will give the critical value..

How do you find the critical value of 5% significance level?

The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value. For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645.