Engineering Tables/Student's T-Distribution

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Table of Critical Values, t_α,ν, in a Student T-Distribution with ν degrees of freedom and a confidence limit p where α=1–p.

ν

Confidence Limits (top) and α (bottom) for a One-Tailed Test.

60%

75%

80%

85%

90%

95%

97.5%

98%

99%

99.5%

99.75%

99.9%

99.95%

0.4

0.25

0.2

0.15

0.1

0.05

0.025

0.02

0.01

0.005

0.0025

0.001

0.0005

1

0.32492

1.00000

1.37638

1.96261

3.07768

6.31375

12.70620

15.89454

31.82052

63.65674

127.32134

318.30884

636.61925

2

0.28868

0.81650

1.06066

1.38621

1.88562

2.91999

4.30265

4.84873

6.96456

9.92484

14.08905

22.32712

31.59905

3

0.27667

0.76489

0.97847

1.24978

1.63774

2.35336

3.18245

3.48191

4.54070

5.84091

7.45332

10.21453

12.92398

4

0.27072

0.74070

0.94096

1.18957

1.53321

2.13185

2.77645

2.99853

3.74695

4.60409

5.59757

7.17318

8.61030

5

0.26718

0.72669

0.91954

1.15577

1.47588

2.01505

2.57058

2.75651

3.36493

4.03214

4.77334

5.89343

6.86883

6

0.26483

0.71756

0.90570

1.13416

1.43976

1.94318

2.44691

2.61224

3.14267

3.70743

4.31683

5.20763

5.95882

7

0.26317

0.71114

0.89603

1.11916

1.41492

1.89458

2.36462

2.51675

2.99795

3.49948

4.02934

4.78529

5.40788

8

0.26192

0.70639

0.88889

1.10815

1.39682

1.85955

2.30600

2.44898

2.89646

3.35539

3.83252

4.50079

5.04131

9

0.26096

0.70272

0.88340

1.09972

1.38303

1.83311

2.26216

2.39844

2.82144

3.24984

3.68966

4.29681

4.78091

10

0.26018

0.69981

0.87906

1.09306

1.37218

1.81246

2.22814

2.35931

2.76377

3.16927

3.58141

4.14370

4.58689

11

0.25956

0.69745

0.87553

1.08767

1.36343

1.79588

2.20099

2.32814

2.71808

3.10581

3.49661

4.02470

4.43698

12

0.25903

0.69548

0.87261

1.08321

1.35622

1.78229

2.17881

2.30272

2.68100

3.05454

3.42844

3.92963

4.31779

13

0.25859

0.69383

0.87015

1.07947

1.35017

1.77093

2.16037

2.28160

2.65031

3.01228

3.37247

3.85198

4.22083

14

0.25821

0.69242

0.86805

1.07628

1.34503

1.76131

2.14479

2.26378

2.62449

2.97684

3.32570

3.78739

4.14045

15

0.25789

0.69120

0.86624

1.07353

1.34061

1.75305

2.13145

2.24854

2.60248

2.94671

3.28604

3.73283

4.07277

16

0.25760

0.69013

0.86467

1.07114

1.33676

1.74588

2.11991

2.23536

2.58349

2.92078

3.25199

3.68615

4.01500

17

0.25735

0.68920

0.86328

1.06903

1.33338

1.73961

2.10982

2.22385

2.56693

2.89823

3.22245

3.64577

3.96513

18

0.25712

0.68836

0.86205

1.06717

1.33039

1.73406

2.10092

2.21370

2.55238

2.87844

3.19657

3.61048

3.92165

19

0.25692

0.68762

0.86095

1.06551

1.32773

1.72913

2.09302

2.20470

2.53948

2.86093

3.17372

3.57940

3.88341

20

0.25674

0.68695

0.85996

1.06402

1.32534

1.72472

2.08596

2.19666

2.52798

2.84534

3.15340

3.55181

3.84952

21

0.25658

0.68635

0.85907

1.06267

1.32319

1.72074

2.07961

2.18943

2.51765

2.83136

3.13521

3.52715

3.81928

22

0.25643

0.68581

0.85827

1.06145

1.32124

1.71714

2.07387

2.18289

2.50832

2.81876

3.11882

3.50499

3.79213

23

0.25630

0.68531

0.85753

1.06034

1.31946

1.71387

2.06866

2.17696

2.49987

2.80734

3.10400

3.48496

3.76763

24

0.25617

0.68485

0.85686

1.05932

1.31784

1.71088

2.06390

2.17154

2.49216

2.79694

3.09051

3.46678

3.74540

25

0.25606

0.68443

0.85624

1.05838

1.31635

1.70814

2.05954

2.16659

2.48511

2.78744

3.07820

3.45019

3.72514

26

0.25595

0.68404

0.85567

1.05752

1.31497

1.70562

2.05553

2.16203

2.47863

2.77871

3.06691

3.43500

3.70661

27

0.25586

0.68368

0.85514

1.05673

1.31370

1.70329

2.05183

2.15782

2.47266

2.77068

3.05652

3.42103

3.68959

28

0.25577

0.68335

0.85465

1.05599

1.31253

1.70113

2.04841

2.15393

2.46714

2.76326

3.04693

3.40816

3.67391

29

0.25568

0.68304

0.85419

1.05530

1.31143

1.69913

2.04523

2.15033

2.46202

2.75639

3.03805

3.39624

3.65941

30

0.25561

0.68276

0.85377

1.05466

1.31042

1.69726

2.04227

2.14697

2.45726

2.75000

3.02980

3.38518

3.64596

40

0.25504

0.68067

0.85070

1.05005

1.30308

1.68385

2.02108

2.12291

2.42326

2.70446

2.97117

3.30688

3.55097

50

0.25470

0.67943

0.84887

1.04729

1.29871

1.67591

2.00856

2.10872

2.40327

2.67779

2.93696

3.26141

3.49601

60

0.25447

0.67860

0.84765

1.04547

1.29582

1.67065

2.00030

2.09936

2.39012

2.66028

2.91455

3.23171

3.46020

70

0.25431

0.67801

0.84679

1.04417

1.29376

1.66691

1.99444

2.09273

2.38081

2.64790

2.89873

3.21079

3.43501

80

0.25419

0.67757

0.84614

1.04320

1.29222

1.66412

1.99006

2.08778

2.37387

2.63869

2.88697

3.19526

3.41634

90

0.25410

0.67723

0.84563

1.04244

1.29103

1.66196

1.98667

2.08394

2.36850

2.63157

2.87788

3.18327

3.40194

100

0.25402

0.67695

0.84523

1.04184

1.29007

1.66023

1.98397

2.08088

2.36422

2.62589

2.87065

3.17374

3.39049

500

0.25348

0.67498

0.84234

1.03751

1.28325

1.64791

1.96472

2.05912

2.33383

2.58570

2.81955

3.10661

3.31009

1000

0.25341

0.67474

0.84198

1.03697

1.28240

1.64638

1.96234

2.05643

2.33008

2.58075

2.81328

3.09840

3.30028

∞

0.25335

0.67449

0.84162

1.03643

1.28155

1.64485

1.95996

2.05375

2.32635

2.57583

2.80703

3.09023

3.29053

Explanatory Notes

For a Two-Tailed Test, use the α here that corresponds to half the two-tailed α.
- For example if a two-tailed confidence limit of 90% is desired (α=0.1), use a one-tailed α from this table of 0.05
In the limit ν=∞, this distribution is equivalent to a normal distribution X~N(0,1)

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