F-Distribution Critical Values Table

This table contains the upper critical values of the F distribution. It is used for one-sided F tests at the α = 0.001, 0.01, 0.05, and 0.10. It is important to note that when referring to the F-distribution, the numerator degrees of freedom are always presented first, as reversing the order of degrees of freedom alters the distribution. For instance, F(12,10) is not the same as F(10,12). In the provided set of F tables, the rows correspond to the degrees of freedom for the numerator, while the columns represent the degrees of freedom for the denominator. The name of each table indicates the right tail area associated with it. For example, to find the critical value for an F distribution with degrees of freedom 12 and 10 at a significance level of 0.05, you would locate the 12 row (numerator) and the 10 column (denominator) in the appropriate table. The value at the intersection would be F(0.05, 12, 10) = 2.98.

Significance Level (α):

0.005

df1:1

2

3

4

5

6

7

8

9

10

12

15

20

24

30

40

60

120

(∞)

df2:1

16210.723

19999.500

21614.741

22499.583

23055.798

23437.111

23714.566

23925.406

24091.004

24224.487

24426.366

24630.205

24835.971

24939.565

25043.628

25148.153

25253.137

25358.573

25465.000

2

198.501

199.000

199.166

199.250

199.300

199.333

199.357

199.375

199.388

199.400

199.416

199.433

199.450

199.458

199.466

199.475

199.483

199.491

199.500

3

55.552

49.799

47.467

46.195

45.392

44.839

44.434

44.126

43.882

43.686

43.387

43.085

42.778

42.622

42.466

42.308

42.149

41.989

41.830

4

31.333

26.284

24.259

23.154

22.456

21.975

21.622

21.352

21.139

20.967

20.705

20.438

20.167

20.030

19.892

19.752

19.611

19.468

19.320

5

22.785

18.314

16.530

15.556

14.940

14.513

14.200

13.961

13.772

13.618

13.384

13.146

12.903

12.780

12.656

12.530

12.402

12.274

12.140

6

18.635

14.544

12.917

12.027

11.464

11.073

10.786

10.566

10.392

10.250

10.034

9.814

9.589

9.474

9.358

9.241

9.122

9.002

8.880

7

16.236

12.404

10.882

10.050

9.522

9.155

8.885

8.678

8.514

8.380

8.176

7.968

7.754

7.645

7.535

7.422

7.309

7.193

7.080

8

14.688

11.042

9.597

8.805

8.302

7.952

7.694

7.496

7.339

7.211

7.015

6.814

6.608

6.503

6.396

6.287

6.177

6.065

5.950

9

13.614

10.107

8.717

7.956

7.471

7.134

6.885

6.693

6.541

6.417

6.227

6.032

5.832

5.729

5.625

5.519

5.410

5.300

5.190

10

12.826

9.427

8.081

7.343

6.872

6.545

6.303

6.116

5.968

5.847

5.661

5.471

5.274

5.173

5.071

4.966

4.859

4.750

4.640

11

12.226

8.912

7.600

6.881

6.422

6.102

5.865

5.682

5.537

5.418

5.236

5.049

4.855

4.756

4.654

4.551

4.445

4.337

4.230

12

11.754

8.510

7.226

6.521

6.071

5.757

5.524

5.345

5.202

5.085

4.906

4.721

4.530

4.431

4.331

4.228

4.123

4.015

3.900

13

11.373

8.187

6.926

6.234

5.791

5.482

5.253

5.076

4.935

4.820

4.643

4.460

4.270

4.173

4.073

3.970

3.865

3.758

3.650

14

11.060

7.922

6.680

5.998

5.562

5.257

5.031

4.857

4.717

4.603

4.428

4.247

4.059

3.961

3.862

3.760

3.655

3.547

3.440

15

10.798

7.701

6.476

5.803

5.372

5.071

4.847

4.674

4.536

4.423

4.250

4.070

3.883

3.786

3.687

3.585

3.480

3.372

3.260

16

10.575

7.514

6.303

5.638

5.212

4.913

4.692

4.521

4.384

4.272

4.099

3.921

3.734

3.638

3.539

3.437

3.332

3.224

3.110

17

10.384

7.354

6.156

5.497

5.075

4.779

4.559

4.389

4.253

4.142

3.971

3.793

3.607

3.511

3.412

3.311

3.206

3.097

2.980

18

10.218

7.215

6.028

5.375

4.956

4.663

4.445

4.276

4.141

4.030

3.860

3.683

3.498

3.402

3.303

3.201

3.096

2.987

2.870

19

10.072

7.093

5.916

5.268

4.853

4.561

4.345

4.177

4.043

3.933

3.763

3.587

3.402

3.306

3.208

3.106

3.000

2.891

2.780

20

9.944

6.987

5.818

5.174

4.762

4.472

4.257

4.090

3.956

3.847

3.678

3.502

3.318

3.222

3.123

3.022

2.916

2.806

2.690

21

9.829

6.891

5.730

5.091

4.681

4.393

4.179

4.013

3.880

3.771

3.602

3.427

3.243

3.147

3.049

2.947

2.841

2.730

2.610

22

9.727

6.806

5.652

5.017

4.609

4.322

4.109

3.944

3.812

3.703

3.535

3.360

3.176

3.081

2.982

2.880

2.774

2.663

2.550

23

9.635

6.730

5.582

4.950

4.544

4.259

4.047

3.882

3.750

3.642

3.474

3.300

3.116

3.021

2.922

2.820

2.713

2.602

2.480

24

9.551

6.661

5.519

4.890

4.486

4.202

3.990

3.826

3.695

3.587

3.420

3.246

3.062

2.967

2.868

2.765

2.659

2.546

2.430

25

9.475

6.598

5.462

4.835

4.433

4.150

3.939

3.776

3.645

3.537

3.370

3.196

3.013

2.918

2.819

2.716

2.609

2.496

2.380

26

9.406

6.541

5.409

4.785

4.384

4.103

3.893

3.730

3.599

3.492

3.325

3.151

2.969

2.873

2.774

2.671

2.563

2.450

2.330

27

9.342

6.489

5.361

4.740

4.340

4.059

3.850

3.688

3.557

3.450

3.284

3.110

2.928

2.832

2.733

2.630

2.522

2.408

2.250

28

9.284

6.440

5.317

4.698

4.300

4.020

3.811

3.649

3.519

3.412

3.246

3.073

2.890

2.794

2.695

2.592

2.483

2.369

2.290

29

9.230

6.396

5.276

4.659

4.262

3.983

3.775

3.613

3.483

3.377

3.211

3.038

2.855

2.759

2.660

2.557

2.448

2.333

2.240

30

9.180

6.355

5.239

4.623

4.228

3.949

3.742

3.580

3.450

3.344

3.179

3.006

2.823

2.727

2.628

2.524

2.415

2.300

2.180

40

8.828

6.066

4.976

4.374

3.986

3.713

3.509

3.350

3.222

3.117

2.953

2.781

2.598

2.502

2.401

2.296

2.184

2.064

1.930

60

8.495

5.795

4.729

4.140

3.760

3.492

3.291

3.134

3.008

2.904

2.742

2.571

2.387

2.290

2.187

2.079

1.962

1.834

1.690

120

8.179

5.539

4.497

3.921

3.548

3.285

3.087

2.933

2.808

2.705

2.544

2.373

2.188

2.089

1.984

1.871

1.747

1.605

1.430

Infinity

7.880

5.300

4.280

3.720

3.350

3.090

2.900

2.740

2.620

2.520

2.360

2.190

2.000

1.900

1.790

1.670

1.530

1.360

1.000