Humidity Conversion   

By R.L. Snyder                                                (Revised March 24, 2005)

 

This Web page provides the equations used to make humidity conversions and tables of saturation vapor pressure. For a pdf file of this document, click on HumCon.pdf.  The saturation vapor pressure tables in an MS Excel spreadsheet can be downloaded by clicking on es.xls.

 

 

Barometric Pressure

 

Barometric pressure (P) in kPa from elevation (EL) in m above sea level was reported by Jensen, Burman and Allen, 1990 as

                                                                       (1)

 

Latent heat of vaporization

 

Latent heat of vaporization (l) in kJ kg-1 from air temperature (T) in oC

 

                                                                                              (2)

 

Saturation Vapor Pressure

 

Saturation vapor pressure over water is the vapor pressure of the air when the number of water molecules condensing equals the number evaporating from a flat surface of water with both the air and water at some temperature (T). An equation for the saturation vapor pressure (es) over water at temperature (T) in oC was given by Tetens (1930) as

                                                                                (3)

 

Values of es for T = -14.9 to 0 and for T = 0 to 49.9 are given in Tables 1 and 2.

 

When the number of water molecules sublimating equals the number depositing onto a flat surface of ice with both the air and ice at some temperature (T), the saturation vapor pressure (es) in kPa over ice at temperature (T) in oC was given by Tetens (1930) as

                                                                                  (4)

 

Values of es for T = 0 to -14.9 are given in Table 3.

 

Dew point and Ice point Temperature

 

Dew-point temperature (Td) in oC from air temperature (T) in oC and relative humidity (RH) in %

                                                                  (5)

 

 

Ice-point temperature (Ti) in oC from air temperature (T) in oC and relative humidity (RH) in %

                                                                    (6)

 

 

 

Note that the actual vapor pressure (e) is equal to the saturation vapor pressure (ed) at the dew-point temperature (Td) and, for subzero temperatures, e equals the saturation vapor pressure (ei) at the ice point temperature (Ti).

 

Dew-point temperature (Td) in oC from vapor pressure (e = ed) in kPa over water is calculated in two steps

                                                                                                (7)

                                                                                              (8)

 

Ice-point temperature (Ti) in oC from vapour pressure (e = ei) in kPa over ice is calculated in two steps

                                                                                                (9)

                                                                                              (10)

 

 

Psychrometric Constant

 

Psychrometric constant (g) in kPa oC-1 for liquid water as a function of barometric pressure (P) in kPa and wet-bulb temperature (Tw) in oC was given by Fritschen and Gay (1979) as

                                                                            (11)

 

Psychrometric constant (g) in kPa oC-1 for ice as a function of barometric pressure (P) in kPa and frost-bulb temperature (Tf) in oC is

                                                                           (12)

 

Vapor Pressure

 

Vapor pressure (e = ed) in kPa at the dew point temperature (Td) in oC

                                                                              (13)

 

Vapor pressure (e = ei) in kPa at the subzero ice point temperature (Ti) in oC

                                                                                (14)

 

Vapor pressure (e) in kPa from dry (T) and wet-bulb (Tw) temperature in °C and barometric pressure (P) and kPa

                                 (15)

 

where ew in kPa is the saturation vapor pressure at the wet-bulb temperature (Tw) in oC. It is calculated by substituting Tw for T in Equation 4.

 

Vapor pressure (e) in kPa from dry (T) and frost-bulb (Tf) temperature in °C and barometric pressure (P) in kPa

                            (16)

 

where ef is the saturation vapor pressure at the frost-bulb temperature. It is calculated by substituting Tf in oC for T in Equation 4.

 

Slope of Saturation Vapor Pressure

 

Slope of Saturation Vapor Pressure (D) in kPa oC-1 over liquid water with saturation vapor pressure (es) in kPa at temperature T in oC

                                                                                                (17)

 

 

Equivalent Temperature

 

Equivalent temperature (Te) in oC from temperature T in oC, vapor pressure e in kPa and the psychrometric constant g in kPa oC-1

                                                                                                        (18)

 

 

Absolute Humidity

 

Absolute humidity (c) in g m-3 from vapor pressure (e) in kPa and temperature (T) in oC

                                                                                                (19)

 

 

 

 

 

 

 

Table 1.  Saturation vapor pressure (es) in kPa over a flat surface of liquid water calculated using Tetens’ formula (Equation 4) for temperature between 0.0 °C and -14.9 °C.

Temperature (°C)

 

-0.0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.8

-0.9

-14

0.207

0.205

0.203

0.202

0.200

0.199

0.197

0.195

0.194

0.192

-13

0.224

0.223

0.221

0.219

0.217

0.216

0.214

0.212

0.210

0.209

-12

0.243

0.241

0.240

0.238

0.236

0.234

0.232

0.230

0.228

0.226

-11

0.264

0.262

0.260

0.258

0.256

0.253

0.251

0.249

0.247

0.245

-10

0.286

0.283

0.281

0.279

0.277

0.275

0.272

0.270

0.268

0.266

-9

0.309

0.307

0.304

0.302

0.300

0.297

0.295

0.293

0.290

0.288

-8

0.334

0.332

0.329

0.327

0.324

0.322

0.319

0.317

0.314

0.312

-7

0.361

0.359

0.356

0.353

0.350

0.348

0.345

0.342

0.340

0.337

-6

0.390

0.387

0.384

0.381

0.378

0.376

0.373

0.370

0.367

0.364

-5

0.421

0.418

0.415

0.412

0.409

0.405

0.402

0.399

0.396

0.393

-4

0.454

0.451

0.447

0.444

0.441

0.437

0.434

0.431

0.428

0.424

-3

0.490

0.486

0.482

0.479

0.475

0.472

0.468

0.465

0.461

0.458

-2

0.527

0.524

0.520

0.516

0.512

0.508

0.504

0.501

0.497

0.493

-1

0.568

0.564

0.559

0.555

0.551

0.547

0.543

0.539

0.535

0.531

-0

0.611

0.606

0.602

0.598

0.593

0.589

0.585

0.580

0.576

0.572

 


Table 2.  Saturation vapor pressure (kPa) over a flat surface of liquid water calculated using Tetens’ formula (Equation 4) for temperature between 0 °C and 49.9 °C.

Temperature (°C)

 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

0.611

0.615

0.620

0.624

0.629

0.633

0.638

0.643

0.647

0.652

1

0.657

0.661

0.666

0.671

0.676

0.681

0.686

0.691

0.696

0.701

2

0.706

0.711

0.716

0.721

0.726

0.731

0.737

0.742

0.747

0.752

3

0.758

0.763

0.769

0.774

0.780

0.785

0.791

0.796

0.802

0.808

4

0.813

0.819

0.825

0.831

0.836

0.842

0.848

0.854

0.860

0.866

5

0.872

0.878

0.885

0.891

0.897

0.903

0.910

0.916

0.922

0.929

6

0.935

0.942

0.948

0.955

0.961

0.968

0.975

0.981

0.988

0.995

7

1.002

1.009

1.016

1.023

1.030

1.037

1.044

1.051

1.058

1.065

8

1.073

1.080

1.087

1.095

1.102

1.110

1.117

1.125

1.133

1.140

9

1.148

1.156

1.164

1.172

1.179

1.187

1.195

1.203

1.212

1.220

10

1.228

1.236

1.245

1.253

1.261

1.270

1.278

1.287

1.295

1.304

11

1.313

1.321

1.330

1.339

1.348

1.357

1.366

1.375

1.384

1.393

12

1.403

1.412

1.421

1.431

1.440

1.449

1.459

1.469

1.478

1.488

13

1.498

1.508

1.517

1.527

1.537

1.547

1.558

1.568

1.578

1.588

14

1.599

1.609

1.619

1.630

1.641

1.651

1.662

1.673

1.684

1.694

15

1.705

1.716

1.727

1.739

1.750

1.761

1.772

1.784

1.795

1.807

16

1.818

1.830

1.842

1.853

1.865

1.877

1.889

1.901

1.913

1.925

17

1.938

1.950

1.962

1.975

1.987

2.000

2.013

2.025

2.038

2.051

18

2.064

2.077

2.090

2.103

2.116

2.130

2.143

2.157

2.170

2.184

19

2.197

2.211

2.225

2.239

2.253

2.267

2.281

2.295

2.309

2.324

20

2.338

2.353

2.367

2.382

2.397

2.412

2.427

2.442

2.457

2.472

21

2.487

2.502

2.518

2.533

2.549

2.564

2.580

2.596

2.612

2.628

22

2.644

2.660

2.676

2.693

2.709

2.726

2.742

2.759

2.776

2.792

23

2.809

2.826

2.844

2.861

2.878

2.896

2.913

2.931

2.948

2.966

24

2.984

3.002

3.020

3.038

3.056

3.075

3.093

3.112

3.130

3.149

25

3.168

3.187

3.206

3.225

3.244

3.263

3.283

3.302

3.322

3.342

26

3.361

3.381

3.401

3.422

3.442

3.462

3.483

3.503

3.524

3.544

27

3.565

3.586

3.607

3.629

3.650

3.671

3.693

3.714

3.736

3.758

28

3.780

3.802

3.824

3.846

3.869

3.891

3.914

3.937

3.960

3.983

29

4.006

4.029

4.052

4.076

4.099

4.123

4.147

4.171

4.195

4.219

30

4.243

4.267

4.292

4.317

4.341

4.366

4.391

4.416

4.442

4.467

31

4.493

4.518

4.544

4.570

4.596

4.622

4.648

4.675

4.701

4.728

32

4.755

4.782

4.809

4.836

4.863

4.891

4.918

4.946

4.974

5.002

33

5.030

5.058

5.087

5.115

5.144

5.173

5.202

5.231

5.260

5.290

34

5.319

5.349

5.379

5.409

5.439

5.469

5.500

5.530

5.561

5.592

35

5.623

5.654

5.685

5.717

5.748

5.780

5.812

5.844

5.876

5.908

36

5.941

5.974

6.007

6.039

6.073

6.106

6.139

6.173

6.207

6.241

37

6.275

6.309

6.343

6.378

6.413

6.448

6.483

6.518

6.553

6.589

38

6.625

6.661

6.697

6.733

6.769

6.806

6.843

6.880

6.917

6.954

39

6.991

7.029

7.067

7.105

7.143

7.181

7.220

7.258

7.297

7.336

40

7.376

7.415

7.455

7.494

7.534

7.574

7.615

7.655

7.696

7.737

41

7.778

7.819

7.861

7.902

7.944

7.986

8.028

8.071

8.113

8.156

42

8.199

8.242

8.285

8.329

8.373

8.417

8.461

8.505

8.550

8.595

43

8.640

8.685

8.730

8.776

8.821

8.867

8.914

8.960

9.007

9.053

44

9.101

9.148

9.195

9.243

9.291

9.339

9.387

9.436

9.484

9.533

45

9.582

9.632

9.681

9.731

9.781

9.832

9.882

9.933

9.984

10.035

46

10.086

10.138

10.190

10.242

10.294

10.347

10.399

10.452

10.506

10.559

47

10.613

10.667

10.721

10.775

10.830

10.885

10.940

10.995

11.051

11.107

48

11.163

11.219

11.276

11.333

11.390

11.447

11.504

11.562

11.620

11.679

49

11.737

11.796

11.855

11.914

11.974

12.034

12.094

12.154

12.215

12.276

 

Table 3.  Saturation vapor pressure (kPa) over a flat surface of ice calculated using Tetens’ formula (Equation 5) for temperature between 0.0 °C and -14.9 °C.

Temperature (°C)

 

0.0

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.8

-0.9

-14

0.181

0.179

0.177

0.176

0.174

0.173

0.171

0.169

0.168

0.166

-13

0.198

0.196

0.194

0.193

0.191

0.189

0.187

0.186

0.184

0.182

-12

0.217

0.215

0.213

0.211

0.209

0.207

0.205

0.204

0.202

0.200

-11

0.237

0.235

0.233

0.231

0.229

0.227

0.225

0.223

0.221

0.219

-10

0.259

0.257

0.255

0.253

0.250

0.248

0.246

0.244

0.242

0.239

-9

0.284

0.281

0.279

0.276

0.274

0.271

0.269

0.266

0.264

0.262

-8

0.310

0.307

0.304

0.302

0.299

0.296

0.294

0.291

0.289

0.286

-7

0.338

0.335

0.332

0.329

0.326

0.323

0.321

0.318

0.315

0.312

-6

0.368

0.365

0.362

0.359

0.356

0.353

0.350

0.347

0.344

0.341

-5

0.401

0.398

0.395

0.391

0.388

0.385

0.381

0.378

0.375

0.372

-4

0.437

0.433

0.430

0.426

0.422

0.419

0.415

0.412

0.408

0.405

-3

0.476

0.472

0.468

0.464

0.460

0.456

0.452

0.448

0.445

0.441

-2

0.517

0.513

0.509

0.505

0.500

0.496

0.492

0.488

0.484

0.480

-1

0.562

0.558

0.553

0.548

0.544

0.539

0.535

0.530

0.526

0.522

0

0.611

0.606

0.601

0.596

0.591

0.586

0.581

0.576

0.572

0.567

 

 

References

 

Fritschen, L.J. & Gay, L.W.  1979.  Environmental Instrumentation. New York, NY: Springer-Verlag.

 

Jensen, M.E., R.D. Burman, and R.G. Allen, Eds. 1990. Evapotranspiration and Irrigation Water Requirements. Amer. Soc. of Civil Eng., New York.

 

Tetens, V.O. 1930. Uber einige meteorologische. Begriffe, Zeitschrift fur Geophysik. 6:297-309.