# Formulas

### Temperature conversions

Fahrenheit to Celsius
```C = (F - 32.0) / 1.8
```
Celsius to Fahrenheit
```F = (C * 1.8) + 32.0
```

### Specific Gravity temperature corrections

Relative to 15C (59F) single range
```All temperatures are in expressed in degrees F.

correction = 1.313454 - 0.132674*F + 0.002057793*F*F - 0.000002627634*F*F*F

SG_corrected = SG + (correction * 0.001)
```

Relative to 15C (59F) and divided into 3 ranges
```All temperatures are in expressed in degrees C.

For temperatures less than 3.98 C:

correction = -0.000032692*C - 0.000740644

For temperatures less than 50.0 C and greater than or equal to 3.98 C:

correction = -0.0008031922 - 0.0000473773*C + 0.000007231263*C*C - 0.00000003078278*C*C*C

For temperatures greater than or equal to 50.0 C:

correction = -0.005431719 + 0.0001963596*C + 0.000002661056*C*C

SG_corrected = SG + correction
```

### Weight conversions

Pounds to kilograms
```Kgs = lbs * 0.453592
```
Kilograms to pounds
```lbs = kgs * 2.204623
```

### Volume conversions

Gallons to liters
```liters = gals * 3.785412
```
Liters to gallons
```gallons = liters * 0.264272
```
Quarts to liters
```liters = qts * 0.946353
```
Liters to quarts
```quarts = liters * 1.056688
```

Here we find the volume of a water addition to raise/lower the temperature of a mash
```Vadd = (Vmash * (TCm - TFm)) / (TFm - Ta)

where:
Vmash = current volume of the mash
TCm   = current temperature of the mash
TFm   = final (target) temperature of the mash
Ta    = temperature of the water addition
```

### SG to plato

```Reference: Manning, M.P., Understanding Specific Gravity and Extract, Brewing Techniques, 1,3:30-35 (1993)

Plato = -676.67 + 1286.4*SG - 800.47*SG*SG + 190.74*SG*SG*SG
```

### Dilutions

New volume from current volume, current SG, and target SG
```Vnew = ((SGc - 1.0)/(SGt - 1.0)) * Vcur

where:
Vcur = current volume
SGc  = current SG
SGt  = target SG
```
New SG from current SG, current volume, and target volume
```SGnew = ((SGc - 1.0) * (Vcur / Vtar)) + 1.0

where:
SGc  = current SG
Vcur = current volume
Vtar = target volume
```

### Alcohol content

Alcohol by weight according to George Fix:

```Abw = (OE - RE) / (2.0665 - (0.010665 * OE))

where:
OE = Original extract in degrees Plato
RE = (0.1808 * OE) + (0.8192 * AE)

where:
AE = Final (apparent) extract in degrees Plato
```
Use SG to Plato conversion above to find OE and AE from specific gravity

Alcohol by weight according to A.J. de Lange:

```Abw = (PO - PF) * BF

where:
PO = Original degrees Plato
PF = Finished degrees Plato
BF = Ballings factor = 0.39661 + (0.0017091*Plato) + (0.000010788*Plato*Plato)
```
Use SG to Plato conversion above to find PO and PF from specific gravity

### Calories in 12 ounces of beer

Calories from alcohol:
```Ca = (1881.22 * FSG) * ((OSG - FSG)/(1.775 - OSG))

where:
OSG = Original Specific Gravity
FSG = Final Specific Gravity
```
Calories from extract:
```Ce = 3550.0 * FSG * ((0.1808 * OSG) + (0.8192 * FSG) - 1.0004)

where:
OSG = Original Specific Gravity
FSG = Final Specific Gravity
```

### Refractometer

Brix to Specific Gravity
```Formula was derived from the 69th edition (1988-1989) of the CRC Handbook of
Chemistry and Physics, "Concentrative Properties of Aqueous Solutions:
Conversion Tables", Table 88 Sucrose

MathCAD was used to curvefit the data for Degrees Brix @ 20 C (% sucrose
by weight) and specific gravity @ 15 C

SG = 1.000898 + 0.003859118*B + 0.00001370735*B*B + 0.00000003742517*B*B*B

where:

B  = measured refractivity in Brix
SG = calculated specific gravity at 15 C
```
Final Specific Gravity from original and final Brix
```SG = 1.001843 - 0.002318474*OB - 0.000007775*OB*OB - 0.000000034*OB*OB*OB + 0.00574*FB + 0.00003344*FB*FB + 0.000000086*FB*FB*FB

where:

SG = estimated specific gravity of the sample
OB = Original Brix
FB = Final Brix
```
Brix to Index of Refraction
```RI = 1.33302 + 0.001427193*B + 0.000005791157*B*B

where:

B  = measured refractivity in Brix
RI = calculated Refractive Index
```
Alcohol by weight content from Final SG and Final Brix
```RI  = 1.33302 + 0.001427193*FB + 0.000005791157*FB*FB
ABW = 1017.5596 - (277.4*SG) + RI*((937.8135*RI) - 1805.1228)

where:
FB = Final Brix
RI = calculated Refractive Index
SG = Final SG
```