# Gravity

So, the specific gravity is the ratio of the density of substance to the density of the reference substance.
Pure water has a specific gravity of 1.000. But of course we have a questions that concerns our beer. Well in that case the specific gravity is the amount of sugars (and some other compounds, but their impact is minor) dissolved in your worth.

Original gravity is the gravity of your worth before pitching yeast.
It depends of:
– amount of grain used for brewing,
– the amount of sugars that the grain contains
– the efficiency (the amount of sugars that you maneged to extract from grain)

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#### 1. Units

DBFG or Extract fine D.M. (extract dry basis fine grind – you get this value from supplier on analysis sheets and it means maximum possible yield from precise malt) Units: %
SGP (specific gravity points in wort – we can calculate it by using US or metric units, this is decimal value of original gravity) Units: gravity points/gallon
EP (extract potential – how many gravity points of sugar are contained in a pound of the malt) Units:gp/lb
OG (original specific gravity of wort) Units: /
EE (extract efficiency – the percentage of potential extract you get from mash; the values could be teoretically from 0 to 1, but practically homebrewers get the efficiency somewhere between 0,45 and 0,85) Units: /
W (malt weight) Units: lb or kg
V (volume – final) Units: gal or l
8,364 (factor for conversion USmetric units at EP and SGP calculation)

#### 2. Equations

Equations for US units:
EP = ((DBFG or Extract fine D.M.)/100) x 46,21
SGP = (W x EP x EE)/V

…for metric units:
EP = ((DBFG or Extract fine D.M.)/100) x (46,21 x 8,364)
SGP = (W x EP x EE)/V

…all other equations are:

EE = (SGP x V) / (W x EP)

Each one of the homebrewers (well the homebrewer’s system) has its own efficiency. So you will get the efficiency when you will check your system (measure the specific gravity before pitching). So after this measurment you will be able to calculate the efficiency of your system (from the equation above) and you will be able to make some recipies with this information.

#### 3. Calculations

Ok, we want to calculate gravity on example

Step 1: is that you need to decide what gravity you are shooting for. Let’s say 1,055 (OG = 1,055 and so SGP = 55) and final volume 5 gal/18,93 L. We want to find out the amount (weight of malt to start).
Step 2: decide which malt/malts you will use. We choose Pale Ale (DBFG=80%), Cara 50 (DBFG=75%), Mroost 1400 (DBFG=70%).
Step 3: we will calculate how much sugar is in the malt (we will calculate EP)

US units:
EP(Pale Ale) = (80/100) x 46,21

EP(Pale Ale) = 37

EP(Cara 50) = (75/100) x 46,21
EP(Cara 50) = 34,7

EP(Mroost 1400) = (70/100) x 46,21
EP(Mroost 1400) = 32,3

Metric units:
EP(Pale Ale) = (80/100) x (46,21 x 8,364)
EP(Pale Ale) = 309,2

EP(Cara 50) = (75/100) x (46,21 x 8,364)
EP(Cara 50) = 289,9

EP(Mroost 1400) = (70/100) x (46,21 x 8,364)
EP(Mroost 1400) = 270,6

Step 4: we need to select malt(sugar) shares. We will select Pale Ale 90%, Cara 50 8,5 % and Mroost 1,5 %
Step 5: we will calculate weight of each malt we need to add (we need to consider our efficiency – let’s say it is 70%).

100 % SGP = 90 % SGP (Pale ale) + 8,5 % SGP (Cara 50) + 1,5 % SGP (Mroost 1400)
SGP = (W x EP x EE) / V  …so… W = (SGP x V) / (EP x EE)

US units:
W(Pale ale) = ((0,9 x 55) x 5) / (37 x 0,7) = 9,56 lb
W(Cara 50) = ((0,085 x 55) x 5 / (34,7 x 0,7) = 0,96 lb
W(Mroost 1400) = ((0,015 x 55) x 5 / (32,3 x 0,7) = 0,18 lb

Metric Units:
W(Pale ale) = ((0,9 x 55) x 18,93) / (309,2 x 0,7) = 4,33 kg
W(Cara 50) = ((0,085 x 55) x 18,93 / (289,9 x 0,7) = 0,44 kg

W(Mroost 1400) = ((0,015 x 55) x 18,93 / (270,6 x 0,7) = 0,08 kg

So we have all malt weights!

You should know that this way of calculating is not the only way, you can calculate OG after you decide which malt and how much of the one you will take and mix together… you really need to know that brewing is an art, so here are no limits at all!