# Original Gravity

Original gravity is a measure of the amount of sugar in a wort that has the potential of becoming alcohol through fermentation. You can caluclate the original gravity o with the following formula, where p is the parts per pound per gallon of sugar, w is the weight in pounds, g is the batch size in gallons and e is the efficiency where the default efficiencies for mashed, steeped, and boiled fermentables are 75%, 50%, and 100% respectively:

o = 1 + (sum((p * w * e) / g)) / 1000

# Final Gravity

Final gravity is a measure of the amount of sugar remaining in a wort after fermentation has converted much of the sugar to alcohol. You can calculate the final gravity f with the following formula, where o is the original gravity and a_1, a_2, a_3, etc are the percentage attenuation values of the yeast in the recipe:

f = o - ((o - 1) * (max(a_1, a_2, a_3, ...)) / 100)

# Brew Color

Brew color is usually given in degrees SRM, and is a function of the colors of each fermentable sugar. You can calculate the SRM color value c with the following formula, where s is the fermentable color value, w is the weight in pounds, and g is the batch size in gallons:

c = sum((s * w) / g)

# SRM to RGB

The brew color is usually given in degrees SRM, which can be problematic if it is to be displayed on a digital screen. Digital screens usually use red, green, and blue value triplets. You can calculate approximate red, green, and blue 8-bit values r, g, and b with the following formulas, where c is the SRM color value in degrees:

r = min(255, max(0, 255 * 0.975^c))
g = min(255, max(0, 245 * 0.88^c))
b = min(255, max(0, 220 * 0.7^c))

# Alcohol By Volume

Alcohol by volume is a percentage of the brew's volume that is alcohol compared to that which is not. You can calculate the amount of alcohol a with the following formula, where o is the original gravity and f is the final gravity:

a = (1.05 * (o - f)) / (.0079f)

# Real Extract

Real extract is an intermediate value based on gravities converted to units plato that is used in other calculations, such as the number of calories. You can calculate the real extract r with the following formulas, where o is the original gravity and f is the final gravity.

p = -205.35o^2 + 668.72o - 463.37
q = -205.35f^2 + 668.72f - 463.37
r = 0.1808p + 0.8192q

# Calories Per Bottle

Calories are a measure of energy that is available per bottle of finished brew. You can calculate the calorie content k with the following formula, where a is the alcohol percentage by volume, b is the bottle size in ml, f is the final gravity, and r is the real extract:

k = (6.9 (0.79a / f) + 4 (r - 0.1)) * f * b / 100

# Bitterness Units

Bitterness is usually measured in IBUs, an international measure of how bitter something tastes. Malt.io uses the Tinseth formula for accurate IBU calculation. You can calculate the IBU value i with the following formula, where o is the original gravity, t is the time in minutes that hops are boiled, d is the hop alpha acid percentage, z is the weight of the hops in ounces, h is the average boil size in gallons, and u is the utilization factor (1.0 for whole hops, 1.15 for pellet hops):

i = sum(1.65 * 0.000125^(o - 1) * (1 - 2.718^(-0.04t) / 4.15) * (7490duz) / (100h))

# Bitterness Ratio

The bitterness ratio BU:GU is a measure of how bitter a brew is in comparison to the original gravity, i.e. the alcohol potential of a recipe. You can calculate the ratio v using the following formula, where i is the recipe bitterness in IBU and o is the original gravity:

v = i / (1000(o - 1))

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