# IBU Calculator

The IBU Calculator will use your recipes pre-boil and target batch size to calculate your beers estimated bitterness rating (IBU).

All of the calculations have been adjusted for full & partial mash batches and will also take into account the average utilization differences between whole leaf hops and pellet hops.

IBU Chart by Beer Style located below.

***The general consensus is that full batch recipes will get a more accurate number by using Tinseth’s formula, while Rager’s tends to be more accurate for partial boils. That said, IBU calculation is not an exact science, there are simply too many variables to account for. The truth is we still don’t know what drives hop utilization! For what it’s worth though, I personally prefer taking the average from all of the above formulas.*

**About the IBU Calculator**

Depending on the formula, hop utilization will be adjusted 10% up or down based on the type of hops you are using *(Whole leaf Vs Pellet)* and Estimated Boil gravity will be substituted in place of Original Gravity in the above calculator to compensate for adjustments in Partial + Full Mash pre-boil volumes and water additions.

So for example, if you are using a partial mash formula, you would enter something like 3 gallons for the pre-boil volume and 5 gallons for the target batch volume. The formula used to calculate this Estimated Boil Gravity is as follows:

**((final volume x (final gravity – 1)) / estimated boil volume) + 1 = estimated boil gravity**

Finally, The IBU calculator then uses the information you’ve supplied about your hop additions and finds your average IBU rating by combining the results from 4 of the most popular IBU formula’s.

**Average IBU’s = (Tinseth + Rager + Garetz + Daniels) / 4**

Below you will find a detailed break down of each of the formula’s used in this calculator, along with some real word examples.

**Tinseth’s IBU Formula**

**IBUs = **decimal alpha acid utilization * mg/l of added alpha acids

Tenseth’s base formula is simple enough, We just need to solve for our **mg/l of alpha acids** and **decimal alpha acid utilization%** to find our brews estimated IBU.

**mg/l of added alpha acids = (**decimal AA rating * ozs hops * 7490) / gallons of wort

**Decimal Alpha Acid Utilization = **Bigness Factor * Boil Time Factor

**Bigness factor** = 1.65 * 0.000125^(wort gravity – 1)

**Boil Time factor** = (1 – **e^**(-0.04 * time in mins) )/4.15

***Note: e = 2.71828*

### Tenseth’s Formula Example

**Batch Information**

Pre-Boil Volume: 6.5 gallons

Target Batch Size: 5 gallons

Original Gravity: 1.050

**Hop Additions**

1.5oz Hops – 6.4% AA @ 45 mins

1 oz Hops – 5% AA @ 15 mins

The nice thing about Tenseth’s formula is that it can easily be broken down into smaller components. We just have to solve the foundation equations, then we can plug in our variables to find our IBU for the example beer recipe above.

**mg/l of added alpha acids:**

(.064 * 1.5oz * 7490) / 5 = **143.808**

(.050 * 1oz * 7490) / 5 = **74.9**

Next we need to solve for our **Decimal Alpha Acid Utilization** by solving for our Bigness Factor and Boil Time Factor:

**Bigness factor:**

1.65 * 0.000125^(1.05- 1) = **1.052**

**Boil Time factor:**

Hop Addition #1: (1 – *2.71828^*(-0.04 * 45))/4.15 = **.201**

Hop Addition #2: (1 – *2.71828^*(-0.04 * 15))/4.15 = **.108**

Now we can go ahead and solve for Utilization % for our hop additions.

Hop Addition #1:1.052 * .201 = **.211**

Hop Addition #2:1.052 * .108 = **.113**

**IBUs = **decimal alpha acid utilization * mg/l of added alpha acids

Hop Addition #1: **.211 * 143.808 = 30.34 IBU’s**

Hop Addition #2: **.108 * 74.9 **= **8.08 IBUs**

**30.34+8.08=38.42 Total IBUs**

***Remember your order of operations! *

Parenthesis > Exponent >Multiplication >Division > Addition > Subtraction

**Rager IBU Formula**

**IBU** = (OUNCES OF HOPS * %UTILIZATION * %ALPHA * 7462) / (Batch Volume* (1 + GA))

Ragers formula uses the Gravity Adjustment factor (GA) to compensate for batches of higher gravity. *(anything over 1.050) So If Boil Gravity is less than 1.050 GA = 0.*

otherwise,

**GA** = (BOIL_GRAVITY – 1.050) / 0.2

**%UTILIZATION** = 18.11 + (13.86 * hyptan[(MINUTES – 31.32) / 18.27] )

### Rager’s Formula Example

**Batch Information**

Pre-Boil Volume: 6.5 gallons

Target Batch Size: 5 gallons

Original Gravity: 1.050

**Hop Additions**

1.5oz Hops – 6.4% AA @ 45 mins

1 oz Hops – 5% AA @ 15 mins

Using are example batch information from above, We already know that because our Original Gravity value is not GREATER than 1.050, our Gravity adjustment factor will equal 0.

Now let’s find our **Utilization factor:**

Hop Addition #1: 18.11 + (13.86 * hyptan[(45 – 31.32) / 18.27] ) =

**26.90%**

Hop Addition #2: 18.11 + (13.86 * hyptan[(15 – 31.32) / 18.27] ) =

**8.22%**

Lastly, Know that we know our Utilization factors and our GA value, we can solve for IBUs.

Hop Addition #1: (1.5oz * .2690 * .064 * 7462) / (5* (1 + 0)) = **38.54 IBUs**

Hop Addition #2: (1oz * .0822 * .050 * 7462) / (5* (1 + 0)) = **6.13 IBUs**

**Total IBUs = 38.54 + 6.13 = 44.67 Total IBUs**

**Garetz IBU Formula**

According to Garetz, There are several ‘combined adjustements’ (CA) required to calculate a beers IBU rating more accurately. Where GF is Gravity Factor, HF stands for the hopping factor and TF stands for temperature factor.

In the calculator above we use a similar formula to calculate for estimated Boil Gravity. Garetz is essentially doing the same thing here by first finding the ‘concentration factor’ (CF) and then the Boil Gravity(BG) value.

**IBU = **(%Utilization * %Alpha * Hop weight(oz) * 0.749) / (Volume in gallons * CA)

**Utilization % = **7.2994 + (15.0746 * tanh((minutes – 21.86) / 24.71))

**CA = **GF * HF * TF

So in order to find CA for the above formula, we first need to calculate our CF number.

**CF = **Final Volume / Pre-Boil Volume

Once we’ve solved for CF, We then need to find our BG value.

**BG = **(CF * (Starting Gravity – 1)) + 1

Now that we’ve solved for Boil gravity, we can then begin calculating for **GF**:

**GF = **(BG – 1.050)/.2 +1**HF = **((CF * Desired IBUs)/260) + 1**TF = **((Elevation in feet) / 550) * 0.02) + 1

### Garetz Formula Example

**Batch Information**

Pre-Boil Volume: 6.5 gallons

Target Batch Size: 5 gallons

Original Gravity: 1.050

**Hop Additions**

1.5oz Hops – 6.4% AA @ 45 mins

1 oz Hops – 5% AA @ 15 mins

There is a lot of calculations involved this time around, so Let’s break it down in chunks. First let’s solve for Utilization:

7.2994 + (15.0746 * tanh((45mins – 21.86) / 24.71))** = 22.374 %**

7.2994 + (15.0746 * tanh((15mins – 21.86) / 24.71))** = 3.218 %**

Next we will need to solve for CA.

**CF =** 5 / 6.5 =** .769**

**BG **= (CF * (Starting Gravity – 1)) + 1 =** 1.384**

**GF **= (1.384 – 1.050)/.2 +1 =** 1.167**

Typically you would need to enter your own Target IBU number(HF) and elevation(TF), however I’ve pre-filled those factors in the HF & TF calculations for the following example:

**HF **= ((.769 * 25)/260) + 1 =** 1.073**

**TF **= ((2,500 ft) / 550) * 0.02) + 1 =** 1.09**

Now we solve for CA

**CA **= 1.167 * 1.037 * 1.09 =** 1.319**

Now that we’ve figured out all of our variables – Let’s solve for our IBU’s.

**(22.374%) * (6.4%) * 1.5* 0.749 = 160.878—————————————–_ 5 * 1.319 = 6.596**

**160.878 / 6.596 =** **24****.39 IBU’s**

**(3.218%) * (5%) * 1 * 0.749 = 11.714————————————_ 5 * 1.319 = 6.596**

**11.714 / 6.596 = 1.77 IBU’s**

**24.39 + 1.77 = 26.16 Total IBU’s**

***It should be noted that the Garetz formula is the only one of the 4 that calls for you to use whole numbers when entering in your alpha acid & utilization percentages.*

**Daniels IBU Formula**

Created by Ray Daniels *(Author of Designing Great Beers), *Daniels formula has been used for years to calculate a beers estimated bitterness. While it has fallen out of favor since Tinseth’s and Ragers formula have come along, it has consistently proven to be the best representative of the average IBU’s I get by averaging all 4 formulas together.

**U% * (ALPHA% * W_OZ * 7489) / (V_Gal)**

Using Daniels Formula and the Utilization Rates table shown below – Calculate the IBU rating for the following beer:

**Batch Information**

Pre-Boil Volume: 6.5 gallons

Target Batch Size: 5 gallons

Original Gravity: 1.050

**Hop Additions**

1.5oz Hops – 6.4% AA @ 45 mins

1 oz Hops – 5% AA @ 15 mins

**.12 * ( .064% * 1.5oz * 7489) / 5** = **17.25 IBU’s**

**.22 * (.050% * 1oz * 7489) / 5** = **16.48 IBU’s**

Then simply add the calculated IBU numbers from each hop addition to get our total.

**16.48 + 17.25 =** **33.73 Total IBU’s**

***It should be noted that I could not find the Utilization formula that Daniels used for his equation. Instead, I’ve actually substituted Tinseth’s formula for utilization since it so closely mirrors the Utilization Rates of Daniels formula. (Since nesting a ton of If/Else statements in the calculator would be a complete nightmare) If anyone is able to find Daniels utilization formula, Please share it in the comments below and I’ll go ahead and update the calculator accordingly!*