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

Calculation

A simplified equation from Ray Daniel’s Book Designing Great Beers for IBUs is:

• IBUs = U% * (ALPHA% * W_OZ * 0.7489) / (V_Gal)

Where:

•  U% is the hop utilization in percent
• ALPHA% is the percent alpha for the hop variety
• W_OZ is the hop weight in ounces
• V_GAL is the volume of hops in gallons.

...

Example:

IBUs = U% * (ALPHA% * W_OZ * 0.7489) / (V_Gal)

= U% (0.082  x 2 x0.7489 ) / 13.8 gal

=  

References