Tinseth Method for IBU Calculation

IBU Calculation

The Tinseth Method for IBU calculation can be deceptively simple. However, he derived it based on documented experimentation and results from multiple analyses. The Tinseth Method  is the system used for calculations within this site, and requires only a bit of practice. It is adjustable based on each brewery’s equipment which makes it handy.

Because his formula is wordy, I have assigned variables to make it easier to visualize. As before, each variable will be defined briefly, but to a level that should give a good understanding.

IBU=U*A_ppm

U      = the utilization (from Table A1-2) expressed as a decimal

Appm = the concentration of iso-alpha acids in milligrams per liter (mg/l) or parts per million

The concentration of the iso-alpha acids (Appm) is calculated thus:

Metric:  A_(ppm )=  ((%A)*W_grams*1000)/V_Liters

 

Imperial (U.S.):  A_(ppm )=  ((%A)*W_ounces*7490)/V_gallons

%A     = Alpha acid level for the hop as a decimal

Wunits = the weight, in ounces or grams, of hops to be added

Vunits  = the final volume of finished beer in either gallons or liters

You could stop here if you wish. The tables below gives the standard utilization as expressed by the Tinseth Method, and they will work well for estimating bitterness in your finished product. I have expanded his tables to give per-minute utilization. However, we’re brewers! We are tinkerers. We like to fiddle with stuff! Thankfully Tinseth has provided more details for us to work out.

In order to tweak the formula to your own system, Tinseth has conceived of a “Bigness Factor”, and a “Boil Time Factor”. These two calculations allow for the tweaking of some constants to adjust utilization within individual brewing systems.

To determine a system’s utilization:

U=Bf*Tf

U    = decimal value of alpha acid utilization

Bf   = Bigness Factor

Tf    = Boil Time Factor

Tinseth does provide a starting point based off of the system he used at the time of development:

The numbers 1.65 and 0.000125 are empirically derived to fit my data. The number 0.04 controls the shape of the util vs. time curve. The factor 4.15 controls the max util value–make it smaller if your util is higher than mine.

I’d suggest fiddling with 4.15 if necessary to match your system, only play with the other three if you like to muck around. I make no guarantees if you do. (Tinseth, n.d.)

The Bigness Factor requires the use of the average specific gravity from pre-boil to final boil in order to account for the boil off of wort.

Bf=1.65*〖0.000125〗^((G_av-1) )

Gav   = Average specific gravity of the wort from pre-boil to final wort volume.

Boil Time Factor is determined using a few system constants that are tweaked to each brewery.

Tf=  (1- e^((-0.04*t_min)))/4.15

e     = 2.718 this is a mathematical constant derived by Leonhard Euler and John Napier. [6]

tmin  = total boil time in minutes

As with the Rager and Garetz formulas, you will need to make a calculation for each hop addition then add those together to get your IBU estimate.

So a three hop IBU calculation would look like:

IBU= (U*A_ppm )+ (U*A_ppm )+ (U*A_ppm )

Tinseth Utilization Rates (1.030 – 1.060 Gravity)

This table gives the standard utilization as expressed by Tinseth, and they will work well for estimating bitterness in your finished product. I have expanded on Tinseth by calculating per-minute utilization and adding a half step increase between his base gravity levels.

 Tinseth Utilization
Boil Time (minutes)Original Gravity
 1.0301.0351.0401.0451.0501.0551.060
00.0000.0000.0000.0000.0000.0000.000
10.0120.0110.0110.0100.0100.0100.009
20.0230.0220.0210.0200.0200.0190.018
30.0340.0330.0310.0300.0290.0270.026
40.0450.0430.0410.0390.0380.0360.034
50.0550.0530.0500.0480.0460.0440.042
60.0650.0620.0590.0570.0540.0520.049
70.0740.0710.0680.0650.0620.0590.057
80.0830.0790.0760.0730.0690.0660.063
90.0920.0880.0840.0800.0770.0730.070
100.1000.0960.0910.0870.0840.0800.076
110.1080.1030.0990.0940.0900.0860.083
120.1160.1110.1060.1010.0970.0920.088
130.1230.1180.1130.1080.1030.0980.094
140.1300.1240.1190.1140.1090.1040.099
150.1370.1310.1250.1200.1140.1090.105
160.1440.1370.1310.1250.1200.1150.110
170.1500.1430.1370.1310.1250.1200.114
180.1560.1490.1420.1360.1300.1240.119
190.1620.1550.1480.1410.1350.1290.123
200.1670.1600.1530.1460.1400.1340.128
210.1730.1650.1580.1510.1440.1380.132
220.1780.1700.1620.1550.1480.1420.136
230.1830.1750.1670.1600.1530.1460.139
240.1870.1790.1710.1640.1570.1500.143
250.1920.1830.1750.1680.1600.1530.147
260.1960.1880.1790.1720.1640.1570.150
270.2010.1920.1830.1750.1680.1600.153
280.2050.1960.1870.1790.1710.1630.156
290.2080.1990.1910.1820.1740.1660.159
300.2120.2030.1940.1850.1770.1690.162
310.2160.2060.1970.1890.1800.1720.165
320.2190.2100.2000.1920.1830.1750.167
330.2230.2130.2030.1940.1860.1780.170
340.2260.2160.2060.1970.1890.1800.172
350.2290.2190.2090.2000.1910.1830.175
360.2320.2210.2120.2020.1940.1850.177
370.2350.2240.2140.2050.1960.1870.179
380.2370.2270.2170.2070.1980.1890.181
390.2400.2290.2190.2100.2000.1920.183
400.2420.2320.2210.2120.2020.1940.185
410.2450.2340.2240.2140.2040.1950.187
420.2470.2360.2260.2160.2060.1970.189
430.2490.2380.2280.2180.2080.1990.190
440.2510.2400.2300.2200.2100.2010.192
450.2530.2420.2320.2210.2120.2020.194
460.2550.2440.2330.2230.2130.2040.195
470.2570.2460.2350.2250.2150.2060.196
480.2590.2480.2370.2260.2160.2070.198
490.2610.2490.2380.2280.2180.2080.199
500.2630.2510.2400.2290.2190.2100.200
510.2640.2530.2410.2310.2210.2110.202
520.2660.2540.2430.2320.2220.2120.203
530.2670.2550.2440.2330.2230.2130.204
540.2690.2570.2460.2350.2240.2150.205
550.2700.2580.2470.2360.2260.2160.206
560.2710.2590.2480.2370.2270.2170.207
570.2730.2610.2490.2380.2280.2180.208
580.2740.2620.2500.2390.2290.2190.209
590.2750.2630.2510.2400.2300.2200.210
600.2760.2640.2520.2410.2310.2210.211
610.2770.2650.2530.2420.2320.2210.212
620.2780.2660.2540.2430.2320.2220.212
630.2790.2670.2550.2440.2330.2230.213
640.2800.2680.2560.2450.2340.2240.214
650.2810.2690.2570.2460.2350.2250.215
660.2820.2700.2580.2460.2360.2250.215
670.2830.2700.2580.2470.2360.2260.216
680.2840.2710.2590.2480.2370.2270.217
690.2840.2720.2600.2490.2380.2270.217
700.2850.2730.2610.2490.2380.2280.218
710.2860.2730.2610.2500.2390.2280.218
720.2870.2740.2620.2500.2390.2290.219
730.2870.2750.2630.2510.2400.2290.219
740.2880.2750.2630.2520.2410.2300.220
750.2890.2760.2640.2520.2410.2300.220
760.2890.2760.2640.2530.2420.2310.221
770.2900.2770.2650.2530.2420.2310.221
780.2900.2770.2650.2540.2420.2320.222
790.2910.2780.2660.2540.2430.2320.222
800.2910.2780.2660.2550.2430.2330.222
810.2920.2790.2670.2550.2440.2330.223
820.2920.2790.2670.2550.2440.2330.223
830.2930.2800.2670.2560.2450.2340.223
840.2930.2800.2680.2560.2450.2340.224
850.2930.2810.2680.2560.2450.2340.224
860.2940.2810.2690.2570.2460.2350.224
870.2940.2810.2690.2570.2460.2350.225
880.2950.2820.2690.2570.2460.2350.225
890.2950.2820.2700.2580.2460.2360.225
900.2950.2820.2700.2580.2470.2360.226
910.2960.2830.2700.2580.2470.2360.226
920.2960.2830.2710.2590.2470.2360.226
930.2960.2830.2710.2590.2480.2370.226
940.2970.2840.2710.2590.2480.2370.226
950.2970.2840.2710.2590.2480.2370.227
960.2970.2840.2720.2600.2480.2370.227
970.2970.2840.2720.2600.2480.2380.227
980.2980.2850.2720.2600.2490.2380.227
990.2980.2850.2720.2600.2490.2380.227
1000.2980.2850.2720.2600.2490.2380.228
1010.2980.2850.2730.2610.2490.2380.228
1020.2980.2850.2730.2610.2490.2380.228
1030.2990.2860.2730.2610.2500.2390.228
1040.2990.2860.2730.2610.2500.2390.228
1050.2990.2860.2730.2610.2500.2390.228
1060.2990.2860.2740.2620.2500.2390.229
1070.2990.2860.2740.2620.2500.2390.229
1080.3000.2860.2740.2620.2500.2390.229
1090.3000.2870.2740.2620.2500.2390.229
1100.3000.2870.2740.2620.2510.2400.229
1110.3000.2870.2740.2620.2510.2400.229
1120.3000.2870.2740.2620.2510.2400.229
1130.3000.2870.2750.2620.2510.2400.229
1140.3000.2870.2750.2630.2510.2400.229
1150.3010.2870.2750.2630.2510.2400.230
1160.3010.2870.2750.2630.2510.2400.230
1170.3010.2880.2750.2630.2510.2400.230
1180.3010.2880.2750.2630.2510.2400.230
1190.3010.2880.2750.2630.2520.2400.230
1200.3010.2880.2750.2630.2520.2410.230
 

Tinseth Utilization Rates (1.065 – 1.095 Gravity)

This table gives the standard utilization as expressed by Tinseth, and they will work well for estimating bitterness in your finished product. I have expanded on Tinseth by calculating per-minute utilization and adding a half step increase between his base gravity levels.

 Tinseth Utilization
Boil Time (minutes)Original Gravity
 1.0651.0701.0751.0801.0851.0901.095
00.0000.0000.0000.0000.0000.0000.000
10.0090.0080.0080.0080.0070.0070.007
20.0170.0160.0160.0150.0140.0140.013
30.0250.0240.0230.0220.0210.0200.019
40.0330.0310.0300.0290.0270.0260.025
50.0400.0380.0370.0350.0340.0320.031
60.0470.0450.0430.0410.0400.0380.036
70.0540.0520.0490.0470.0450.0430.041
80.0610.0580.0550.0530.0510.0480.046
90.0670.0640.0610.0590.0560.0540.051
100.0730.0700.0670.0640.0610.0580.056
110.0790.0750.0720.0690.0660.0630.060
120.0850.0810.0770.0740.0710.0670.065
130.0900.0860.0820.0790.0750.0720.069
140.0950.0910.0870.0830.0790.0760.073
150.1000.0960.0910.0870.0840.0800.076
160.1050.1000.0960.0920.0880.0840.080
170.1090.1050.1000.0960.0910.0870.084
180.1140.1090.1040.0990.0950.0910.087
190.1180.1130.1080.1030.0990.0940.090
200.1220.1170.1120.1070.1020.0980.093
210.1260.1200.1150.1100.1050.1010.096
220.1300.1240.1190.1130.1080.1040.099
230.1330.1270.1220.1170.1110.1070.102
240.1370.1310.1250.1200.1140.1090.104
250.1400.1340.1280.1220.1170.1120.107
260.1430.1370.1310.1250.1200.1140.109
270.1460.1400.1340.1280.1220.1170.112
280.1490.1430.1370.1310.1250.1190.114
290.1520.1450.1390.1330.1270.1220.116
300.1550.1480.1420.1350.1290.1240.118
310.1580.1510.1440.1380.1320.1260.120
320.1600.1530.1460.1400.1340.1280.122
330.1620.1550.1480.1420.1360.1300.124
340.1650.1580.1510.1440.1380.1320.126
350.1670.1600.1530.1460.1400.1330.128
360.1690.1620.1550.1480.1410.1350.129
370.1710.1640.1560.1500.1430.1370.131
380.1730.1660.1580.1510.1450.1380.132
390.1750.1670.1600.1530.1460.1400.134
400.1770.1690.1620.1550.1480.1410.135
410.1790.1710.1630.1560.1490.1430.136
420.1800.1720.1650.1580.1510.1440.138
430.1820.1740.1660.1590.1520.1450.139
440.1840.1750.1680.1600.1530.1470.140
450.1850.1770.1690.1620.1550.1480.141
460.1860.1780.1700.1630.1560.1490.142
470.1880.1800.1720.1640.1570.1500.143
480.1890.1810.1730.1650.1580.1510.144
490.1900.1820.1740.1660.1590.1520.145
500.1920.1830.1750.1680.1600.1530.146
510.1930.1840.1760.1690.1610.1540.147
520.1940.1850.1770.1700.1620.1550.148
530.1950.1860.1780.1700.1630.1560.149
540.1960.1870.1790.1710.1640.1570.150
550.1970.1880.1800.1720.1650.1570.151
560.1980.1890.1810.1730.1650.1580.151
570.1990.1900.1820.1740.1660.1590.152
580.2000.1910.1830.1750.1670.1600.153
590.2010.1920.1830.1750.1680.1600.153
600.2020.1930.1840.1760.1680.1610.154
610.2020.1930.1850.1770.1690.1620.155
620.2030.1940.1860.1770.1700.1620.155
630.2040.1950.1860.1780.1700.1630.156
640.2050.1960.1870.1790.1710.1630.156
650.2050.1960.1880.1790.1710.1640.157
660.2060.1970.1880.1800.1720.1640.157
670.2060.1970.1890.1800.1730.1650.158
680.2070.1980.1890.1810.1730.1650.158
690.2080.1990.1900.1810.1730.1660.159
700.2080.1990.1900.1820.1740.1660.159
710.2090.2000.1910.1820.1740.1670.159
720.2090.2000.1910.1830.1750.1670.160
730.2100.2010.1920.1830.1750.1680.160
740.2100.2010.1920.1840.1760.1680.161
750.2110.2010.1930.1840.1760.1680.161
760.2110.2020.1930.1840.1760.1690.161
770.2110.2020.1930.1850.1770.1690.162
780.2120.2030.1940.1850.1770.1690.162
790.2120.2030.1940.1860.1770.1700.162
800.2130.2030.1940.1860.1780.1700.162
810.2130.2040.1950.1860.1780.1700.163
820.2130.2040.1950.1860.1780.1700.163
830.2140.2040.1950.1870.1790.1710.163
840.2140.2050.1960.1870.1790.1710.163
850.2140.2050.1960.1870.1790.1710.164
860.2150.2050.1960.1880.1790.1710.164
870.2150.2050.1960.1880.1800.1720.164
880.2150.2060.1970.1880.1800.1720.164
890.2150.2060.1970.1880.1800.1720.164
900.2160.2060.1970.1880.1800.1720.165
910.2160.2060.1970.1890.1800.1720.165
920.2160.2070.1980.1890.1810.1730.165
930.2160.2070.1980.1890.1810.1730.165
940.2170.2070.1980.1890.1810.1730.165
950.2170.2070.1980.1890.1810.1730.166
960.2170.2070.1980.1900.1810.1730.166
970.2170.2080.1980.1900.1810.1730.166
980.2170.2080.1990.1900.1820.1740.166
990.2170.2080.1990.1900.1820.1740.166
1000.2180.2080.1990.1900.1820.1740.166
1010.2180.2080.1990.1900.1820.1740.166
1020.2180.2080.1990.1900.1820.1740.166
1030.2180.2080.1990.1910.1820.1740.167
1040.2180.2090.1990.1910.1820.1740.167
1050.2180.2090.2000.1910.1820.1740.167
1060.2180.2090.2000.1910.1830.1750.167
1070.2190.2090.2000.1910.1830.1750.167
1080.2190.2090.2000.1910.1830.1750.167
1090.2190.2090.2000.1910.1830.1750.167
1100.2190.2090.2000.1910.1830.1750.167
1110.2190.2090.2000.1910.1830.1750.167
1120.2190.2100.2000.1920.1830.1750.167
1130.2190.2100.2000.1920.1830.1750.167
1140.2190.2100.2010.1920.1830.1750.168
1150.2190.2100.2010.1920.1830.1750.168
1160.2200.2100.2010.1920.1830.1750.168
1170.2200.2100.2010.1920.1830.1750.168
1180.2200.2100.2010.1920.1840.1750.168
1190.2200.2100.2010.1920.1840.1760.168
1200.2200.2100.2010.1920.1840.1760.168
 

Tinseth Utilization Rates (1.100 – 1.130 Gravity)

This table gives the standard utilization as expressed by Tinseth, and they will work well for estimating bitterness in your finished product. I have expanded on Tinseth by calculating per-minute utilization and adding a half step increase between his base gravity levels.

 Tinseth Utilization
Boil Time (minutes)Original Gravity
 1.1001.1051.1101.1151.1201.1251.130
00.0000.0000.0000.0000.0000.0000.000
10.0060.0060.0060.0060.0050.0050.005
20.0120.0120.0110.0110.0100.0100.010
30.0180.0170.0170.0160.0150.0150.014
40.0240.0230.0220.0210.0200.0190.018
50.0290.0280.0270.0260.0250.0230.022
60.0350.0330.0320.0300.0290.0280.026
70.0400.0380.0360.0350.0330.0320.030
80.0440.0420.0410.0390.0370.0350.034
90.0490.0470.0450.0430.0410.0390.037
100.0530.0510.0490.0470.0450.0430.041
110.0580.0550.0530.0500.0480.0460.044
120.0620.0590.0560.0540.0520.0490.047
130.0660.0630.0600.0570.0550.0520.050
140.0690.0660.0630.0610.0580.0550.053
150.0730.0700.0670.0640.0610.0580.056
160.0770.0730.0700.0670.0640.0610.058
170.0800.0760.0730.0700.0670.0640.061
180.0830.0790.0760.0730.0690.0660.063
190.0860.0820.0790.0750.0720.0690.066
200.0890.0850.0810.0780.0740.0710.068
210.0920.0880.0840.0800.0770.0730.070
220.0950.0910.0870.0830.0790.0760.072
230.0970.0930.0890.0850.0810.0780.074
240.1000.0950.0910.0870.0830.0800.076
250.1020.0980.0940.0890.0850.0820.078
260.1050.1000.0960.0910.0870.0840.080
270.1070.1020.0980.0930.0890.0850.082
280.1090.1040.1000.0950.0910.0870.083
290.1110.1060.1020.0970.0930.0890.085
300.1130.1080.1030.0990.0940.0900.086
310.1150.1100.1050.1010.0960.0920.088
320.1170.1120.1070.1020.0980.0930.089
330.1190.1130.1080.1040.0990.0950.091
340.1200.1150.1100.1050.1010.0960.092
350.1220.1170.1110.1070.1020.0970.093
360.1240.1180.1130.1080.1030.0990.094
370.1250.1200.1140.1090.1040.1000.095
380.1260.1210.1160.1110.1060.1010.097
390.1280.1220.1170.1120.1070.1020.098
400.1290.1230.1180.1130.1080.1030.099
410.1300.1250.1190.1140.1090.1040.100
420.1320.1260.1200.1150.1100.1050.101
430.1330.1270.1210.1160.1110.1060.101
440.1340.1280.1220.1170.1120.1070.102
450.1350.1290.1230.1180.1130.1080.103
460.1360.1300.1240.1190.1140.1090.104
470.1370.1310.1250.1200.1150.1100.105
480.1380.1320.1260.1210.1150.1100.105
490.1390.1330.1270.1220.1160.1110.106
500.1400.1340.1280.1220.1170.1120.107
510.1410.1350.1290.1230.1180.1120.108
520.1420.1350.1290.1240.1180.1130.108
530.1420.1360.1300.1240.1190.1140.109
540.1430.1370.1310.1250.1200.1140.109
550.1440.1380.1320.1260.1200.1150.110
560.1450.1380.1320.1260.1210.1160.110
570.1450.1390.1330.1270.1210.1160.111
580.1460.1400.1330.1280.1220.1170.111
590.1470.1400.1340.1280.1220.1170.112
600.1470.1410.1350.1290.1230.1180.112
610.1480.1410.1350.1290.1230.1180.113
620.1480.1420.1360.1300.1240.1180.113
630.1490.1420.1360.1300.1240.1190.114
640.1490.1430.1370.1310.1250.1190.114
650.1500.1430.1370.1310.1250.1200.114
660.1500.1440.1370.1310.1260.1200.115
670.1510.1440.1380.1320.1260.1200.115
680.1510.1450.1380.1320.1260.1210.115
690.1520.1450.1390.1320.1270.1210.116
700.1520.1450.1390.1330.1270.1210.116
710.1520.1460.1390.1330.1270.1220.116
720.1530.1460.1400.1340.1280.1220.117
730.1530.1460.1400.1340.1280.1220.117
740.1530.1470.1400.1340.1280.1230.117
750.1540.1470.1410.1340.1280.1230.117
760.1540.1470.1410.1350.1290.1230.118
770.1540.1480.1410.1350.1290.1230.118
780.1550.1480.1410.1350.1290.1240.118
790.1550.1480.1420.1350.1290.1240.118
800.1550.1480.1420.1360.1300.1240.119
810.1560.1490.1420.1360.1300.1240.119
820.1560.1490.1420.1360.1300.1240.119
830.1560.1490.1430.1360.1300.1250.119
840.1560.1490.1430.1370.1310.1250.119
850.1560.1500.1430.1370.1310.1250.119
860.1570.1500.1430.1370.1310.1250.120
870.1570.1500.1430.1370.1310.1250.120
880.1570.1500.1440.1370.1310.1250.120
890.1570.1500.1440.1370.1310.1260.120
900.1570.1510.1440.1380.1320.1260.120
910.1580.1510.1440.1380.1320.1260.120
920.1580.1510.1440.1380.1320.1260.120
930.1580.1510.1440.1380.1320.1260.121
940.1580.1510.1440.1380.1320.1260.121
950.1580.1510.1450.1380.1320.1260.121
960.1580.1510.1450.1380.1320.1270.121
970.1590.1520.1450.1390.1320.1270.121
980.1590.1520.1450.1390.1330.1270.121
990.1590.1520.1450.1390.1330.1270.121
1000.1590.1520.1450.1390.1330.1270.121
1010.1590.1520.1450.1390.1330.1270.121
1020.1590.1520.1450.1390.1330.1270.122
1030.1590.1520.1460.1390.1330.1270.122
1040.1590.1520.1460.1390.1330.1270.122
1050.1590.1520.1460.1390.1330.1270.122
1060.1600.1530.1460.1390.1330.1270.122
1070.1600.1530.1460.1390.1330.1270.122
1080.1600.1530.1460.1400.1330.1280.122
1090.1600.1530.1460.1400.1330.1280.122
1100.1600.1530.1460.1400.1340.1280.122
1110.1600.1530.1460.1400.1340.1280.122
1120.1600.1530.1460.1400.1340.1280.122
1130.1600.1530.1460.1400.1340.1280.122
1140.1600.1530.1460.1400.1340.1280.122
1150.1600.1530.1460.1400.1340.1280.122
1160.1600.1530.1470.1400.1340.1280.122
1170.1600.1530.1470.1400.1340.1280.122
1180.1600.1530.1470.1400.1340.1280.123
1190.1600.1530.1470.1400.1340.1280.123
1200.1610.1530.1470.1400.1340.1280.123