Volume additions needed to achieve a mash step
Temp. Now	Desired mash temp. (F)

	170	166	162	158	154	150	146	142	138	134	130	126	122

40	3.17	2.80	2.49	2.23	2.00	1.80	1.63	1.48	1.34	1.22	1.11	1.01	0.92
50	2.93	2.58	2.29	2.04	1.82	1.64	1.48	1.33	1.21	1.09	0.99	0.89	0.81
60	2.68	2.36	2.08	1.85	1.65	1.48	1.32	1.19	1.07	0.96	0.86	0.78	0.70
70	2.44	2.13	1.88	1.66	1.47	1.31	1.17	1.04	0.93	0.83	0.74	0.66	0.58
80	2.20	1.91	1.67	1.47	1.30	1.15	1.02	0.90	0.79	0.70	0.62	0.54	0.47
90	1.95	1.69	1.47	1.28	1.12	0.98	0.86	0.75	0.66	0.57	0.49	0.42	0.36

96	1.80	1.56	1.35	1.17	1.02	0.89	0.77	0.67	0.58	0.49	0.42	0.35	0.29
99	1.73	1.49	1.29	1.11	0.96	0.84	0.72	0.62	0.53	0.45	0.38	0.32	0.26
102	1.66	1.42	1.22	1.06	0.91	0.79	0.68	0.58	0.49	0.42	0.35	0.28	0.22
105	1.59	1.36	1.16	1.00	0.86	0.74	0.63	0.54	0.45	0.38	0.31	0.25	0.19
108	1.51	1.29	1.10	0.94	0.81	0.69	0.58	0.49	0.41	0.34	0.27	0.21	0.16
111	1.44	1.22	1.04	0.89	0.75	0.64	0.54	0.45	0.37	0.30	0.23	0.18	0.12
114	1.37	1.16	0.98	0.83	0.70	0.59	0.49	0.41	0.33	0.26	0.20	0.14	0.09
117	1.29	1.09	0.92	0.77	0.65	0.54	0.45	0.36	0.29	0.22	0.16	0.11	0.06
120	1.22	1.02	0.86	0.72	0.60	0.49	0.40	0.32	0.25	0.18	0.12	0.07	0.02
123	1.15	0.96	0.80	0.66	0.54	0.44	0.35	0.28	0.21	0.14	0.09	0.04
126	1.07	0.89	0.73	0.60	0.49	0.39	0.31	0.23	0.16	0.10	0.05
129	1.00	0.82	0.67	0.55	0.44	0.34	0.26	0.19	0.12	0.06	0.01
132	0.93	0.76	0.61	0.49	0.39	0.30	0.22	0.14	0.08	0.03
135	0.85	0.69	0.55	0.43	0.33	0.25	0.17	0.10	0.04
138	0.78	0.62	0.49	0.38	0.28	0.20	0.12	0.06
141	0.71	0.56	0.43	0.32	0.23	0.15	0.08	0.01
144	0.63	0.49	0.37	0.26	0.18	0.10	0.03
147	0.56	0.42	0.31	0.21	0.12	0.05
150	0.49	0.36	0.24	0.15	0.07
153	0.41	0.29	0.18	0.09	0.02
156	0.34	0.22	0.12	0.04
159	0.27	0.16	0.06
162	0.20	0.09
165	0.12	0.02
168	0.05

Note: all temperatures in Fahrenheit; values are volumes of original mash of hot (211F) liquor added to achieve a given temperature.

As can be seen in the tabled values, the degree of linearity is generally high (but note the change in scale between 90F and 96F) so interpolation within the tabled values is easy and accurate. Exact values can also be calculated by formula; this is the only safe method when desired temperatures approach the vicinity of 32F or 212F.

The exact formula for the amount, x, of hot water to add to a given quantity, y, of water to achieve a total volume of x+y at the desired temperature is:

x =	(t₃ - t₁)	y
	(t₂ - t₃)

where t₁ is the current temperature of the water, t₂ is the temperature of the added water, and t₃ is the desired final temperature. Note that while this equation is for water, it should hold at least approximately for any two substances which can be mixed fairly rapidly (so mash and decoction infusions should work fine). The values tabled above are the temperature ratios (so you multiply them by y to get x) assuming that boiling (211F) water is infused. I chose 211F to try to account for losses. Obviously losses could be greater; each degree makes approximately 1-3 ounces difference in the tabled ranges.

Note that x and y should be in identical metrics.

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