No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
The density of water (at refrigerator temperatures) is ~1 g/cm^3. 1 oz. = ~28.35 g; 1 fl. oz. = ~ 29.57 cm^3; thus the density of water is (1/28.35) / (1/29.57) = ~1.043 = oz./fl. oz. (This is, of course, equal to 0.95033293516 / 0.911, allowing for rounding and floating point errors.)
Note that the composition of butter varies. In particular, it varies by the ratio of butterfat to water (there are also butter solids, i.e. protein, but those are a very small part of the total mass). American supermarket butter has approx. 80% butterfat; Amish butter, European butters (e.g. Kerrygold), or premium American butters (e.g. Vital Farms brand) have more butterfat (up to 85%). Butterfat is less dense than water (thus the more butterfat is present, the lower the average density of the stick of butter as a whole—although this doesn’t make a very big difference, given the range of variation).
Given the numbers in the paper at the last link, we can calculate the average density (specific gravity) of butter (assuming butterfat content of a cheap American supermarket brand) as 0.8 * 0.9 + 0.2 * 1.0 = 0.92. This approximately matches our 0.911 kg/m^3 number above.
No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
But 1⁄2 cup of butter weighs 4 ounces according to every source I can find: https://www.wolframalpha.com/input?i=density+of+butter+*+(1%2F2+cup)+in+ounces
Which means a 4 ounce stick of butter is 1⁄2 cup by volume.
The density of butter is reasonably close to 1 avoirdupois ounce per 1 fluid ounce, but is definitely not exactly equal:
https://kg-m3.com/material/butter gives the density as 0.95033293516 oz./fl. oz., or 0.911 kg/m^3.
(The link you provide doesn’t give a source; the data at the above link is sourced from the International Network of Food Data Systems (INFOODS).)
Further commentary:
The density of water (at refrigerator temperatures) is ~1 g/cm^3. 1 oz. = ~28.35 g; 1 fl. oz. = ~ 29.57 cm^3; thus the density of water is (1/28.35) / (1/29.57) = ~1.043 = oz./fl. oz. (This is, of course, equal to 0.95033293516 / 0.911, allowing for rounding and floating point errors.)
Note that the composition of butter varies. In particular, it varies by the ratio of butterfat to water (there are also butter solids, i.e. protein, but those are a very small part of the total mass). American supermarket butter has approx. 80% butterfat; Amish butter, European butters (e.g. Kerrygold), or premium American butters (e.g. Vital Farms brand) have more butterfat (up to 85%). Butterfat is less dense than water (thus the more butterfat is present, the lower the average density of the stick of butter as a whole—although this doesn’t make a very big difference, given the range of variation).
Given the numbers in the paper at the last link, we can calculate the average density (specific gravity) of butter (assuming butterfat content of a cheap American supermarket brand) as 0.8 * 0.9 + 0.2 * 1.0 = 0.92. This approximately matches our 0.911 kg/m^3 number above.
Plus, butter is churned, so it is a few percent air by volume when solid.