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I think I have heard that one should not measure or weigh things on Shabbat.
However, I wonder if this rule applies to Yom Tov related food needs, e.g., can one stick a food thermometer into meat to know if the meat is safe to eat or not, or measure flour for baking?
Measuring precisely is forbidden on Yom Tov because it resembles mundane acts (uvdin d'chol). However some permit using measuring instruments (e.g., baking cups) if one uses them for approximate measures (some even permit if it is critical to the recipe and is done all the time). There are also exceptions for the sake of a mitzva (e.g., measuring a mikve or measures for one who has to eat on Yom Kippur) as these are not mundane acts.
It is also permitted to look at a thermometer, as such if the thermometer was of the type you put in the oven before Yom Tov, you can look at it, but inserting one in meat (if it even existed in a non-electric version) appears forbidden. See below for sources. and, of course, consult your rabbi before implementing anything you learn here.
R Yirmiyohu Kaganoff writes (under "Measuring")
In general, it is prohibited to measure on Yom Tov, just as it is prohibited to measure on Shabbos. Thus, one may not measure out how much flour, sugar, or oil to use in a recipe (Shulchan Aruch Orach Chayim 506:1). However, one may approximate how much flour, oil, or sugar is needed. It is permitted to use a measuring cup, as long as one does not fill the cup exactly to its measuring points (Mishnah Berurah 506:3).
The poskim dispute whether one may measure spices on Yom Tov, some permitting (even though it is prohibited to measure other items) because approximating spices may ruin the recipe if one errs (Beitzah 29a). However, Magen Avraham (504:10) contends that since most women cook without measuring spices on weekdays, but simply estimate how much they use, they may not measure spices on Yom Tov. Others contend that someone who measure spices on weekdays may measure them on Yom Tov.
R Moshe Lazarus at ohr writes
If baking on Yom Tov, it is forbidden to measure the flour if the precise amount is not critical, as in baking bread, because one could have measured it Erev Yom Tov. However, in baking cakes, etc., it may be done (Pri Megadim).
HalachaYomit (here and here) brings R Ovadia Yosef's rulings
For this reason, it is forbidden to weigh food items on a mechanical scale on Shabbat or Yom Tov. It is likewise forbidden to place liquids in special measuring cups in order to determine their weight or volume, for this constitutes measuring on Shabbat and Yom Tov.
Maran Rabbeinu Ovadia Yosef zt”l rules (in his Chazon Ovadia-Shabbat, Part 6, page 26, among other places) that on the night of the Pesach Seder, one may measure the Kezayit amounts of Matzah and Maror, for this is also considered measuring for the purpose of a Mitzvah and this does not resemble a mundane act.
It is nevertheless clear that although cooking on Yom Tov for the holiday meals is permissible and is a Mitzvah of enjoying and honoring the holiday, measuring or weighing food items for the purpose of cooking or baking is not considered measuring for the purpose of a Mitzvah, for only when something is completely recognizable as being done for the purpose of a Mitzvah, such as measuring Matzah and Maror or measuring a Mikveh, is this permissible. However, measuring for the purpose of cooking on Yom Tov is forbidden.
R Chaim Hillel Raskin at halacha.co writes
Chazal prohibited any form of measuring on Shabbos or on Yom Tov since it is a degradation of Shabbos and is similar to weekday activity, and also because it may cause a person to write. Some examples include: Measuring ingredients for a salad dressing, determining the size of a room (even just by counting the tiles), checking one’s weight or measuring height, or timing how long an activity takes. Only precise measuring is prohibited (even if later used in an imprecise manner), however approximate measuring (e.g. a cupful of baby cereal) is permissible.
Thus, when cooking on Yom Tov one should not measure the ingredients precisely, (measuring flour which can be done just the same before Yom Tov is not permitted even though cooking is permitted). However, spices may be measured if an imprecise amount will positively ruin the dish. [...]
Only actual measuring is prohibited. However, there is no prohibition to look at a clock or read the temperature from an already hanging thermostat.
