What oven temp and time is required to get medium rare
There is no simple, single answer to this question. It is a myth to think that you can plug the weight of a roast into a formula and get a time and temperature.
You can roast at any temperature you prefer, from about 250 F to 450 F.
The lower the temperature, the longer it will take to roast and the more even the doneness will be from center to edge; with hotter roasting, you will get more crust development, but more gradient of doneness, with the edges being perhaps well done when the center gets to medium rare. For this reason, there are many cooking methods that are hybrids, using searing in a skillet or very hot oven to develop crust and browning, but a lower temperature for the main roasting.
Beef is medium rare when it has an internal temperature of approximately 135 F as measured in the center of the thickest part with an instant read thermometer. This is an essential tool for getting the desired results when cooking meat; fortunately, they are inexpensive. You may wish to remove it from the oven when it is about 5 F below your target temperature, especially if you are doing high temperature roasting, so that so-called carry-over cooking (which is really just the heat evening out from the perimeter which is the hottest to the center which is the coolest) to bring it up to temperature.
It is not possible to give you an exact time, because that would depend on many variables including:
- The shape and thickness of your particular roast.
- Its starting temperature
- The actual temperature of your oven
- Whether the moon is full
This is why it is so important to use a thermometer to test for the desired level of doneness.
You can google a myriad of roast beef recipes, to find detailed approaches.
Note also: pot roasts, while called roasts, are really braises (you can tell a recipe is a braise if the main cooking period for the meat is done partially submerged in liquid), and are an entirely different type of cooking. If you have a very tough cut, such as chuck, this can be a far better approach.