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How many dry ounces are in a cup?

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It depends on what you are measuring in the cup. A cup is a measure of volume, but a dry ounce is a measure of weight.

Depending on the density of the material you are going to have in the cup, the weight in ounces of the material will vary. For example, if you fill the cup with lead, the cup will weigh much more than if you fill with feathers.
This question would be similar to asking how much does a 6 foot person weight. It depends on the person of course. A cup of water will weigh more than a cup of flour.

For cooking, you can find tables that convert cups to ounces and vice versa for a variety of food. To the left is a link with a table for standard cooking ingredients. Make sure you look carefully and scroll down to find the correct conversion table specific ingredient you are using! The conversion is different for each ingredient!

Here are A FEW COMMON FOODS and their conversion from cups to ounces
(notice how much the weight varies!):

Granulated sugar: 1 cup = 7.055 ounces
Brown sugar: 1 cup, packed = 7.760 ounces
White flour: 1 cup = 4.409 ounces
White rice, uncooked: 1 cup = 6.526 ounces
White rice, cooked: 1 cup = 6.173 ounces
Butter: 1 cup = 8.007 ounces
Almonds, slivered: 1 cup = 3.810 ounces
Oil: 1 cup = 7.901 ounces
Maple syrup: 1 cup = 11.358 ounces
Milk, non-fat: 1 cup = 8.642 ounces
Milk, sweetened condensed: 10.794 ounces
Broccoli, florets: 1 cup = 2.504 ounces
Raisins: 1 cup, packed = 5.820 ounces
Milk, dry: 1 cup = 2.399 ounces
Yogurt: 1 cup = 8.642 ounces
Water: 1 cup = 8.325 ounces
Confectioners sugar: 1 C = 3.880 ounces
Cocoa: 1 C = 4.409 ounces

**Please refer to the related link to find out more on the automatic calculator. It will allow you to enter the food and the amount and then it will convert it into units for you.
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It matters on what you are measuring. 8 ounces of flour would be 2 cups. 8 ounces of sugar would be one. 8 ounces of feathers is going to take up a lot more space (cups) than
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How many cups in 4.9 dry ounces?

There is 8 ounces in 1 cup. There is approximately 0.612 cups in  4.9 ounces. Knowing conversion rates is important when cooking.