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I was gifted a ball of yarn, but don't know the yardage. Is there a formula to calculate the yardage based on weight of ball and type (light worsted to worsted) of yarn?
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The most accurate way to
The most accurate way to measure the yardage of your ball of your yarn would be to measure off a length -- say 10 yards -- then weigh it. If you have a scale that can accurately measure very small weights such as a McMorran balance, you could measure off just a yard.
Worsted weight yarn rounds around 200-225 yards/100 grams. The fiber can make a difference since yarn is usually heavier than wool so that the same weight of cotton would be expected to give less yardage than the same weight of wool. I have also found that merino wool tends to provide less yardage for the same weight -- it could be because most of the merino yarns I have worked with are tightly twisted.
If you happen to have an idea of what the yarn is, you might check a site like Yarndex.com to see if you can obtain yarn information.
Also, keep in mind that the official US measure for yarn is weight so yardage is actually an approximation.