Peel carrots and then cut carrots with a mandolin into small to medium matchsticks. In a bowl, combine salt and carrots. Toss to evenly coat. Let sit for 20 minutes.
Squeeze as much moisture out of the carrots as you can. Rinse thoroughly to remove salt. Transfer to jar, bowl or storage container you plan to store your carrots in.
Boil water and add sugar and vinegar. Stir to dissolve. Pour liquid into container with carrots. Cover with a lid and allow to cool. Refrigerate. Carrots will last for several weeks.