Preheat your oven to 350°F (175°C). Line a muffin tin with cupcake liners.
In a mixing bowl, combine sugar, eggs, and vegetable oil. Mix well.
Add grated carrots and vanilla extract to the mixture. Stir to combine.
In another bowl, whisk together flour, baking powder, baking soda, cinnamon, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Divide the batter evenly among the cupcake liners.
Bake for 20 minutes or until a toothpick inserted into the center comes out clean.
Allow the cupcakes to cool in the tin for 10 minutes, then transfer to a wire rack to cool completely.