Preheat oven to 350°F (175°C). Line a muffin tin with cupcake liners.
In a large bowl, mix together pumpkin puree, sugar, and vegetable oil. Beat in eggs one at a time.
In another bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Gradually add dry ingredients to wet ingredients, mixing until just combined.
Fill cupcake liners ⅔ full with batter. Bake for 20 minutes or until a toothpick inserted into the center comes out clean.
Let cupcakes cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.