Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Whisk flour, sugar, cocoa powder, baking soda, and baking powder together in a large bowl.
Mix water, oil, vinegar, and vanilla together in a separate bowl; pour wet ingredients into dry ingredients and beat with an electric mixer until smooth. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes. Remove from the oven and let cool in the pan, about 30 minutes.