The simple answer: about 15 grams of ground coffee per 8-ounce (240ml) cup of brewed coffee. This works out to roughly two heaping tablespoons, though weighing is far more accurate.
Why the answer depends on what you mean by cup
An American cup measure is 240ml. A coffee mug is often 350-400ml. A small espresso cup is 60-80ml. Different vessels need different amounts. The ratio stays roughly constant; the absolute amount scales.
Brewing math made simple
Use a 1:16 ratio as your starting point. That means 1 gram of coffee for every 16 grams of water. For one 240ml cup: 240 divided by 16 equals 15 grams of coffee. For a 350ml mug: about 22 grams. For a 12-cup drip machine making 1.5 liters: about 95 grams.
Why the math is approximate
Some water is absorbed by the grounds rather than ending up in your cup. Each gram of coffee retains about 2 grams of water. So if you brew with 240g of water and 15g of coffee, you will end up with roughly 210g (or 210ml) of liquid in the cup. Plan accordingly if precise serving size matters.
Adjustments by taste
If your coffee tastes weak at 1:16, push to 1:15 or even 1:14. If it tastes too intense, try 1:17. The ratio is a starting point, not a rule. Your beans, your brewing method, and your preferences all shift the right number for you.