The formula
cost of a level = base × level^exponent
Where it comes from
Almost every game uses a power curve: the experience for a level is a base multiplied by the level raised to an exponent. With an exponent of one the curve is linear and every level costs the same; with two, level fifty costs two and a half thousand times what level one did, and that is what makes the end of a progression drag. Fitting the exponent to what you actually see in the game is what makes the estimate useful: you only need what two different levels cost.
How to work it out by hand
- Work out the base and exponent from what two levels cost in your game
- Calculate the cost of every level in the range
- Add them all up
- Subtract the experience you have and divide by your rate per hour
What is worth knowing
How many times more expensive the last level is than the first of the range is what explains how a progression feels: under five and the curve feels gentle; over twenty and the end becomes a wall. Many games break the formula past a certain level and insert flat stretches or jumps, so if the numbers stop matching halfway through, the curve changed — the arithmetic did not.