How high is the production bonus of a great engineer in Civ5?

Solution 1:

The amount of production of a great engineer on normal speed is calculated using the formula

300 + 30 * city population

So in a city with a population of 1 the engineer only results in 330 production, in a size 15 it results in 750 production.

For quick speed the formula is:

200 + 20 * city population

For epic speed it is:

450 + 45 * city population

and for marathon it is:

900 + 90 * city population

The amount of hammers does not seem to be influenced by era, map size or difficulty level.

Conclusion: If you want to hurry late game wonders, build it in a city with a large population.