There are 1 train company operating 6 routes - ICE41, ICE12, ICE42, ICE11, ICE10, ICE91. The cheapest train costs $36 and is 3h 24min.
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There are 4 ways to travel from Essen to Hanau. 4 buses, 1 train, 2 flights and 1 by car are possible between the two areas. The by car from Essen to Hanau is the cheapest and fastest. The train operated by DB running from Essen-Borbeck Süd to Steinheim (Main) is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!