Deutsche Bahn use a fairly reasonable and systematic numbering scheme for designating their locomotives. Numbers are of the form xxx yyy-z, where xxx is the Baureihe (Class) and yyy the serial number. z is a checksum.

The three-digit class numbers work like this:

**0xx** -- steam locomotives
**01x and 02x** -- tender engines for express passenger trains
**02x and 03x** -- tender engines for passenger trains
**04x and 05x** -- tender engines for freight trains
**06x and 07x** -- tank engines for passenger trains
**08x and 091 through 096** -- tank engines for freight trains and shunting
**097** -- rack locomotives
**098** -- old locomotives for local trains
**099** -- narrow-gauge locomotives

**1xx** -- electric locomotives
**10x and 11x** -- passenger service
**12x and 13x** -- universal locomotives
**14x and 15x** -- freight service
**16x** -- electric shunters
**17x** -- locomotives incompatible with 15 kV / 16-2/3 Hz AC
**18x** -- multisystem locomotives

**2xx** -- diesel locomotives
**20x through 28x** -- road diesels
**29x** -- diesel shunters

**3xx** -- small shunters
**31x** -- power class I (up to 29.4 kW)
**32x** -- power class II (29.4 - 110.3 kW)
**33x** -- power class III (110.3 kW - 480 kW)
**38x** -- battery-powered

**4xx** -- EMUs
**40x** -- high speed
**42x** -- commuter AC
**47x and 48x** -- commuter DC

**5xx** -- battery-powered EMUs
**6xx** -- DMUs
**60x and 61x** -- long-distance
**62x through 69x** -- short-distance

**7xx** -- service and maintenance vehicles and rail buses
**70x through 78x** -- service and maintenance
**79x** -- rail buses

**8xx** -- motorless EMU trailers
**9xx** -- motorless trailers for DMUs and 7xx-series vehicles

The second and third digit for 8xx and 9xx trailers are always the same as on the corresponding 4xx, 5xx, 6xx or 7xx MU.

The three-digit serial number is 001 for the first vehicle in a series. Vehicles of the same physical class may be classified under two different classes because, obviously, the serial numbers only allow for a maximum of 999 vehicles per class.

To obtain the checksum that goes after the dash:

- Replace the second, fourth and sixth digit in the number with the doubled digit; i.e. 110 184 becomes 120 288 and 111 049 becomes 121 0418
- Compute the sideways sum, i.e. 21 for 100 184 and 17 for 121 0418
- Subtract the last digit of this result from 10 unless it's 0; thus, the complete numbers are 110 184-9 and 111 049-3.