Yes, but only in certain rooms. On-board showers on the Caledonian Sleeper are en-suite and provided in the two higher grades of accommodation: the Club En-suite Room and the Caledonian Double. Both give you a private compartment with a toilet and a shower, so you can freshen up before arriving in Edinburgh, Glasgow, Aberdeen, Fort William or Inverness. The cheaper Classic Room does not have a shower — it has a washbasin in the room instead — and there is no shower for guests travelling in a reclining Seat. Toilets are available in all carriages regardless of your ticket. If you are booked in a Classic Room or Seat and want to shower, your best option is at your destination or accommodation, as there are no separate communal shower cars on the train. Guests in Club and Caledonian Double rooms also get access to the station Guest Lounges, which offer additional facilities. If a shower matters to you overnight, book a Club En-suite or Caledonian Double rather than a Classic Room. The operator's accommodation pages are the best place to confirm exactly what your chosen room includes for your travel date.
Sources: sleeper.scot
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