How to sum every fields in a sub document of MongoDB?

You have made the classical mistake to have arbitrary field names. MongoDB is "schema-free", but it doesn't mean you don't need to think about your schema. Key names should be descriptive, and in your case, f.e. "S2" does not really mean anything. In order to do most kinds of queries and operations, you will need to redesign you schema to store your data like this:

_id:...
Segment:[
    { field: "S1", value: 1 },
    { field: "S2", value: 5 },
    { field: "Sn", value: 10 },
]

You can then run your query like:

db.collection.aggregate( [
    { $unwind: "$Segment" },
    { $group: {
        _id: '$_id', 
        sum: { $sum: '$Segment.value' } 
    } } 
] );

Which then results into something like this (with the only document from your question):

{
    "result" : [
        {
            "_id" : ObjectId("51e4772e13573be11ac2ca6f"),
            "sum" : 16
        }
    ],
    "ok" : 1
}

Starting Mongo 3.4, this can be achieved by applying inline operations and thus avoid expensive operations such as $group:

// { _id: "xx", segments: { s1: 1, s2: 3, s3: 18, s4: 20 } }
db.collection.aggregate([
  { $addFields: {
      total: { $sum: {
        $map: { input: { $objectToArray: "$segments" }, as: "kv", in: "$$kv.v" }
      }}
  }}
])
// { _id: "xx", total: 42, segments: { s1: 1, s2: 3, s3: 18, s4: 20 } }

The idea is to transform the object (containing the numbers to sum) as an array. This is the role of $objectToArray, which starting Mongo 3.4.4, transforms { s1: 1, s2: 3, ... } into [ { k: "s1", v: 1 }, { k: "s2", v: 3 }, ... ]. This way, we don't need to care about the field names since we can access values through their "v" fields.

Having an array rather than an object is a first step towards being able to sum its elements. But the elements obtained with $objectToArray are objects and not simple integers. We can get passed this by mapping (the $map operation) these array elements to extract the value of their "v" field. Which in our case results in creating this kind of array: [1, 3, 18, 42].

Finally, it's a simple matter of summing elements within this array, using the $sum operation.