{
    "_id" : ObjectId("5b453cc7799fb211dc44a1e8"),
    "id" : 1.0,
    "nestedDoc" : {
        "nestedArray" : [
            {
                "field1" : "value1",
                "field2" : "value2",
                "field3" : "value3"
            },
            {
                "field1" : "value11",
                "field2" : "value21",
                "field3" : "value31"
            },
            {
                "field1" : "value12",
                "field2" : "value22",
                "field3" : "value32"
            }
        ]
    }
}
{
    "_id" : ObjectId("5b453d23799fb211dc44a1e9"),
    "id" : 2.0,
    "nestedDoc" : {
        "nestedArray" : [
            {
                "field1" : "value1",
                "field2" : "value29",
                "field3" : "value39"
            },
            {
                "field1" : "value118",
                "field2" : "value281",
                "field3" : "value381",
                "field4" : "value281"
            },
            {
                "field1" : "value172",
                "field2" : "value272",
                "field3" : "value372"
            }
        ]
    }
}

db.test1.aggregate(
    [
        // Stage 1 : filter documents
        {
            $match: {
            id:1
            }
        },
        // Stage 2 : count array size and return only it.
        {
            $project: {
                arraySize:{$size:"$nestedDoc.nestedArray"},
                _id:0
            }
        },
    ]
);

db.test1.aggregate(
    [
        // Stage 1 count array size for each document
        {
            $project: {
                _id:0,
                arraySize:{$size:"$nestedDoc.nestedArray"}
            }
        },
        // Stage 2 group all documents and sum arraySize
        {
            $group: {
            _id:null,
            totalArraysSize:{$sum:"$arraySize"}
            }
        },
    ]
);