Converting numerical rating into k, d, or p

[princepawn]

In this one game detail we see the ratings of the 2 players listed in a numerical fashion:

    "players": {
        "black": {
            "id": 1084282,
            "username": "e71621056",
            "country": "un",
            "icon": "https://secure.gravatar.com/avatar/6a672d6bfdf67f18a37973a3266572c3?s=32&d=retro",
            "ratings": {
                "version": 5,
                "overall": {
                    "rating": 1333.3032734729904,
                    "deviation": 61.33815873444767,
                    "volatility": 0.059992528356333175
                }
            },
            "ranking": 21.576182986490565,
            "professional": false,
            "ui_class": ""
        },
        "white": {
            "id": 1084709,
            "username": "thequietcenter",
            "country": "us",
            "icon": "https://b0c2ddc39d13e1c0ddad-93a52a5bc9e7cc06050c1a999beb3694.ssl.cf1.rackcdn.com/e5d0e76b38575706ab829b5eb1ac528b-32.png",
            "ratings": {
                "version": 5,
                "overall": {
                    "rating": 1260.121194467763,
                    "deviation": 70.71625100034467,
                    "volatility": 0.059993821035258195
                }
            },
            "ranking": 20.269327870540423,
            "professional": false,
            "ui_class": ""
        }

In the actual game we see that the players are rated 9k and 10k.

Is there software or a published algorithm about how to convert those numerical ratings into the commonly recognized ratings of kyu, dan, and professional dan?