Gear Engineering
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Outside Dia. of a Standard External Gear

(Number of Teeth + 2) / Diametral Pitch

Example: 21tooth 6DP Gear

(21 + 2) / 6 = 3.833
        
Outside Dia. of an External Involute Spline

(Number of Teeth + 1) / Diametral Pitch

Example: 24 Tooth 16/32DP Spline

(24 + 1) / 16 = 1.563
Tech Links
Admrial Steel Hardness Conversion

Boston Centeless Conversions