After performing the calculation for estimating the ship's displacement, deadweight, as well as the lightweight of a new design, the next step a naval architect will usually calculate is the length. There are many books about ship design that deal with the estimation of ship's length. I recommend Merchant Ship Design by Munro-Smith, Ship Design and Construction published by SNAME, or two other books that I will mention below.
If the new ship is going to operate on international shipping, it might pass through Panama Canal which only allows the maximum length to be 289.56 m. Length of the ship can be estimated using Sneekluth's formula. Please, see page 2 of Ship Design for Efficiency and Economy, written by H. Sneekluth and V. Bertram.
LPP = Length Between Perpendiculars (meters)
Δ = ship's displacement (ton)
V = speed (knots)
Fn = Froude number
The length of the new ship can also be calculated using cube root format which is presented on page 5 of Ship Design and Performance for Masters and Mates as follows:
Cube root format
L = LBP
p= density of sea water = 1.025 metric tons/ m3
CB = block coefficient
CD = deadweight coefficient
Although I only present two formulas here, actually, there are still other formulas for estimating the length of a new ship. If you are now designing a new ship, I suggest that you design its lines plan using delftship. Also read: How to calculate displacement of newly designed ship and Ship rudder