Enter the displacement (weight) and the length at waterline (LWL) into the Displacement to Length Ratio Calculator. The calculator will evaluate and display the Displacement to Length Ratio (DLR). 

Displacement to Length Ratio Calculator

Enter any 2 values to calculate the missing variable

Displacement to Length Ratio Formula

The following formula is used to calculate the Displacement to Length Ratio (DLR) used in boat design (naval architecture). Displacement should be expressed in long tons (1 long ton = 2,240 lb ≈ 1,016.05 kg) and LWL should be expressed in feet. 

DLR = \frac{D_{LT}}{(0.01 \cdot LWL_{ft})^3}
  • Where DLR is the Displacement to Length Ratio (dimensionless)
  • DLT is the displacement in long tons
  • LWLft is the length at waterline in feet

To calculate DLR, convert displacement to long tons and LWL to feet, then divide the displacement by (0.01 × LWL) cubed.

How to Calculate Displacement to Length Ratio?

The following example problems outline how to calculate Displacement to Length Ratio.

Example Problem #1:

  1. First, determine the displacement (in long tons).
    • The displacement is given as: 5 long tons.
  2. Next, determine the length at waterline (LWL) (in feet).
    • The LWL is provided as: 30 ft.
  3. Finally, calculate the Displacement to Length Ratio using the equation above: 

DLR = DLT / (0.01 · LWLft)3

The values given above are inserted into the equation below and the solution is calculated:

DLR = 5 / (0.01 × 30)3 = 5 / 0.33 ≈ 185.19

FAQ

What is the significance of the Displacement to Length Ratio in boat design?

The Displacement to Length Ratio (DLR) is a common index in boat design that helps indicate how “light” or “heavy” a boat is for its length at the waterline. In general, a lower DLR indicates a lighter boat (often associated with higher potential speed), while a higher DLR indicates a heavier boat (often associated with greater load-carrying and comfort in rougher conditions). Actual performance depends on many other factors (hull form, sail area, power, etc.).

Can the Displacement to Length Ratio be applied to other fields besides boat design?

DLR as defined here (using displacement in long tons and LWL in feet) is primarily a naval-architecture metric. Other fields may use different mass-to-size or weight-to-length indices, but they typically use different definitions and units.

How does one obtain the values for displacement and length at waterline (LWL)?

For boats, displacement is the vessel’s weight (equal to the weight of the water it displaces at a specified loading condition) and is usually provided by the designer or measured from draft/displacement data. LWL (length at waterline) is the length of the hull at the waterline for the same loading condition; it is not necessarily the same as the overall length (LOA), which is measured from the bow to the stern.