Moment to Change Trim by 1 cm (MCT 1 cm)

Measure longitudinal stiffness of a vessel. Compute MCT 1 cm from longitudinal metacentric height (GML) or from waterplane inertia.

Common Inputs
Sea ≈ 1.025, fresh ≈ 1.000
Longitudinal Metacentric Height Route
MCT 1 cm = Δ · GML / 100   (t·m/cm)
Waterplane Inertia Route
MCT 1 cm = (100 · Δ · IT) / Lpp   (t·m/cm)
MCT Result

MCT 1 cm: — t·m/cm

Equivalent per inch: — t·m/in

Report: Moment to Change Trim by 1 cm
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Moment to Change Trim by 1 cm (MCT 1 cm)

MCT 1 cm (Moment to Change Trim by 1 cm) is a longitudinal stability / stiffness quantity. It tells you how much trimming moment is required to change the vessel’s trim by exactly 1 cm. In practice, it’s one of the most useful hydrostatic values for quick trim & draft change calculations during loading, discharging, bunkering, ballasting, or weight shifts.

What does MCT 1 cm mean?

If your ship has MCT 1 cm = 350 t·m/cm, that means applying a trimming moment of 350 t·m will change the trim by 1 cm. A larger MCT means the ship is harder to trim (more longitudinal stiffness), and a smaller MCT means the ship trims more easily.

Units & quick conversions

  • MCT 1 cm is commonly reported as t·m/cm (metric tonnes · meter per centimeter of trim).
  • This calculator also shows the equivalent t·m/in using 1 in = 2.54 cm.
  • Be consistent with Δ in tonnes and lengths in meters.

Method A: From Δ and GML

The simplest route uses displacement and longitudinal metacentric height:

  • Input: Displacement Δ (t) and longitudinal metacentric height GML (m)
  • Formula: MCT 1 cm = Δ · GML / 100 (t·m/cm)

This route is common when your hydrostatics already provide GML for the condition. It’s also a quick check against the value printed in the hydrostatic book.

Method B: From waterplane inertia and Lpp

If you don’t have GML but you do have waterplane inertia, you can calculate MCT from geometry:

  • Input: Waterplane second moment of area IT (m⁴), displacement Δ (t), and Lpp (m)
  • Use case: Early-stage estimates, comparisons between hullforms, or when extracting from hydrostatic tables.

Note: depending on your reference, you may see alternative forms derived from longitudinal stability relations. The important part is to keep units consistent and verify against ship-specific hydrostatics.

How MCT 1 cm is used in trim calculations

Once you know MCT 1 cm, you can compute total trim change from a trimming moment:

  • Trimming moment: TM = Σ(w · x), where w is weight (t) and x is longitudinal lever (m)
  • Trim change: trim (cm) = TM / (MCT 1 cm)
  • Then distribute trim to drafts at FP and AP using LCF (Longitudinal Centre of Flotation)

Practical notes & common mistakes

  • Δ is displacement for the condition (not deadweight). If Δ changes, MCT changes.
  • Sign convention comes from your trim calculation step (moment about LCF / midship). MCT itself is typically a magnitude.
  • Use the correct Lpp used by your hydrostatic source (not LOA).
  • If results look off by a factor of 10–100, it’s usually a unit mismatch (cm vs m, tonnes vs kN, etc.).

Related calculators

If you’re working through a full stability/trim workflow, these tools pair naturally with MCT 1 cm:

FAQ

Is MCT 1 cm the same as MCTC?

Many references use MCT 1 cm or MCTC interchangeably. Always check the units (per cm or per meter).

Does MCT 1 cm depend on draft?

Yes. As displacement and waterplane geometry change with draft, MCT 1 cm typically changes across loading conditions.

Should I use seawater or freshwater density?

Use whatever density your hydrostatic source assumes for the condition. For most practical ship work, seawater is often taken as 1.025 t/m³, but your loading computer or hydrostatic book is the reference.