TPC (Tonnes Per Centimetre immersion) is the weight, in tonnes, that must be loaded or discharged to change a ship’s mean draft by exactly one centimetre.
If a vessel’s TPC is 26 t/cm, loading 26 tonnes sinks her 1 cm deeper; discharging 26 tonnes lifts her 1 cm. TPC is read from the ship’s hydrostatic tables and changes with draft and water density. It is the single number that connects cargo weight to draft — which makes it central to loading calculations, draft surveys, and freight earnings.
That short answer passes the exam question. But if you work in commercial operations — as a charterer, agency, stevedoring, draft surveys — TPC is not an academic figure. It is the reason a chief officer and a shipper argue over 40 centimetres, and the reason those 40 centimetres can be worth over a thousand tonnes of cargo. In this guide we’ll cover both sides: the formula and worked examples deck officers need, and the practical port-side reality we deal with as agents on every bulk call.
What does TPC stand for?
TPC stands for Tonnes Per Centimetre immersion (you’ll also see “tons per centimeter” in daily shipping communication). Some older texts call it TPC immersion or simply “immersion.” Its imperial cousin is TPI — Tons Per Inch — still seen on ships built to imperial hydrostatics, mainly in US trades.
The definition worth memorizing: the TPC for any given draft is the weight which must be loaded or discharged to change the ship’s mean draft by one centimetre.
How is TPC calculated? (The formula)
TPC comes from a simple piece of physics. By the law of flotation, when you load a weight, the ship sinks until she displaces an extra “slice” of water whose mass equals that weight.
If the slice is 1 cm thick, its mass is the TPC.
TPC = (WPA × ρ) / 100
Where:
WPA = waterplane area in m² — the area of the ship’s hull cut at the waterline
ρ = density of the water the ship floats in, in t/m³ (1.025 for salt water, 1.000 for fresh water, somewhere between for dock/river water)
÷ 100 converts the 1 cm slice into metres
If you don’t have WPA directly, it can be estimated from the ship’s dimensions:
WPA = L × B × Cw
where L is length, B is breadth at the waterline, and Cw is the waterplane coefficient (how “full” the waterline shape is compared to a rectangle).
Worked example 1 — calculating TPC from dimensions
A bulk carrier is 140 m long with a 22 m beam at the waterline and a waterplane coefficient of 0.83, floating in salt water (1.025 t/m³).
WPA = 140 × 22 × 0.83 = 2,556.4 m²
TPC = 2,556.4 × 1.025 / 100 = 26.2 t/cm
So every 26.2 tonnes loaded puts this ship 1 cm deeper.
Worked example 2 — sinkage from a known cargo weight
Same ship loads 1,310 tonnes of steel coils. How much does the draft increase?
Sinkage (cm) = weight / TPC = 1,310 / 26.2 = 50 cm, i.e. the mean draft increases by 0.50 m.
The same formula in reverse tells you how much cargo corresponds to a draft change — which is exactly what a draft survey does.
Why does TPC change with draft?
Because the waterplane area changes as the ship sinks. In practice:
Box-shaped hulls (barges, some pontoons): the waterline area is the same at every draft, so TPC is constant.
Ship-shaped hulls: the hull flares outward from the keel, so the waterplane area — and therefore TPC — increases as draft increases. A ship near her marks needs more tonnes per centimetre than the same ship in ballast.
This is why you never use a single TPC for a large loading calculation. You take TPC from the hydrostatic tables at the relevant draft, interpolating between tabulated drafts when needed — and for a big draft change, you use the TPC at the mean of the initial and final drafts, or work in stages.
The commercial side: why every centimetre is money?
Here is the part the textbooks skip, and the part we live with as port agents such as Heisenberg Shipping.
Each centimetre of available draft is worth one TPC of cargo. On our 26 t/cm bulk carrier, at a freight rate of, say, USD 25 per tonne, one centimetre is roughly USD 655 of freight. Ten centimetres left unused at sailing is over USD 6,500 the owner never earns — on a single call.
This is where TPC turns from a formula into a negotiation:
- Maximum draft at the berth or channel. The port sets a limit; the master plans backwards from it. Cargo to lift = available centimetres × TPC at that draft (corrected for density). At draft-restricted ports, the loading plan is built centimetre by centimetre around this number.
- Draft surveys. Initial and final surveys convert draft readings into displacement, and the difference is the cargo figure the Bill of Lading and often the freight invoice rest on. TPC (with corrections for trim and density) is one of the core inputs. A misread density or a wrong TPC interpolation shifts the cargo figure by tens of tonnes — which is a claim waiting to happen.
- Deadweight maximization. On the final pour of a bulk loading, the chief officer is watching the marks and the TPC together: “we have 6 cm to the mark, TPC 26 — give me 150 tonnes, no more.” From the agency side, we’ve seen loadings at Turkish bulk berths come down to exactly this exchange between the chief officer, the terminal, and the draft surveyor in the last half hour before completion.
- Bunkers, ballast, fresh water. TPC applies to any weight, not just cargo. Taking 100 tonnes of bunkers before sailing costs you 100/TPC centimetres of cargo draft. On a tight-draft call, bunker planning and cargo planning are the same conversation.
Frequently asked questions about TPC
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