Estimating

Time charter equivalent

Published 20 August 2026 · updated 17 October 2026

A charterer offers freight per tonne. Somewhere else, an owner is offered hire per day. You cannot compare these numbers until you convert one of them, and the conversion only works one way: take the freight, subtract everything the owner will spend on the voyage, and divide by the number of days the voyage takes. The result is the time charter equivalent (TCE). A voyage estimate exists to produce this one figure.

The TCE formula

TCE per day = (net freight - voyage costs) / voyage days

  net freight    gross freight less address commission and brokerage
  voyage costs   bunkers + port charges + canal dues + other costs of this voyage
  voyage days    sea days (ballast and laden) + port days + waiting days

The ship's daily running costs (crew, insurance, maintenance) are not in the formula. They are the same whichever cargo is chosen.

Listed shipowners report the same measure for a whole fleet. One recent annual report filed with the US Securities and Exchange Commission defines TCE revenues as total vessel revenues "net of charterers' commissions, less voyage expenses", divided by the number of available days to give a daily TCE rate. It adds that its calculation "may not be comparable to those reported by other companies". So ask what was taken off and which days were counted.

Why the answer has to be per day

Imagine two cargoes on a broker’s screen: one is grain at one rate, on a short voyage with cheap ports, and the other is steel at a much better rate, on a long voyage with an expensive discharge port and a canal on the way. Comparing the two freight rates tells you nothing. Comparing the total revenue tells you nothing either, because the bigger number may take three weeks longer to earn and burn twice the fuel.

A ship’s scarcest resource is its time. Every voyage uses days that cannot be spent on another cargo, so the fair unit is what the ship earns per day after the voyage has paid its costs. It is also the unit the time charter market prices in, so once a voyage is shown as a daily figure, an owner can compare it with the hire offered for a trip or a period and choose.

The arithmetic

Here it is written out, for a Supramax carrying grain. The figures are round and made up to keep the arithmetic easy to read, not a market quote.

Supramax, 55,000 mt grain, one voyage. Illustrative figures only.

  Gross freight    55,000 mt x 22.00 /mt                1,210,000
  Less commission  5.00% (address plus brokerage)         -60,500
                                                       ----------
  Net freight                                           1,149,500

  Bunkers   ballast   6.0 days x 20 mt/day = 120 mt
            laden    14.0 days x 20 mt/day = 280 mt
            in port  10.0 days x  3 mt/day =  30 mt
                     430 mt x 500.00 /mt                -215,000
  Port charges, load port                                -45,000
  Port charges, discharge port                           -60,000
  Canal dues                                             -95,000
                                                       ----------
  Voyage result                                           734,500

  Voyage days   ballast   6.0
                laden    14.0
                loading   4.0
                discharge 5.0
                waiting   1.0
                                                            30.0

  TCE = 734,500 / 30.0 = 24,483 per day

The TCE calculator runs exactly this sum, including the waiting days row.

That is the whole model. The rest of voyage estimating is deciding what belongs on each line and what number to put on it.

What each line is really made of

• Quantity. Freight is earned on the cargo loaded, not on deadweight, so take the intake from the ship’s particulars and the port’s draught limit, not from the size class. The quantity option (five or ten per cent), and who chooses the figure, change the top line before anything else does.
• Commissions. Address commission to the charterer and brokerage to the brokers come off the gross freight, and off demurrage too unless the fixture says otherwise. If you estimate on gross freight, the answer is too high by the whole percentage.
• Bunkers. Fuel use at sea times the sea days, plus a smaller use in port for generators and cargo gear, times a price per tonne. Fuel grades matter: a voyage that crosses an emission control area burns compliant fuel at a different price for that part, and an estimate that uses one average price for the whole voyage hides the difference.
• Port charges. Tonnage dues, pilots, tugs, berth hire, agency fees, light dues. They vary between ports much more than people expect, and this is the line most often copied from an old disbursement account.
• Canal dues. Zero on most routes and very large on the routes that have them. Keep the line in the template even at zero, because people forget it on exactly the routes that have it.
• Days. Sailing days come from the sea distance divided by speed. Port days are a guess about berth availability and cargo rates. Waiting days are a guess about congestion. Only the first of these three is arithmetic.

Where the inputs are soft

An estimate looks like a calculation, but many of its inputs are opinions. Be clear about which inputs are facts and which are opinions.

Speed and consumption are a warranty, not a measurement. The figures in a ship’s description are its performance under stated conditions: a set sea state, a set wind force, no adverse current. There is usually a good weather definition that decides how a claim is tested later. A loaded ship crossing a monsoon will not reach its warranted speed or burn its warranted tonnes. Estimating on the description is normal and correct, but treating the description as a forecast for this voyage is not.

Port time is the least certain input. Nobody guarantees it. It depends on the loading rate, berth congestion, holds that need cleaning between cargoes, a surveyor who will not pass the ship the first time, and weather working days that stop counting when it rains. The ten port days in the example above are a judgement about someone else’s terminal.

Bunker price is a market number that will have moved. Fuel is usually the largest single voyage cost. An estimate based on last month’s price is not cautious. It is wrong, and you do not know in which direction.

A useful habit is to mark which numbers are hard facts, which are warranted and which are guesses. If every input looks equally certain, nobody questions the weak ones, and people end up defending the estimate after the ship has lost money.

The ballast leg, and why the next cargo changes the answer

The six ballast days (sailing empty to the load port) in the example earn nothing and cost fuel, but the voyage still pays for them, and that one line is why the best cargo on the board is often not the one with the best freight rate. A high rate two thousand miles away can give a worse daily figure than an ordinary rate on a cargo right next to the ship, and the only way to see this is to run both estimates, each with its own ballast leg.

Where the ship ends up also matters. A voyage that discharges in an area with plenty of cargo leaves the ship ready for work the next day. The same voyage into a quiet area means a long empty voyage out, and that is a cost of this fixture even though it will show up on the next one. Desks handle this in different ways: some estimate the round trip back to a usual load area, some estimate one leg and adjust the answer by judgement, and some ask for a ballast bonus (an extra payment for the empty approach) in the negotiation. All three are reasonable. What is not reasonable is to compare a single loaded leg with a round voyage and call them the same number.

Demurrage is an expected value, not revenue

Demurrage is real money, but it is not certain money. A ship that goes over its laytime (the time allowed for cargo work) earns demurrage and a ship that finishes early may owe despatch, and either way the money comes after the event, and often after an argument about the statement of facts. If you put a full demurrage claim into an estimate as if it were freight, a weak voyage looks attractive.

The workable approach is to estimate the port days honestly, including the waiting a broker expects, and then decide. If the port history says a ship of this size waits several days at that berth, those days belong in the day count, and the demurrage they would earn belongs in the revenue only at the probability the estimator really believes. Some desks run two cases, one clean and one congested, and look at the difference between them rather than an average. Both methods are better than a common mistake: leaving congestion out of the days and then adding demurrage to the revenue to make the voyage look better.

Where the answer actually moves

Run a sensitivity check, because it changes what a broker argues about in the negotiation. Here is the example above with one input changed at a time:

Compare the two cost rows with the freight row. On this voyage, a hundred dollars a tonne on the bunker price costs about the same as eighty-two cents a tonne on the freight rate. Two days of unexpected waiting cost a little more than that. A broker who negotiates hard on the rate, but accepts the charterer’s optimistic loading rate without question, has negotiated over the smaller number.

The same arithmetic, read backwards

Everything above assumes you are the owner, deciding if a rate is worth accepting. A desk that has taken the ship on time charter and now relets it (charters it out again) for a cargo asks the reverse question. It pays hire at a known figure every day, so the unknown is not the daily return but the freight: what must I charge a tonne to cover the hire and the voyage?

For an owner, the same formula turned round:

Freight per tonne = (target TCE x voyage days + voyage costs)
                    / (1 - commission) / cargo quantity

Target 20,000 a day on the voyage above:
  20,000 x 30.0 days                    600,000
  Plus voyage costs                     415,000
  Net freight needed                  1,015,000
  Gross, with 5.00% commission        1,068,421
  Per tonne, on 55,000 mt                 19.43

So 19.43 a tonne pays 20,000 a day. The calculator does this step too. A desk with the ship on time charter adds its hire.

It is the same calculation, with one line added and solved the other way. Hire becomes a voyage cost like any other, charged on every day of the voyage including waiting days, and the freight rate is whatever makes the voyage result zero. Many working estimators are built this way, and on a short voyage the hire line is bigger than everything else on the sheet: thirty-seven days at eight thousand a day is three hundred thousand dollars before any fuel is burned.

Two results of this surprise people. First, the daily figure now means something different: with hire on the sheet, it is the margin over hire, not what the ship earns. Second, the waiting days matter more, not less, because hire is charged on every one of them, working or not.

Show port fuel line by line, not as a total. Whether the load port’s fuel is your cost or the owner’s is a commercial question, not an arithmetic one, and two brokers can hold opposite views while both think the same total looks right. An estimate that shows fuel port by port makes that disagreement visible, while one that adds it up first hides it, sometimes for years.

What the figure does not include

TCE is a gross earning, and that is why it compares with a hire rate. Under a time charter the charterer buys the fuel and pays the ports, so hire and TCE are on the same side of the voyage costs. Neither one is profit: the ship’s daily running cost (crew, insurance, stores, maintenance, class and surveys) comes off both, and the cost of the capital comes off after that. A daily figure that beats one owner’s breakeven can be a loss for another owner with the same ship and different finances.

The last point is about what an estimate is for. It will not be right. The ports will work at a different rate, the weather will not match the description, and the fuel will not cost what the sheet said. It is a decision tool that puts two cargoes in the same units, so you can choose the better one and write down why. Judge an estimate by whether its assumptions were stated and its sensitivity was checked, not by whether the number came true.

The calculator linked above works this out on figures you type in. The estimator inside the product works it out on a real sea distance for a named hull, prices the two fuel grades separately, and can rank one cargo across several ships at once.

References

• Baltic Exchange, Guide to Market Benchmarks.
• Castor Maritime Inc., Annual Report on Form 20-F for the year ended 31 December 2025, definitions of TCE revenues and daily TCE rate, filed with the US Securities and Exchange Commission, 2026. sec.gov
• Baltic Exchange, Guide to Modern Shipping: Chartering, on voyage costs and running costs, read 12 October 2026. balticexchange.com
• Steamship Mutual, Speed and performance, FAQs. steamshipmutual.com
• International Maritime Organization, IMO 2020, cutting sulphur oxide emissions. imo.org

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