A voyage estimate is the single calculation that decides whether a ship gets fixed. Before an owner accepts a cargo or a charterer nominates a ship, someone on a chartering desk builds the voyage as a profit-and-loss: gross freight in, voyage costs out, the result spread over the days the voyage takes, expressed as a daily earning. That daily earning is the Time Charter Equivalent, and it is the number every fixture is judged against. Get the estimate wrong by a dollar a tonne on a 170,000-tonne cargo and the desk has misjudged the voyage by 170,000 dollars before the ship has moved. The time charter equivalent calculator runs the core arithmetic, and the voyage profit calculator carries it through to the bottom line on a specific fixture.
This article is the cornerstone of the voyage-estimation cluster. It treats the estimate as what it is on a chartering desk: a structured P&L built from distances, speeds, fuel consumption, port rates, and canal dues, reconciled at the end against the spot market the Baltic Dry Index and freight indices publish. It covers the revenue side (lumpsum, dollars per tonne, Worldscale), the cost side (bunkers across laden and ballast legs, port disbursements, canal tolls, agency, extras), the V-cubed speed-fuel law that drives slow steaming, break-even freight and the ballast bonus, and the routing question that the canals force: pay the toll or sail the long way.
The voyage estimate as a profit-and-loss
Strip away the spreadsheet and a voyage estimate is one subtraction and one division. Gross freight revenue, minus voyage costs, gives the voyage result. The voyage result, divided by round-voyage days, gives the daily earning. Everything else is detail feeding those two operations.
Gross freight is the money the cargo pays before address commission and brokerage. It comes in three shapes depending on the trade. A lumpsum fixture pays one agreed figure for the whole cargo regardless of the exact quantity loaded, common where the cargo fills the ship or where the charterer wants cost certainty. A dollars-per-tonne fixture, the dry-bulk norm, pays a rate times the tonnes of cargo intake, so the freight scales with how much the ship actually loads. A Worldscale fixture, the tanker convention, pays a percentage of a published flat rate per tonne, which separates the slow-moving cost geography of a route from the fast-moving market level. The voyage profit calculator accepts any of the three and reduces them to one gross-freight figure.
Voyage costs are the direct, owner-paid spend of running that specific voyage, and nothing else. Bunkers for the laden and ballast legs, port disbursements at load and discharge, canal dues where the routing transits Suez or Panama, agency fees, and voyage extras such as hold cleaning, war-risk premiums, or extra insurance for a difficult port. What voyage costs deliberately exclude is the ship’s daily running cost (crew, stores, lubricants, maintenance & insurance) and its capital cost. Those are left out on purpose, because the TCE is built to sit on the same line as a timecharter hire rate, and under a time charter the charterer pays the voyage costs while the owner keeps paying running and capital costs out of the hire. So the TCE answers a clean question: after fuel and ports and canals, how many dollars a day is this voyage putting on the table to cover everything the owner still has to pay.
Gross freight, commissions, and net to the owner
Gross freight is the headline number, but it is not what reaches the owner. Two deductions sit between the gross figure and the cash. Address commission is a percentage the charterer retains, conventionally a few percent, as the cost of doing the business; it is deducted off the top of the freight before the owner sees it. Brokerage is the commission paid to the brokers who arranged the fixture, typically a smaller percentage, paid by the owner out of the freight. A careful estimate runs the TCE on the freight net of address commission, because that net figure is the money the voyage actually earns, and an estimate built on the gross freight overstates the daily earning by the commission percentage. On a large lump-sum fixture a few percent of address commission is real money, so the estimate carries it as a line, not a rounding.
Voyage extras round out the cost side and are easy to forget because they are irregular. Hold cleaning between cargoes, war-risk and additional-premium insurance for a transit through a high-risk area, extra fuel for cargo heating on a parcel that must be kept warm, ice-class surcharges, security escorts, and any survey or fumigation the cargo requires all fall into voyage extras when they attach to the specific voyage rather than the ship’s standing costs. They are individually small but collectively material on a difficult trade, and an estimate that omits them flatters the voyage by the sum of the lines it left out.
The TCE formula
The whole estimate collapses to this:
| Symbol | Meaning | Unit |
|---|---|---|
| Hire / freight gross of commissions | USD | |
| Direct voyage spend | USD |
Source: Stopford - Maritime Economics
Calculate Time Charter Equivalent →The numerator is gross freight minus voyage costs, the voyage result. The denominator is the total round-voyage days: the ballast leg to the load port, loading time, the laden passage, discharge time, and any waiting or weather delay. Using round-voyage days rather than the laden leg alone is what makes the figure honest. A Capesize that ballasts 12 days from a discharge port in China to a load port in Brazil is earning across the whole cycle, not only the days it carries cargo, and charging the freight against the full round trip is the only way to compare it fairly with a ship that picked up a back-haul. The Baltic Exchange publishes many of its dry-bulk timecharter routes directly as a dollar-per-day TCE for exactly this reason, so an owner’s own estimate and the index sit in the same unit and can be read against each other without conversion.
The break-even freight calculator runs the same relationship backward. Fix the target daily earning and the voyage costs, and it solves for the freight per tonne the owner must quote to hit that target. That is the number a chartering manager carries into a negotiation: not the freight they would like, but the freight below which the voyage stops earning the benchmark.
Building the cost side: distance, speed, and sea days
The first input is distance, and distance is not a single number. A voyage estimate needs the laden distance from load port to discharge port and the ballast distance from the ship’s current open position to the load port, because both legs burn fuel and both consume days. Distances come from a routing table or a voyage-distance service that already accounts for the realistic sailing track, not a great-circle straight line, since a ship sails around continents and through traffic-separation schemes, not across them.
Sea days follow from distance and speed. A ship covering 11,000 nautical miles laden at 12 knots is at sea for about 38 days on that leg (11,000 divided by 12, divided by 24). Add the ballast leg the same way. Speed is a choice, not a fixed property, and the speed an estimate assumes drives both the days and the fuel, which is why speed is the single most consequential variable in the whole estimate. Most estimates run at a stated “eco” service speed below the ship’s design speed, because the cubic relationship between speed and fuel, treated below, makes the design speed expensive.
Port days are the other half of the time budget, and they are governed by cargo rates and laytime, not by the ship. A load rate of 30,000 tonnes per day on a 170,000-tonne cargo implies about 5.7 days alongside loading, before any waiting for a berth. Discharge rates are often slower, especially at grain terminals or ports with shore-crane bottlenecks, so a Supramax discharging at 6,000 tonnes a day takes far longer per tonne than a Capesize at a dedicated ore terminal. The laytime allowed in the charter, and the demurrage or despatch that flows from beating or missing it, sit on top of these physical rates; the mechanics are set out in the laytime article. A careful estimate adds a margin of waiting days for ports known to queue, because a voyage that looks profitable on zero waiting can turn negative on a fortnight at anchor.
Bunkers: the cubic speed-fuel law and the cost of fuel
Bunkers are usually the largest single voyage cost, often more than half of total voyage spend on a long ocean passage, and they are where an estimate is most easily wrong. The fuel burned on a leg is daily consumption times days at sea, and daily consumption is not constant: it rises steeply with speed.
The governing relationship is the cubic law, also called the propeller law or the V-cubed law. Hull resistance rises with roughly the square of speed through water, and propulsion power equals resistance times speed, so power scales with about the cube of speed: if resistance is proportional to V-squared, then power is proportional to V-squared times V, which is V-cubed. Daily fuel burn tracks power, so daily bunker consumption also scales with roughly the cube of speed near service speed. The practical consequence is sharp. Cut speed by 10% and required power, and daily fuel, fall by about 27%, because 0.9 cubed is 0.729. The cubic law is an approximation valid near the service speed of a displacement hull; it weakens at very low speeds where auxiliary and hotel loads dominate, and it shifts in heavy weather where added resistance breaks the clean cube. But as the working rule for a voyage estimate it holds, and it is why no estimate quotes a single fuel figure without a speed attached to it.
Consumption converts to tonnes, and tonnes convert to dollars at the price of the relevant fuel grade. A modern ship under the global sulphur cap burns very-low-sulphur fuel oil (VLSFO) at 0.50% sulphur on most of the world’s oceans, and marine gas oil (MGO) where a cleaner or lighter fuel is needed. Each grade carries its own price, and the spread between VLSFO and MGO is itself a cost the estimate must respect, because MGO usually trades at a premium. The bunker voyage cost calculator takes the leg distances, the speed, the consumption curve, and the grade prices and returns the total bunker bill for the laden and ballast legs together. The engine bunker economics calculator goes deeper into the consumption-versus-speed relationship for a specific engine and hull.
ECA fuel switching and the 0.10% limit
Inside an Emission Control Area the fuel rule tightens, and the estimate has to account for it explicitly. Under MARPOL Annex VI Regulation 14, fuel oil used by ships operating in an ECA cannot exceed 0.10% sulphur by mass, against the 0.50% global cap that has applied since 1 January 2020. The 0.10% ECA limit has been in force since 1 January 2015. The designated areas include the Baltic Sea, the North Sea, the North American area, the United States Caribbean Sea area, and the Mediterranean Sea, with further areas designated for the Norwegian Sea and Canadian Arctic. A ship without a scrubber that enters one of these zones must burn a compliant low-sulphur distillate, typically MGO at 0.10% sulphur, which trades above VLSFO.
For a voyage estimate this means splitting the bunker calculation by zone. The miles steamed inside the ECA burn the more expensive 0.10% fuel; the miles outside burn the cheaper VLSFO. On a North Europe to US East Coast voyage a meaningful slice of the passage at each end sits inside an ECA, and ignoring the grade switch understates the bunker bill. A scrubber-fitted ship sidesteps the switch by cleaning the exhaust and burning cheaper high-sulphur fuel oil throughout, which changes its voyage economics against an unscrubbed sister and is part of why scrubber and non-scrubber ships are estimated differently.
Cargo intake: deadweight, stowage, and draught
Freight on a dollars-per-tonne fixture is rate times tonnes, so the tonnes the ship can actually load drive the revenue, and intake is rarely the full deadweight. Three limits compete, and the binding one wins.
Deadweight is the total cargo plus bunkers, fresh water, stores, and constants the ship can carry at its load line. Cargo intake is deadweight minus everything else the ship carries, so a long voyage that needs more bunkers aboard at departure leaves less deadweight for cargo, a real trade-off on a fuel-hungry passage. Stowage factor is the second limit: a light, bulky cargo such as grain or woodchips fills the holds by volume before it reaches the deadweight, so the ship “cubes out” and loads fewer tonnes than its deadweight allows. A dense cargo such as iron ore “deadweights out,” filling the deadweight while the holds are part empty. Draught is the third limit. A load port or discharge port with a depth restriction, or a seasonal load-line zone, can cap the sailing draught below the ship’s full marks, so the ship loads to the draught the port allows rather than to its deepest line. An estimate has to take the smallest of the three as the real intake, and pricing the freight on full deadweight when the cargo cubes out or the port restricts draught overstates the revenue.
Slow steaming: trading days against fuel
Slow steaming is the direct application of the cubic law to the voyage estimate, and it is a genuine optimization with a cost on both sides. Drop the speed and the daily fuel burn falls with the cube of speed, a steep saving. But the same miles now take more days, which adds running cost (the daily crew, stores, and overhead the ship incurs at sea) and ties up the ship longer, deferring the next fixture. The estimate weighs the bunker saved against the days added.
Work it through. A ship that drops from 14 knots to 12.6 knots, a 10% cut, reduces daily propulsion fuel by about 27% per the cube law. On a long ocean leg that is a large absolute tonnage of fuel saved at the VLSFO price. Against it, the leg now takes about 11% longer, so the ship spends more days at sea, burns its lower daily rate over more days, and adds running cost per extra day. Whether slowing down wins depends on the bunker price and the value of a ship-day, which is itself set by the freight market: when freight is strong, a ship-day is worth a lot and slowing down to save fuel can cost more in deferred earning than it saves in bunkers; when freight is weak and bunkers are dear, slowing down is the right call.
The arithmetic is worth stating because the cube law makes the saving non-linear, and intuition undershoots it. Halve the absolute speed and daily fuel falls to one-eighth, since 0.5 cubed is 0.125, but the leg takes twice as long, so total fuel for the leg falls to one-quarter (one-eighth per day over twice the days). That is the deep reason slow steaming saves total voyage fuel and not just daily fuel: the per-day saving outruns the extra days. The limit on the saving is the ship-day value. Each day added at sea is a day the ship is not available for the next fixture, so in a rising market the deferred earning can swamp the bunker saved, and the optimal speed climbs back up. The chartering desk solves this every voyage, and the speed it picks is the one where the marginal day saved at higher speed costs exactly the marginal bunkers that day burns. Below the design speed there is also a mechanical floor: an engine has a minimum continuous load below which it runs poorly or risks fouling, so the estimate cannot assume a speed the engine cannot sustain. The slow steaming savings calculator sizes the bunker saving against the added time for a stated leg, and the weather routing savings calculator quantifies the parallel gain from routing around adverse weather rather than ploughing through added resistance. Slow steaming also lowers a ship’s annual carbon intensity, which ties the operational choice to the regulatory measure treated in slow steaming and CII.
Port costs and disbursements
Port costs are the second-largest voyage cost after bunkers on many fixtures, and they are the least standardized, which makes them the part of an estimate most often carried as a round assumption that later proves wrong. A port disbursement account, the DA, is the itemized bill the local agent presents for a call: port and harbor dues, pilotage in & out, towage, mooring and unmooring gangs, light dues, berth hire, garbage & sludge removal, fresh water, the agency fee itself, and any cargo-handling charges that fall to the ship rather than the charterer. Each line is set by the port authority’s published tariff and the local service providers, so the same class of ship pays different DAs at different ports for reasons that have nothing to do with the cargo.
The variables that move a DA are the ship’s tonnage (most dues scale with gross or net tonnage), the time alongside (berth hire and some dues accrue per day), and the port’s own tariff structure. A ship calling a high-cost European port pays far more than the same ship at a low-cost bulk terminal, and an estimate built on a flat per-call figure across both ports misstates the result. The port DA calculator builds the disbursement from the tariff components rather than a single guess, which matters most on short-sea voyages where two port calls can rival the bunker cost in size. A good estimate sources each major DA from a recent comparable call or an agent’s pro-forma, not from a corporate average.
Canal economics: Suez and Panama
The two interoceanic canals turn a routing question into a cost question, because the toll is large, ship-specific, and unavoidable if the routing uses the canal. Both canals charge on a tonnage basis, but they measure tonnage in their own ways, and a voyage estimate has to use the right basis for each.
Suez Canal Net Tonnage
The Suez Canal charges transit dues on the Suez Canal Net Tonnage (SCNT), a canal-specific net tonnage that differs from the ship’s ordinary net tonnage and is shown on the vessel’s Suez Canal Special Tonnage Certificate, issued by a recognized classification society and confirmed by Suez Canal Authority surveyors. The tolls are set in Special Drawing Rights (SDR) per SCNT ton, the IMF currency basket, and converted to dollars at the SDR exchange rate, which is why a Suez toll quoted today and the same transit next month can differ on the currency alone. The rate structure is tiered: the SDR rate per ton steps down across tonnage brackets as the ship gets larger, and the Authority charges a lower rate for a ship in ballast than for the same ship laden. The Suez SCNT toll calculator applies the bracket structure and the laden-or-ballast distinction to a stated SCNT, and an estimate that uses a flat toll guess instead of the SCNT-based calculation can be off by a wide margin on a large laden transit.
Panama Canal PC/UMS
The Panama Canal has charged on the Panama Canal Universal Measurement System (PC/UMS) since 1 October 1994. One PC/UMS ton equals 100 cubic feet of net volumetric capacity, derived from the International Convention on Tonnage Measurement of Ships, 1969, so the basis is volume of revenue-earning space, not weight. The toll for most commercial ships combines a fixed transit component, which depends on the size class and whether the ship uses the original or the Neopanamax locks, with a per-PC/UMS-ton capacity component whose rate depends on the ship type (tanker, dry bulk, LNG, passenger, container). Full container ships are measured differently, on total TEU capacity including on-deck slots, since a 2005 change. The Panama Canal Authority publishes the tariff and revises it periodically, so an estimate uses the current schedule, not a remembered figure. The Panama PC/UMS toll calculator builds the toll from the fixed and capacity components for the relevant ship type and lock set.
Toll figures change with each tariff revision and with the SDR rate, so an estimate must pull the current published rate rather than carry an old one. The structural point that does not change is the basis: Suez on SCNT in SDR, Panama on PC/UMS in dollars, both tied to a tonnage certificate the ship carries.
Cape versus canal: the routing decision
A canal is a shortcut a ship pays for, and the estimate decides whether the shortcut is worth it. The classic comparison is the canal route against the long way around a cape: Suez against the Cape of Good Hope on Asia-to-Europe trades, Panama against Cape Horn or the Strait of Magellan on certain Pacific-to-Atlantic trades. The canal route is shorter, so it saves sea days and the bunkers those days would burn, but it costs the toll. The cape route avoids the toll but adds thousands of miles, more sea days, more bunkers, and more running cost, and it ties the ship up longer.
The decision is a straight cost comparison inside the estimate: toll plus the canal route’s bunkers and time, against the cape route’s larger bunkers and time with no toll. When bunkers are cheap and the toll is high relative to the miles saved, the cape can win, which is what drove the large-scale rerouting of tankers and bulkers around the Cape of Good Hope during periods of Red Sea disruption. When bunkers are expensive and the canal saves a long passage, the toll is easily justified. Ship size matters too: a Capesize too large for the canal in its laden trade has no choice & routes by the cape, which is the origin of the class name. The estimate makes this explicit by running both routings to a TCE and taking the higher, rather than assuming the canal is always the answer.
Break-even freight and the ballast bonus
Two figures fall out of the estimate that a chartering desk reads directly. Break-even freight is the freight rate at which the voyage TCE equals a chosen benchmark, usually the daily running cost or a target hire. Below break-even the voyage earns less per day than the benchmark and loses money against it; above it the voyage earns a margin. The break-even is what an owner needs to know before quoting: it is the floor under the negotiation. The break-even freight calculator solves for it given the target daily earning and the voyage costs.
The ballast bonus is the other figure, and it addresses an asymmetry the freight alone hides. When a charterer wants a ship that is open far from the load port, the ship must ballast a long way to start the cargo, burning fuel and spending days with no revenue. A ballast bonus is a lump sum the charterer pays to compensate for that positioning leg, agreed on top of the freight or hire. In the voyage estimate the bonus is revenue that offsets the cost of the ballast leg, and an owner positioning a ship into a distant load region prices the bonus to recover the ballast bunkers and the days lost. The laden-versus-ballast split runs through the whole estimate: the laden leg earns freight and the ballast leg does not, but both burn fuel and both count in round-voyage days, which is why an estimate that ignores the ballast leg flatters the voyage.
Comparing the estimate to the spot benchmark
A voyage estimate is not finished when it produces a TCE; it is finished when that TCE is set against the market. The market level comes from the Baltic Exchange, which publishes many dry-bulk routes as a dollar-per-day TCE for a defined standard ship, the consensus of a panel of shipbrokers reporting where real cargoes are fixing. An owner’s estimate beating the relevant Baltic route TCE is the evidence of a well-traded book; trailing it flags a voyage that the market would price higher elsewhere. The full machinery of the indices, the route codes, the panel method & the Worldscale system that prices tanker freight, is set out in the Baltic Dry Index and freight indices article.
The benchmark also structures the spot-versus-period choice. A spot fixture is a single voyage at today’s rate, estimated as above. A period charter fixes the ship for months at an agreed daily hire. An owner compares the spot voyage TCE, and the forward curve of expected spot TCEs, against the period hire on offer: if the period rate sits above where the forward market values the spot earnings over the same horizon, fixing period locks in a premium; if below, staying spot keeps the upside. Both sides of that decision run on the same index data, so the estimate and the benchmark are not separate exercises but two ends of one calculation. The charter TCE voyage calculator runs the voyage-versus-charter comparison for a specific cargo, and the Capesize TCE calculator does the class-specific version for iron-ore and coal fixtures.
A worked shape of the estimate
Put the pieces together on a single dry-bulk voyage to show how they interact, without inventing precise figures that would date. Take a Panamax open in the Far East, fixed to ballast to the US Gulf, load grain, and carry it to North Europe. The estimate starts with the ballast distance from the open position to the US Gulf and the laden distance from the US Gulf to the discharge range, each divided by the assumed speed for sea days. It adds load days at the grain elevator’s rate and discharge days at the European terminal’s rate, plus a margin for the queue at a busy export berth.
Bunkers come next: ballast-leg consumption at the chosen speed times ballast days, plus laden-leg consumption times laden days, with the slice inside the North European ECA priced at 0.10% MGO and the rest at VLSFO. Port DAs at the US Gulf load port and the European discharge port come from agent pro-formas, not a flat guess. The grain cubes the ship out before it deadweights out, so the intake is the volumetric limit, and the freight is rate times that intake. Gross freight minus the bunkers, the two DAs, and any voyage extras gives the voyage result; dividing by the full round-voyage days gives the TCE. That TCE is then set against the published Baltic Panamax route for the comparable trade. If it trails the index, the desk looks for a better cargo or a back-haul to lift the round-voyage earning; if it beats the index, the voyage is worth fixing. Every number in that chain is a real input the calculators in this cluster compute, which is the point of building the estimate as a structured P&L rather than a single guess.
Limitations
A voyage estimate is a forecast, and every input carries uncertainty. Bunker prices move daily, so an estimate priced on today’s VLSFO and MGO is only as good as the bunkers actually stemmed; a voyage fixed weeks ahead can see its largest cost shift before the ship loads. Port costs are quoted from agent pro-formas that omit lines or underestimate berth hire, and a port that queues longer than assumed adds waiting days that the freight does not cover. Speed and consumption assume a clean hull in moderate weather; a fouled hull, heavy weather, or strong adverse current raises consumption above the cube-law figure and stretches the sea days, which is why a prudent estimate carries a weather and sea margin rather than the calm-water optimum.
The cubic speed-fuel law is an approximation, accurate near the service speed of a displacement hull and degrading at very low speeds where auxiliary and hotel loads dominate and in heavy weather where added resistance breaks the clean cube. Canal tolls change with each Authority tariff revision and, for Suez, with the SDR exchange rate, so an estimate must use the current published schedule rather than a remembered figure; the toll calculators here apply the published basis but the operator must confirm the live rate before fixing. The TCE itself excludes the ship’s running and capital cost by design, so a positive TCE is not the same as a profitable voyage: the running cost still has to be netted against it, which is what the voyage profit calculator does. Finally, an estimate prices one voyage in isolation, while a real chartering position weighs the next cargo the ship can reach, the back-haul that lifts the round-voyage earning, and the freight-market direction; the estimate is the necessary first step, not the whole decision.
See also
- Time charter equivalent calculator: converts voyage freight and costs into dollars per day on a timecharter basis.
- Voyage profit calculator: full voyage profit-and-loss netting TCE against running cost.
- Break-even freight calculator: solves for the freight per tonne needed to hit a target daily earning.
- Bunker voyage cost calculator: laden and ballast bunker bill from distance, speed, consumption, and grade price.
- Slow steaming savings calculator: bunker saving against added time for a speed reduction.
- Weather routing savings calculator: fuel and time gain from routing around adverse weather.
- Port DA calculator: port disbursement account built from tariff components.
- Suez SCNT toll calculator: Suez transit dues on Suez Canal Net Tonnage in SDR, laden and ballast.
- Panama PC/UMS toll calculator: Panama transit toll on PC/UMS measurement, fixed and capacity components.
- Engine bunker economics calculator: consumption-versus-speed economics for a specific engine and hull.
- Charter TCE voyage calculator: voyage-versus-charter TCE comparison for a specific cargo.
- Capesize TCE calculator: Capesize-specific voyage TCE for iron-ore and coal fixtures.
- Baltic Dry Index and freight indices: the spot-market benchmark a voyage estimate is reconciled against.
- Slow steaming and CII: how the speed choice in an estimate ties to the carbon-intensity regulation.
- Laytime: the voyage-charter time accounting behind port days, demurrage, and despatch.