Voyage Bunker Cost Calculator: Speed, Consumption, Price

Formula, assumptions, and limits

A leg’s bunker cost is the tonnes of each fuel grade the voyage burns multiplied by their delivered prices per tonne. To calculate it, take sea days from distance and speed, scale the main-engine burn by the cubic law, add the auxiliary burn across sea and port days, and price each grade:

$$t_{sea} = \frac{d}{24v} \qquad W_{ME} = t_{sea} \cdot w_0 \left(\frac{v}{v_0}\right)^3 \qquad B = W_{ME} , p_{ME} + (t_{sea} + t_{port}) , w_{aux} , p_{aux}$$

d - leg distance in nautical miles; v - voyage speed in knots. w_0 - main-engine consumption at the reference speed v_0, from the ship’s description or recent noon reports. w_aux - auxiliary consumption per day, sea and port. p_ME, p_aux - prices per tonne for the two grades.

The cubic law is the working approximation for displacement hulls in their service range: resistance grows roughly with speed squared, power is resistance times speed, so daily burn tracks the cube. Two things follow. Tons for a fixed leg fall with roughly the square of the speed ratio, because the lower daily burn applies across more days; and the approximation has edges: it weakens near hull speed, in heavy weather, with fouling, and at very low loads where specific consumption rises and turbocharger and auxiliary-blower behavior change the picture. Use a reference point from the ship’s actual performance (recent noon reports beat the builder’s description) and treat sweeps far from it as indicative.

What the tool deliberately excludes: hire and the rest of the voyage estimate (a slower leg saves bunkers and spends days, and only the full estimate nets those), weather and current margins, ECA stretches that force the main engine onto the distillate grade mid-leg (split the leg and run each part), and boiler consumption for tanker cargo heating, which is its own line in any complete estimate.

How to use this calculator

1. Enter the leg distance and the intended speed.
2. Enter the reference speed and the main-engine consumption at it.
3. Enter the auxiliary daily burn and the port days on the leg.
4. Enter the two grades’ prices from a live bunker quotation.
5. Read sea days, tons by grade, and the cost; the sweep chart shows the cost across the speed range, where the slow-steaming saving and the auxiliary claw-back are both visible.

Worked example

A 4,000 nm leg at 12 knots on a ship described at 24 t/day at 14 knots, auxiliaries 3.5 t/day, two port days. Sea days: 4,000 / (24 × 12) = 13.9. Daily main burn at 12 knots: 24 × (12/14)³ = 15.1 t/day, so the leg burns 209.9 t of the main grade. Auxiliaries: 15.9 days × 3.5 = 55.6 t of distillate. At USD 520/t for the main grade and USD 760/t for MGO the leg costs 209.9 × 520 + 55.6 × 760 ≈ USD 151,420, the figure the calculator renders from the unrounded tonnages. The same leg at 14 knots burns 285.7 t main fuel over 11.9 sea days and costs about USD 185,560: roughly USD 34,100 more in bunkers to save two days. Whether two days are worth USD 34,100 is the hire side’s question, which is exactly why this page stops at bunkers.

The reference point and the charter party

The reference speed and consumption pair is the calculation’s anchor, and where it comes from matters. The charter-party description states warranted figures, usually qualified by “about”, which arbitration practice has long read as a tolerance in the order of half a knot on speed with a margin on consumption, tailored to the particular vessel rather than fixed; performance claims are fought on those words. For estimating, recent noon reports in comparable conditions beat the description: they carry the ship’s present fouling, trim habits, and weather reality. Use the description when nothing better exists, and expect the warranted figures to flatter a ship that is due for a hull cleaning.

Common errors

1. Using the charter-party description as gospel. Warranted figures are benchmarks for performance claims; real consumption comes from noon reports, and fouling or weather can sit well above the description.
2. Applying the cubic law across grades. The law scales the main engine’s burn; auxiliaries and boilers run on their own clocks and often on a different, dearer grade.
3. One price for two fuels. MGO commonly runs hundreds of dollars above the residual grade per tonne; pricing the auxiliary tons at the main-grade price flatters the estimate.
4. Ignoring ECA stretches. Inside an emission control area the main engine burns the distillate grade too; a leg that crosses one needs splitting, or the cost lands wrong by the price spread times the tons inside the zone.
5. Reading the sweep as a voyage estimate. Bunker cost always falls with speed; the days it spends are not free, and only the full estimate with hire decides the optimal speed.

About This Voyage Bunker Cost Calculator

Two days of voyage time cost about USD 34,100 in bunkers on the worked leg above. That ratio, days bought against tonnes burned, is what this page exists to expose, and the speed-consumption relationship behind it is the strongest lever an operator holds over the largest variable cost of most voyages. The inputs are the figures an estimating desk actually holds: distance, speed, the ship’s reference consumption, auxiliary burn, port days, and live prices for the two grades.

The arithmetic is the estimator’s standard: sea days from distance and speed, the cubic law scaling the main-engine burn from the reference point, auxiliaries per day across sea and port, each grade priced separately. The cubic relationship is the documented service-range behavior of displacement hulls (the IMO’s GHG studies build their speed-reduction scenarios on it), and its limits, near hull speed, in weather, at very low loads, are stated rather than hidden.

The sweep chart draws the leg’s bunker cost across the speed range around your entry, so the shape of the slow-steaming saving is plain: steep where the cube bites, flattening as the auxiliary days accumulate. The bunker adjustment factor article covers how this cost passes through to freight on liner trades, and the bunker quality article covers what the tonnes you pay for must conform to; for the emissions side of the same tonnes, the CII attained calculator turns fuel into rating.

Further reading

• Bunker quality and ISO 8217
• Bunker adjustment factor
• CII attained calculator
• Ocean freight cost calculator

Frequently asked questions

How do you calculate bunker consumption for a voyage?

Sea days are the distance divided by speed times 24. Main-engine consumption scales with roughly the cube of speed, so daily burn at the voyage speed is the reference consumption times (speed / reference speed) cubed, and the leg's tons are that daily figure times the sea days. Auxiliary burn runs per day at sea and in port on its own grade.

Why does fuel consumption scale with the cube of speed?

Resistance on a displacement hull grows roughly with the square of speed, and power is resistance times speed, giving the cubic relationship between speed and daily fuel burn. It is a service-range approximation: it weakens near hull speed, in heavy weather, and at very low engine loads.

How much fuel does slow steaming save?

Daily burn falls with the cube of speed while the voyage lengthens only linearly, so the tons for the leg fall roughly with the square of the speed ratio: a 10 percent speed cut saves about 19 percent of main-engine tons on the leg, before the extra sea days' auxiliary burn claws a little back.

How much fuel does a cargo ship use per day?

It depends on size, speed, and hull condition, and the spread is wide. The worked example's mid-size bulk carrier burns 24 tonnes of main-engine fuel per day at 14 knots and 15.1 at 12 knots through the cubic law, plus 3.5 tonnes of distillate for auxiliaries; large container ships at service speed burn several times those figures. The reliable number for a specific ship comes from its noon reports.

Which bunker grades should the prices reflect?

Whatever the ship actually burns on the leg: typically a VLSFO or HSFO main grade (HSFO with a scrubber) and MGO for auxiliaries and ECA stretches. Prices move daily by port; take them from a live bunker quotation, and remember ECA legs that force the main engine onto the distillate grade.