Why does fuel burn scale with the cube of speed?

Hull resistance rises roughly with the square of speed, and power equals resistance times speed, so required power and fuel burn scale with the cube. Going 10 percent faster needs about 33 percent more fuel per day, which is why slow steaming saves so much.

What is the reference consumption?

It is the vessel's daily fuel burn in metric tonnes at a stated reference speed, from the trial data, charter party description, or noon reports. The tool scales it to your planned speed, so the more accurate this baseline, the better the estimate.

How is the total voyage fuel found?

Daily burn at the planned speed equals reference burn times (planned speed over reference speed) cubed. Voyage days equal distance divided by speed divided by 24. Multiply daily burn by voyage days for total tonnes, then by bunker price for cost.

Does this include port and auxiliary consumption?

No. It estimates main-engine propulsion fuel at sea only. Add separate allowances for auxiliary engines, boilers, port stays, and manoeuvring, which can be a meaningful share of total bunkers on short voyages with long port times.

How accurate is the cube law in practice?

It is a solid first-order estimate but real exponents range from about 2.7 to 3.5 depending on hull, draft, fouling, weather, and sea state. Use it for planning and charter screening, then refine against actual noon reports for the specific vessel and route.

Ship Fuel Consumption Calculator

Fuel is the largest variable cost of a voyage, and it is exquisitely sensitive to speed. This calculator takes a vessel’s known daily burn at a reference speed, scales it to your planned speed using the cube law, and multiplies through the voyage distance and bunker price to give total tonnes and cost.

How it works

Propulsion power, and therefore fuel burn, rises with roughly the cube of speed. The tool scales a reference daily consumption accordingly and rolls it across the voyage:

daily burn (mt/day) = ref daily × (planned speed / ref speed)³
voyage time (days)  = distance / speed / 24
total fuel (mt)     = daily burn × voyage days
bunker cost         = total fuel × price per tonne

Because of the cube term, a small speed cut produces a large fuel saving: dropping from 14 to 12 knots cuts daily burn by roughly 37 percent, the heart of the slow-steaming economics that dominate liner and tramp operations.

Example and tips

A vessel burning 35 mt/day at a reference 14 knots, planned at 12 knots over 3360 nautical miles: daily burn falls to 35 × (12/14)³ ≈ 22.0 mt/day, the passage takes 3360 / 12 / 24 ≈ 11.67 days, so total fuel ≈ 257 mt. At a bunker price of 600 per tonne that is about 154,000. Run it again at 14 knots and you will see the burn jump despite the shorter voyage — the cube law usually beats the time saving. Treat the result as a planning estimate and refine against real noon reports.