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 tonneBecause 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.
Worked example — slow steaming vs. design speed
A vessel burning 35 mt/day at a reference 14 knots over a 3,360 nm voyage:
| Speed | Daily burn | Voyage days | Total fuel | Cost at 600/t |
|---|---|---|---|---|
| 14 knots (ref) | 35.0 mt | 10.0 days | 350 mt | 210,000 |
| 12 knots | 22.0 mt | 11.7 days | 257 mt | 154,000 |
| 10 knots | 12.6 mt | 14.0 days | 176 mt | 106,000 |
Slowing from 14 to 12 knots adds 1.7 days to the voyage but saves about 93 mt of bunkers — a saving of roughly 56,000. Slowing further to 10 knots saves another 81 mt but adds 2.3 more days. Whether slow steaming is worthwhile depends on the value of time (charter hire per day) relative to the fuel saved per day. The cube law almost always favours slowing when bunker prices are high relative to hire.
Why the cube law is only approximate
The cube-law exponent of 3.0 is a rule of thumb. In practice, the real exponent varies:
- Hull form — finer hulls (container ships, LNG) often have exponents closer to 2.7; full-form vessels (VLCCs, bulk carriers) can be 3.2 or higher.
- Draft and trim — a vessel in ballast has a different hull resistance curve than at design draft.
- Fouling — a fouled hull increases resistance at every speed, raising the effective baseline consumption.
- Sea state and current — adverse weather inflates consumption in ways the cube law cannot capture.
Use the tool’s output as a planning estimate for voyage budgets and fixture comparisons, then refine against the vessel’s actual noon reports for that route and season.
What this calculator does not include
This tool estimates propulsion fuel at sea only. A full bunker estimate should also include:
- Auxiliary generator fuel — running hotel loads, cargo gear, and reefer containers.
- Port consumption — main engine or auxiliary fuel during loading, discharging, and shifting.
- Boiler consumption — relevant for tankers with steam heating or steam-turbine vessels.
- Manoeuvring — approach and departure from port, canal transits, and pilotage.
For a complete voyage estimate, add these as separate allowances based on the vessel’s own data sheets or operational records.