Why does fuel consumption scale with speed cubed?

A ship's propulsion power needed to overcome hull resistance rises roughly with the cube of speed, and daily fuel consumption tracks power. So consumption at a new speed is the reference consumption times (new speed / reference speed) cubed. Halving speed cuts daily burn to about an eighth.

Does slow steaming always save money?

It saves fuel, but slower speed lengthens the voyage, which adds charter hire, crew, and other time-based costs. The fuel saving is real and large, but the net benefit depends on whether those daily costs outweigh it. This tool isolates the fuel side.

How is passage time calculated?

Passage time in days is the distance in nautical miles divided by speed in knots, divided by 24. At 12 knots a 2,400-mile passage takes 2400 / 12 / 24 = 8.33 days. Lower speed increases time, which partly offsets the lower daily consumption.

What is the port idle consumption for?

While in port a vessel still burns fuel for auxiliary engines, boilers, and cargo gear. Adding idle days times idle consumption per day captures this, so the total reflects the whole call, not just the sea passage.

Is total fuel just daily consumption times days?

Yes. Sea fuel is the speed-adjusted daily consumption times passage days; port fuel is idle consumption times idle days. Multiplying total tonnes by the bunker price per tonne gives the bunker cost. The cube law only affects the sea-fuel daily figure.

Sea Passage Fuel Cost Calculator

A ship’s fuel bill is dominated by one relationship: burn rises with the cube of speed. That makes speed the biggest lever on voyage fuel cost, and slow steaming a powerful saving. This calculator applies the cube law to compare bunker cost across several speeds for a passage, including port idle consumption.

How it works

Daily sea consumption at a chosen speed is scaled from a known reference point by the cube of the speed ratio. Multiply by passage days for sea fuel, add port idle fuel, and price it:

daily_at_speed = ref_consumption × (speed / ref_speed)³
passage_days   = distance_nm / speed_kn / 24
sea_fuel       = daily_at_speed × passage_days   (tonnes)
port_fuel      = idle_consumption × idle_days     (tonnes)
bunker_cost    = (sea_fuel + port_fuel) × price_per_tonne

Because consumption falls as the cube of speed but time only rises linearly, the net effect of slowing down is a large reduction in total sea fuel.

Example and tips

Take a ship that burns 40 t/day at a reference 14 knots over a 2,400 nm passage. At 14 knots the passage is 7.14 days and burns about 286 tonnes. Drop to 12 knots and daily burn falls to 40 × (12/14)³ ≈ 25.2 t/day; the passage lengthens to 8.33 days but total sea fuel drops to about 210 tonnes — a 27 percent saving. At 600 per tonne that is roughly 45,000 saved on fuel alone. Weigh that against the extra 1.2 days of hire and crew cost before committing to the slower speed.