Marine & Nautical
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Ship Fuel Consumption

Fuel burn rises with the cube of speed for a ship.

Formula

F=c v3F = c\, v^3

Variables

FFuel rate
cConstant
vSpeed

Example

Cutting speed 20% saves roughly half the fuel (0.8³≈0.51).

How it works

This relation says that a ship’s required fuel rate grows very rapidly as speed increases: if speed doubles, the fuel burn rises by a factor of 8. The cubic dependence is an engineering approximation that comes from the fact that water resistance increases strongly with speed, and the engine must supply more power to overcome that drag. The constant c captures the hull shape, propeller efficiency, loading, and sea conditions, so different ships can have very different fuel use at the same speed.

When to use it

Use this for quick estimates of how changing cruising speed affects fuel consumption on the same vessel in similar conditions. It is especially useful in voyage planning, cost trade-offs, and comparing fuel savings from small speed reductions.

Worked example, step by step

A cargo ship has c = 0.18 and is sailing at v = 14 knots. Step 1: Write the formula: F = c v^3 Step 2: Substitute the values: F = 0.18 × 14^3 Step 3: Calculate the cube: 14^3 = 2744 Step 4: Multiply: F = 0.18 × 2744 = 493.92 Final answer: the fuel rate is about 494 units per hour (in whatever units match c).

Common mistakes to avoid

  • Using speed squared instead of speed cubed
  • Forgetting that c depends on the specific ship and conditions
  • Comparing fuel rates at different loads or sea states without adjusting the constant

Did You Know?

'Slow steaming' exploits this cube law — shipping lines cut speed to slash fuel bills and emissions.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026