Choosing a vessel’s speed is a commercial decision, not just a nautical one. Going faster burns dramatically more fuel; going slower racks up more days of charter hire. This calculator sweeps a range of speeds and finds the one that minimises the total voyage cost for your distance, bunker price, and hire rate.
How it works
Bunker consumption is modelled with the classic cube law, where consumption at speed V relates to a known reference point:
consumption(V) = ref_consumption × (V / ref_speed)^3 tonnes/day
voyage_days = distance / (V × 24)
fuel_tonnes = consumption(V) × voyage_days
fuel_cost = fuel_tonnes × bunker_price
hire_cost = voyage_days × daily_hire
total_cost = fuel_cost + hire_costThe tool evaluates total_cost at every speed in half-knot steps across your range and reports the minimum. Because fuel rises with the cube of speed while days fall only linearly, the cost curve is U-shaped and has a clear minimum somewhere in the middle.
Why the cube law produces a U-shaped cost curve
At the design speed the two costs are in balance for some hire-to-bunker ratio. Push the speed up and fuel cost climbs steeply (cubed relationship) while hire cost drops only in proportion to fewer days — the extra fuel wins, total cost rises. Push speed down and fuel savings are linear in days but the extra hire days add up — hire cost eventually dominates and total cost rises again. The minimum sits at the crossover, and where exactly that falls depends on the ratio of daily hire to bunker price per tonne.
When bunkers are cheap relative to hire, the optimal speed is closer to the design speed (hire savings are worth spending a bit more on fuel). When bunkers are expensive, slow steaming makes more sense. This calculator lets you see the curve shift as you change the input prices.
Worked example
For illustration: a handysize vessel burns 45 t/day at a reference speed of 14 knots over a 5,000 nm voyage. With bunkers at USD 620/t and hire at USD 18,000/day:
- At 14 knots: voyage days ≈ 14.9, fuel tonnes ≈ 671, fuel cost ≈ USD 416,000, hire ≈ USD 268,000, total ≈ USD 684,000.
- At 11 knots: voyage days ≈ 18.9, fuel tonnes ≈ 437 (consumption drops by the cube ratio), fuel cost ≈ USD 271,000, hire ≈ USD 341,000, total ≈ USD 612,000.
- At 9 knots: voyage days ≈ 23.1, fuel tonnes ≈ 240, fuel cost ≈ USD 149,000, hire ≈ USD 416,000, total ≈ USD 565,000.
These are illustrative figures — the exact minimum moves with your specific inputs. The calculator finds it automatically across the speed range you set.
Practical notes for operators
- Use noon-report consumption, not design specs. Hull fouling, propeller pitch, and trim all shift the actual consumption curve away from the shipyard figure.
- Add a weather margin. If the route has predictable headwinds or swell, build in contingency on voyage days before committing to the optimal speed.
- Laytime and demurrage. If arriving early incurs waiting time at berth, the hire clock may run anyway — factor demurrage risk into the voyage-days benefit of going faster.
- Port surcharge windows. Some ports or canals charge differently based on arrival time, which can override the pure speed-optimisation result.