Calculate · Explore · Learn

Maritime Math Center

Explore nautical units, passage illustrations, boat budgets, marine science and port operations. 50 tools with purposes, formulas and worked examples.

Simple mode uses starting defaults for extra scenario controls. Advanced exposes those controls where available. Change an entry, then press Calculate.

Find a tool

Choose a tool

Formula, calculation steps & example

All 50 tools: purposes and formulas

Nautical miles to kilometers — Convert the named marine measurement units.
Output = input × 1.852
Kilometers to nautical miles — Convert the named marine measurement units.
Output = input × 0.5399568034557235
Knots to kilometers per hour — Convert the named marine measurement units.
Output = input × 1.852
Kilometers per hour to knots — Convert the named marine measurement units.
Output = input × 0.5399568034557235
Knots to statute miles per hour — Convert the named marine measurement units.
Output = input × 1.1507794480235425
Miles per hour to knots — Convert the named marine measurement units.
Output = input × 0.8689762419006479
Fathoms to meters — Convert the named marine measurement units.
Output = input × 1.8288
Meters to fathoms — Convert the named marine measurement units.
Output = input × 0.5468066491688539
US marine fuel gallons to liters — Convert the named marine measurement units.
Output = input × 3.785411784
Liters to US marine fuel gallons — Convert the named marine measurement units.
Output = input × 0.26417205235814845
Distance at constant speed — Estimate distance traveled from average speed over ground.
Distance NM = knots × hours
Travel time over water — Estimate time from distance and average speed over ground.
Hours = distance NM / speed knots
Required average passage speed — Solve average speed for a distance and time window.
Knots = distance NM / hours
Two-leg passage time — Add modeled times for two legs with different speeds.
Hours = distance A/speed A + distance B/speed B
Fuel-limited distance illustration — Estimate range from usable fuel and steady consumption.
Range NM = usable liters / liters per hour × knots
Along-track current speed model — Add a following current or subtract an opposing current.
Ground speed = through-water speed + signed along-track current
Current vector ground speed — Combine through-water motion with a current at a relative angle.
Ground speed = sqrt(boat² + current² + 2×boat×current×cos(angle))
Reciprocal bearing — Find the opposite direction of a bearing.
Reciprocal = (bearing + 180) modulo 360
Degrees, minutes, seconds to decimal — Convert a nonnegative angular measurement.
Decimal degrees = degrees + minutes/60 + seconds/3600
Smallest angle between bearings — Find the unsigned smaller angle between two headings.
Difference = min(|A−B|, 360−|A−B|)
Trip fuel budget — Calculate cost from hours and average fuel consumption.
Cost = hours × liters/hour × price/liter
Engine fuel consumed — Estimate fuel used during engine operation.
Liters = hours × liters/hour
Fuel remaining after a reserve — Set aside an entered percentage of tank fuel.
Budgeted liters = available × (1 − reserve%/100)
Annual engine hours — Convert average usage into an annual hours budget.
Annual hours = hours/week × weeks used
Boat maintenance savings — Spread an annual maintenance budget across deposits.
Deposit = annual maintenance budget / deposits per year
Mooring stay budget — Estimate a berth cost charged per night plus fees.
Cost = nightly rate × nights + fixed fees
Charter cost per person — Split a fixed charter price equally.
Per person = total budget / people
Crew water budget — Multiply an entered daily water allowance by people and days.
Water liters = allowance × people × days
Battery nominal energy — Convert rated voltage and amp-hours to nominal energy.
Watt-hours = volts × amp-hours
Solar energy illustration — Model daily generation from panel power and equivalent full-sun hours.
Daily Wh = watts × full-sun hours × yield share
Displaced water volume — Use mass and water density to estimate displaced volume.
Displaced volume = mass / fluid density
Mass of displaced water — Calculate displaced fluid mass from volume.
Fluid mass = displaced volume × density
Buoyant force illustration — Calculate force from displaced fluid density and volume.
Buoyant force = density × volume × gravity
Hydrostatic gauge pressure — Explore pressure below a static fluid surface.
Gauge pressure = density × gravity × depth
Salinity mass mixing lesson — Combine two water masses with entered salt mass fractions.
Mixture salinity = (mass A×salinity A + mass B×salinity B)/(mass A+mass B)
Rectangular boat tank volume — Estimate internal volume from rectangular dimensions.
Liters = length × width × liquid height × 1000
Vertical cylinder tank volume — Estimate fluid in a vertical cylindrical tank.
Liters = π × radius² × liquid height × 1000
Pumping time model — Estimate time to pump a given volume at an effective flow.
Minutes = volume / effective flow
Pumped volume model — Calculate volume moved at a steady effective flow.
Volume = effective flow × runtime
Wave period to frequency — Convert an oscillation period to frequency.
Frequency = 1 / period
Cargo lot mass — Total the mass of identical cargo units.
Total tonnes = unit kg × units / 1000
Container TEU equivalent — Express counts of 20-foot and 40-foot containers in TEU.
TEU = 20-foot count + 2 × 40-foot count
Cargo handling time — Estimate time at a constant effective handling rate.
Hours = cargo tonnes / effective handling rate
Rectangular cargo volume — Total the external volume of identical packages.
Volume = length × width × height × count
Cargo bulk density — Relate cargo mass to occupied volume.
Bulk density = mass / occupied volume
Cargo stowage factor — Calculate occupied volume per metric tonne.
Stowage factor = occupied volume / cargo tonnes
Rope coil length geometry — Model rope length from circular coil size and turn count.
Length = π × mean diameter × turns
Dock deck area — Calculate a rectangular deck surface area.
Area = length × width
Handling cost per tonne — Spread a handling invoice across cargo mass.
Unit cost = handling cost / cargo tonnes
Berth time utilization — Calculate occupancy as a fraction of available time.
Utilization % = occupied hours / available hours × 100

Definitions and source references

Unit definitions and selected model references:

Save this math resource for later
Save to Pinterest