Maritime calculators

Calculators for ship staff, superintendents and cadets: fuel and voyage cost, emissions and CII, hydrostatics and stability, propulsion, navigation and cargo. Each one shows the formula, its assumptions and a worked example, and names the convention or rule it follows.

• Added resistance in waves (STAwave-1)ISO 15016 STAwave-1 added resistance in head waves from beam, bow length and significant wave height, with the power increase at speed.
• Admiralty coefficient and speed–power scalingAdmiralty and fuel coefficients from a known point; power or speed at a new displacement and speed (cube or chosen exponent), with fuel per day and per mile.
• Air draft and bridge clearanceClearance under a bridge or power cable from the charted clearance, tide, the ship's air draft at its actual draft and trim, and the allowances.
• Alternative fuel tank volumeMass, volume and tank capacity of LNG, methanol, ammonia, hydrogen, LPG or biofuels carrying the same energy as a quantity of oil fuel.
• Anchor cable catenary and scopeAnchor cable catenary: chain on the bottom, uplift at the anchor, hawse tension, maximum force before the anchor lifts, wind force, holding and swinging radius.
• Ballast water exchange timeD-1 ballast exchange: sequential, flow-through and dilution times and distance, the 3-volume / 95 % rule from perfect mixing, and the location criteria.
• Beaufort, wind speed and sea state converterConvert between Beaufort force, wind speed, probable wave height and Douglas sea state using the WMO tables.
• Berthing energy and fender selectionPIANC berthing energy from displacement, approach velocity and the mass, eccentricity, configuration and softness factors; fender energy and reaction.
• Bilged compartment (lost buoyancy)Sinkage, end drafts, trim, freeboard and the new GM of a box-shaped vessel after a compartment is bilged, by the lost buoyancy method.
• Bollard pull for a towTowing force to hold a tow in wind, waves and current (DNV method: wind, current and wave-drift forces) and the tug bollard pull required with tug efficiency.
• Bunker quantity and density correctionBunker mass in vacuo and in air from sounded volume, temperature and density at 15 °C (Table 54B VCF), with energy content, cost and BDN comparison.
• Cargo securing (CSS Code Annex 13)Design accelerations, forces and the sliding and tipping balance of a lashed cargo unit by the CSS Code Annex 13 advanced calculation method.
• Cargo ventilation and dew pointDew point and humidity from dry and wet bulb, ventilate-or-not decision by the three-degree and dew-point rules, condensation risk.
• Cathodic protection anodesSacrificial anode mass, number and life for a hull or tank from surface area, coating breakdown and current density (DNV-RP-B401).
• Charter party performance claimTime lost and over-consumption against the warranted speed and consumption by the good-weather method, with the "about" allowances and the claim value.
• CII rating estimatorAttained and required operational CII with the A–E rating, from ship type, capacity, annual fuel or CO₂ and distance.
• Compass error by amplitude or azimuthTrue bearing of the sun or another body by amplitude or time azimuth, then the compass error and deviation from the observed bearing.
• Course to steer with set and driftCourse to steer, speed over ground and passage time to make good a track through a current of known set and drift, with leeway.
• CPA and TCPA from radar plotsTarget course and speed, closest point of approach and its time, bow crossing, aspect and the alteration for a safe passing distance.
• Draft surveySix observed drafts to corrected drafts, quarter-mean draft, trim and density corrections, net displacement and cargo or constant from the hydrostatic tables.
• Dry-docking critical instantUpthrust on the keel blocks and the virtual loss of GM at the critical instant of dry-docking, the draft then, and the largest safe trim.
• Enclosed space purge timeVentilation time for a tank or enclosed space to reach the entry criteria for oxygen, flammable and toxic gas, by dilution with a mixing factor.
• Energy-saving device paybackPayback, NPV, IRR and levelized cost of a fuel-saving retrofit from the saving, fuel and ETS prices, life and discount rate.
• Engine-room ventilation (ISO 8861)Combustion air and heat-removal airflow for an engine room from installed power and heat emissions, fan capacity and air changes.
• EU ETS and FuelEU MaritimeEU ETS allowances and cost with phase-in and voyage scope; FuelEU Maritime GHG intensity against the yearly limit, compliance balance and penalty.
• Fixed CO₂ fire-extinguishing systemRequired CO₂ quantity, cylinders and minimum discharge rate for machinery, cargo, bulk and vehicle spaces under the FSS Code chapter 5.
• Fuel blending and heating viscosityBlend viscosity (Refutas), density and sulphur of two fuels, and the injection or preheating temperature from ASTM D341.
• Fuel changeover before an ECATime and distance before an emission control area to start the changeover so that the fuel at the engines meets the sulphur limit, within the temperature rate.
• Fuel consumption and voyage costFuel burned, time at sea, bunker cost and CO₂ for a passage from distance, speed and engine power or daily consumption.
• Fuel net specific energy and CO₂ factorISO 8217 net and gross specific energy from density, water, ash and sulphur; CO₂ factor by IMO grade or carbon content; g CO₂/MJ.
• Great-circle and rhumb-line distanceGreat-circle distance, initial and final courses, vertex and midpoint, rhumb-line distance and course, WGS-84 geodesic and passage time.
• GZ curve and intact stability criteriaIS Code 2008 general criteria and the severe wind and rolling (weather) criterion from a pasted GZ curve, with the grain heeling check.
• Holtrop–Mennen resistance and powerHoltrop–Mennen (1982/1984) resistance components, effective and brake power, wake fraction and thrust deduction from main particulars.
• Hull roughness and fouling penaltyAdded resistance, power, fuel and speed loss from hull roughness or fouling via the ITTC-57 line and the ISO 15016 roughness allowance.
• Hydrostatics basicsDisplacement from draft and block coefficient, TPC, fresh and dock water allowance, trim and end drafts from LCG, LCB and MCTC.
• Inclining experimentGM and lightship KG from an inclining test: weight-movement moments against pendulum tangents by least squares, free surface and the lightweight survey.
• Initial stability GM and listGM from KM and KG with free-surface correction, list from a weight shift, loading or discharge, rolling period and the IMO minimum-GM check.
• Light, radar and VHF rangeGeographic and luminous range of a light, radar and VHF line-of-sight ranges, and the COLREG minimum intensity of a navigation light.
• Loading condition from an item listDisplacement, deadweight, KG with free surface, GM, trim, end drafts and list from a pasted list of weights and centres and a hydrostatic table.
• Mercator (rhumb-line) sailingRhumb-line course and distance from meridional parts (sphere or WGS84), departure, great-circle comparison and passage time.
• Mooring line and winch brake (MEG4)OCIMF MEG4 values from the ship design MBL: line LDBF range, WLL, tail strength, fitting SWL, brake holding and rendering, and the drum-layer derating.
• NOx tier limit by engine speedMARPOL Annex VI Reg. 13 Tier I/II/III NOx limits from rated speed, the applicable tier, the margin of the certified value and annual NOx mass.
• Optimal hull cleaning intervalCleaning interval that minimises fuel penalty plus cleaning cost, from the fouling growth rate, fuel and ETS prices and the cost per cleaning.
• Optimal speed under charterCost-minimising speed on time charter and profit-maximising speed on a voyage charter from the fuel-speed law, prices, hire or freight and port time.
• Paint coverage and quantityTheoretical and practical spreading rate from volume solids and dry film thickness, litres and cost for an area with loss factors.
• Passage plan from waypointsLeg courses, distances, times and ETAs from a pasted waypoint list, by rhumb line or great circle, with the passage totals.
• Propeller curve and light running marginEngine SMCR from the propeller design point with sea, engine and light running margins, the propeller curves, and the heavy running of a measured point.
• Propeller slip and speed through waterTheoretical propeller speed, apparent and real slip, speed through water and speed of advance from pitch, RPM and observed speed.
• Roll period and synchronous rollingNatural roll period from GM and beam (IS Code) or GM from an observed period, encounter period for speed and heading, synchronous and parametric roll checks.
• Rotor sail (Flettner rotor) thrust and savingThrust, side force, spin power and net power saving of Flettner rotors from the true wind and ship speed, at the best spin, and averaged over a wind table.
• Sea state statisticsWave spectrum moments and periods, the 1/10 and 1/100 highest waves, the expected maximum wave in a storm and exceedance probabilities from Hs and Tp.
• Shallow water correction (Raven / Lackenby)ISO 15016:2025 Annex G (Raven) shallow-water power correction — viscous increase and sinkage — plus the legacy Lackenby speed correction.
• Ship squat and under-keel clearanceBarrass squat in open water and confined channels, Froude depth number, net under-keel clearance against a required margin and the maximum safe speed.
• Sight reduction (intercept method)Observed altitude from the sextant reading, then the intercept, azimuth and intercept terminal point from the assumed position.
• Speed–power curve fitFit P = aVⁿ to speed and power data and compare it with a reference curve: power increase, speed loss and the ISO 19030 performance value.
• Starting air receivers and compressorsReceiver capacity for the consecutive engine starts of IACS UR M61 and the compressor capacity to charge the receivers from atmospheric pressure in one hour.
• Tank sounding trim and heel correctionCorrected sounding or ullage of a rectangular tank for trim and heel at an off-centre sounding pipe, with volume, mass and the wedge check.
• Tidal height (rule of twelfths)Height of tide and depth at any time between high and low water by the rule of twelfths or the cosine curve, and the time a required depth becomes available.
• True wind from apparent windTrue and relative wind conversion per ISO 15016 with the anemometer height correction to the 10 m reference height of wind data.
• Wageningen B-series propellerWageningen B-series KT, KQ and efficiency from the 1975 polynomials at a given J, or the optimum pitch ratio and rpm for a thrust and diameter; Keller check.
• Water temperature and density correctionISO 15016 Annex E resistance and power correction for sea water temperature and density against the 15 °C / 1026 kg/m³ reference.
• Wave properties and encounter periodLinear wave theory: wavelength, celerity, group velocity, deep/shallow regime, orbital velocities and the encounter period for a ship speed and heading.
• Wind resistance (ISO 15016)Added wind resistance and power from the relative wind by ISO 15016:2025 Annex C with the Fujiwara coefficients or wind-tunnel data.