Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Geometry Calculators > Great Circle Distance Calculator

Great Circle Distance Calculator

Calculate the shortest distance between two points on a sphere using the Haversine formula. Enter latitude and longitude coordinates to get the great circle distance in kilometers, miles, and nautical miles, plus initial and final bearing, midpoint coordinates, and step-by-step formulas with an interactive globe diagram.

Great Circle Distance Calculator
Popular Routes:
INTERACTIVE GLOBE PREVIEW
Point A — Origin
↕ to
Point B — Destination
Leave blank for Earth's mean radius (6,371 km)

Embed Great Circle Distance Calculator Widget

About Great Circle Distance Calculator

The Great Circle Distance Calculator computes the shortest distance between two points on the surface of a sphere using the Haversine formula. Enter the latitude and longitude of two locations to get the great circle distance in kilometers, miles, and nautical miles, along with the initial and final bearing, midpoint coordinates, estimated travel times, and a step-by-step breakdown of the Haversine formula with an interactive globe visualization.

What Is Great Circle Distance?

A great circle is the largest circle that can be drawn on the surface of a sphere — its plane passes through the center of the sphere. The great circle distance (also called orthodromic distance) is the shortest distance between two points on a sphere, measured along the surface of the sphere rather than through the interior. On Earth, great circle routes are the paths that airplanes and ships follow to minimize travel distance.

The Haversine Formula

The Haversine formula is the standard method for computing great circle distances. Given two points with latitudes \(\phi_1, \phi_2\) and longitudes \(\lambda_1, \lambda_2\):

StepFormulaDescription
Haversine\(a = \sin^2\!\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_1) \cdot \cos(\phi_2) \cdot \sin^2\!\left(\frac{\Delta\lambda}{2}\right)\)Compute the square of half the chord length
Central angle\(c = 2 \cdot \text{atan2}\!\left(\sqrt{a},\; \sqrt{1-a}\right)\)Angular distance in radians
Distance\(d = R \times c\)Arc length on the sphere surface

Where \(R\) is the radius of the sphere (Earth's mean radius = 6,371 km). The Haversine formula is numerically stable for both small and large distances, making it preferable to the spherical law of cosines for computer calculations.

Real-World Applications

✈
Aviation
Flight path planning and fuel estimation
🚢
Maritime Navigation
Ship routing and nautical charts
📡
Telecommunications
Satellite coverage and signal propagation
🌍
GIS & Mapping
Geospatial analysis and proximity queries
🏃
Logistics
Route optimization and delivery planning
🛰
Space Science
Orbital mechanics on planetary bodies

How to Use the Great Circle Distance Calculator

  1. Enter Point A coordinates: Type the latitude and longitude of the starting location in decimal degrees, or click a popular route example to auto-fill both points. The interactive globe preview updates in real-time as you type.
  2. Enter Point B coordinates: Type the latitude and longitude of the destination.
  3. Set the sphere radius (optional): The default is Earth's mean radius (6,371 km). Change this to calculate distances on other spheres like the Moon (1,737 km) or Mars (3,390 km).
  4. Click Calculate Distance: Press the button to compute all results.
  5. Review results: See the distance in three unit systems, initial and final bearing with compass direction, midpoint coordinates, estimated travel times, and a step-by-step Haversine formula solution. Toggle the globe diagram layers to explore the visualization.

Haversine vs. Vincenty Formula

The Haversine formula assumes a perfect sphere and gives accuracy to within about 0.3% for Earth. The Vincenty formula models Earth as an oblate ellipsoid (WGS-84) and achieves accuracy to approximately 0.5 mm, but is more complex and computationally expensive. For most practical purposes — flight planning, logistics, educational use — the Haversine formula provides sufficient accuracy. The Vincenty formula is preferred for geodetic surveying and high-precision navigation.

Understanding Bearing

The initial bearing (forward azimuth) is the compass direction you would face when departing from Point A towards Point B along the great circle route. Bearings are measured clockwise from true north (0°–360°). Because a great circle curves along the sphere, the direction relative to north changes continuously along the route. The final bearing is the compass direction when arriving at Point B. For example, a flight from New York to London initially heads northeast (~51°) but arrives heading east-southeast (~108°).

Coordinate Format

This calculator uses decimal degrees format. Latitudes range from −90° (South Pole) to +90° (North Pole). Longitudes range from −180° (west) to +180° (east). To convert from degrees-minutes-seconds (DMS), use: decimal = degrees + minutes/60 + seconds/3600. For example, 40°42'46"N = 40.7128° and 74°0'22"W = −74.006°.

FAQ

What is a great circle distance?
A great circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere rather than through the interior. It follows a great circle, which is the largest circle that can be drawn on a sphere's surface and whose center coincides with the center of the sphere.
What is the Haversine formula?
The Haversine formula calculates the great circle distance between two points on a sphere given their longitudes and latitudes. The formula is: a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2), c = 2 × atan2(√a, √(1−a)), d = R × c, where R is the sphere radius. It is numerically stable for all distances.
How accurate is the great circle distance for Earth?
Using Earth's mean radius of 6,371 km, the Haversine formula gives results accurate to about 0.3% because Earth is slightly oblate (flattened at the poles). For higher precision, the Vincenty formula accounts for Earth's ellipsoidal shape and achieves accuracy to about 0.5 mm.
What is the difference between initial and final bearing?
The initial bearing (forward azimuth) is the compass direction when departing from the starting point. The final bearing is the compass direction upon arriving at the destination. Because a great circle changes direction relative to north as it curves along the sphere, these two bearings are generally different.
Why do airplanes fly great circle routes?
Airplanes fly great circle routes because they represent the shortest path between two points on Earth's surface, saving fuel and flight time. On a flat map with Mercator projection, these routes appear curved, but on a globe they are the most direct paths. This is why flights from the US to Europe often fly over the North Atlantic or even near the Arctic.

Reference this content, page, or tool as:

"Great Circle Distance Calculator" at https://MiniWebtool.com/great-circle-distance-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: 2026-04-03

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

Area of a Circle Calculator
Circle Calculator
Circumscribed Circle (Circumcircle) CalculatorNew
Interactive Unit Circle Visualizer
Random Coordinate Generator

Geometry Calculators:

Top & Updated:

Random PickerRandom Name PickerLine CounterRelative Standard Deviation CalculatorBatting Average CalculatorFPS ConverterSort NumbersInstagram User ID LookupERA CalculatorMAC Address GeneratorRemove SpacesJob FinderWord to Phone Number ConverterMAC Address LookupFacebook User ID LookupFeet and Inches to Cm ConverterSum CalculatorRandom Truth or Dare GeneratorOPS CalculatorPercent Off CalculatorSHA256 Hash GeneratorSquare Root (√) CalculatorLog Base 10 CalculatorNumber of Digits CalculatorBitwise CalculatorMP3 LooperVertical Jump CalculatorAudio SplitterSalary Conversion CalculatorSlope and Grade CalculatorRandom Quote GeneratorPhone Number ExtractorRoman Numerals ConverterSlugging Percentage CalculatorRandom IMEI GeneratorNumber to Word ConverterOn Base Percentage CalculatorAI Text HumanizerImage ResizerRandom Poker Hand GeneratorCaffeine Overdose CalculatorSaturn Return CalculatorSun, Moon & Rising Sign Calculator 🌞🌙✨Merge VideosDecimal to BCD ConverterGrade CalculatorCompound Growth CalculatorRandom Object GeneratorRandom Birthday GeneratorRandom Letter GeneratorCm to Feet and Inches ConverterBCD to Decimal ConverterRandom Writing Prompt GeneratorCompare Two StringsVideo to Image ExtractorRandom Fake Address GeneratorRandom Activity GeneratorRandom Movie PickerWHIP CalculatorText FormatterFirst n Digits of PiOctal CalculatorBinary to Gray Code ConverterBingo Card GeneratorInvisible Text GeneratorDoubling Time CalculatorRandom Superpower GeneratorFile Size ConverterAdd Prefix and Suffix to TextWAR CalculatorRemove AccentLove Compatibility CalculatorCM to Inches ConverterOutlier CalculatorWord Ladder GeneratorYouTube Channel StatisticsTime Duration CalculatorRandom Credit Card GeneratorList of Prime NumbersRandom Integer GeneratorImage SplitterPercent Growth Rate CalculatorRandom Loadout GeneratorUnit Rate CalculatorQuotient and Remainder CalculatorMaster Number CalculatorLeap Years ListStair CalculatorDay of Year CalendarRandom Chess Opening GeneratorCryptogram GeneratorPER CalculatorBinary to BCD ConverterAI Punctuation AdderModulo Calculator⬛ Aspect Ratio CalculatorArc Length CalculatorGray Code to Binary ConverterExponential Decay CalculatorEmail ExtractorURL ExtractorAI ParaphraserSHA512 Hash GeneratorDay of the Year Calculator - What Day of the Year Is It Today?Video CompressorIP Address to Hex ConverterSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorBCD to Hex ConverterMedian CalculatorStandard Error CalculatorList RandomizerBreak Line by CharactersAverage CalculatorPVIFA CalculatorReverse VideoHypotenuse CalculatorRemove Audio from VideoActual Cash Value CalculatorScientific Notation to Decimal ConverterNumber ExtractorAngel Number CalculatorLog Base 2 CalculatorRoot Mean Square CalculatorSum of Positive Integers CalculatorSHA3-256 Hash GeneratorAI Sentence Expander📅 Date CalculatorLbs to Kg ConverterHex to Decimal ConverterRandom Group GeneratorConvolution CalculatorMAC Address AnalyzerRandom String GeneratorRemove Leading Trailing SpacesAmortization CalculatorMarkup CalculatorPVIF CalculatorName Number CalculatorDecimal to Hex ConverterInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorTwitter/X Character CounterTwitter/X Timestamp ConverterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorSocial Media Post Time OptimizerSocial Media Username CheckerCTR CalculatorROAS CalculatorInfluencer ROI CalculatorForce CalculatorAcceleration CalculatorVelocity CalculatorMomentum CalculatorProjectile Motion CalculatorKinetic Energy CalculatorPotential Energy CalculatorWork and Power CalculatorDensity CalculatorPressure CalculatorIdeal Gas Law CalculatorFree Fall CalculatorTorque CalculatorHorsepower CalculatorDilution CalculatorChemical Equation BalancerStoichiometry CalculatorPercent Yield CalculatorEmpirical Formula CalculatorBoiling Point CalculatorTitration CalculatorMole/Gram/Particle ConverterIrregular Polygon Area CalculatorFrustum CalculatorTorus Calculator3D Distance CalculatorGreat Circle Distance CalculatorCircumscribed Circle (Circumcircle) CalculatorInscribed Circle (Incircle) CalculatorAngle Bisector CalculatorTangent Line to Circle CalculatorHeron's Formula CalculatorCoordinate Geometry Distance CalculatorVolume of Revolution CalculatorSurface of Revolution CalculatorParametric Curve GrapherRiemann Sum CalculatorTrapezoidal Rule CalculatorSimpson's Rule CalculatorImproper Integral CalculatorL'Hôpital's Rule CalculatorMaclaurin Series CalculatorPower Series CalculatorSeries Convergence Test CalculatorInfinite Series Sum CalculatorAverage Rate of Change CalculatorInstantaneous Rate of Change CalculatorRelated Rates SolverOptimization Calculator (Calculus)Gradient Calculator (Multivariable)Divergence CalculatorCurl CalculatorLine Integral CalculatorSurface Integral CalculatorJacobian Matrix CalculatorNewton's Method CalculatorRREF Calculator (Row Echelon Form)Matrix Inverse CalculatorMatrix Multiplication CalculatorDot Product CalculatorCross Product CalculatorVector Magnitude CalculatorUnit Vector CalculatorAngle Between Vectors CalculatorNull Space CalculatorColumn Space CalculatorCramer's Rule CalculatorMatrix Diagonalization CalculatorQR Decomposition CalculatorCholesky Decomposition CalculatorMatrix Power CalculatorCharacteristic Polynomial CalculatorBayes' Theorem CalculatorF-Test / F-Distribution CalculatorHypergeometric Distribution CalculatorNegative Binomial Distribution CalculatorGeometric Distribution CalculatorExponential Distribution CalculatorWeibull Distribution CalculatorBeta Distribution CalculatorSpearman Rank Correlation CalculatorFisher's Exact Test CalculatorContingency Table CalculatorOdds Ratio CalculatorRelative Risk CalculatorEffect Size CalculatorPermutations with Repetition CalculatorModular Exponentiation CalculatorPrimitive Root CalculatorPerfect Number CheckerAmicable Number CheckerTwin Prime FinderMersenne Prime CheckerGoldbach Conjecture VerifierMöbius Function CalculatorEgyptian Fraction CalculatorFibonacci Number CheckerDigital Root CalculatorPartition Function CalculatorBoolean Algebra SimplifierKarnaugh Map (K-Map) SolverLogic Gate SimulatorGraph Coloring CalculatorTopological Sort CalculatorAdjacency Matrix CalculatorRecurrence Relation SolverInclusion-Exclusion CalculatorLinear Programming SolverTraveling Salesman Solver (TSP)Hamiltonian Path CheckerPlanar Graph CheckerNetwork Flow Calculator (Max Flow)Stable Marriage Problem SolverFirst-Order ODE SolverSecond-Order ODE SolverDirection Field / Slope Field PlotterEuler's Method CalculatorBernoulli ODE SolverSystem of ODEs SolverGroup Theory Order CalculatorRing and Field CalculatorJordan Normal Form CalculatorMatrix Exponential CalculatorTensor Product CalculatorFast Fourier Transform (FFT) CalculatorZ-Transform CalculatorNumerical Integration CalculatorTOML to JSON ConverterJSON to CSV ConverterXML to JSON ConverterSQL to MongoDB Query ConverterCSS Flexbox PlaygroundCSS Grid GeneratorJWT GeneratorBcrypt Hash Generator / CheckerColor Code Converter (All Formats)Git Command Generator.env File GeneratorLorem Picsum / Placeholder Image GeneratorText to Binary/Hex/ASCII ConverterSyllable CounterSentence CounterParagraph CounterSpeaking Time CalculatorReading Time CalculatorWhitespace VisualizerStrikethrough Text GeneratorTorque Converter (Nm, ft-lb, kgf-cm)Data Transfer Rate ConverterFuel Efficiency ConverterAstronomical Unit ConverterRing Size ConverterPaper Size ReferenceClothing Size ConverterGas Mileage CalculatorEV Range CalculatorEV Charging Time Calculator0–60 / Quarter Mile CalculatorCar Lease CalculatorVehicle Towing Capacity CalculatorExposure Triangle CalculatorCrop Factor CalculatorMegapixel to Print Size CalculatorPhoto File Size EstimatorMusic BPM TapperMusic Key TransposerVideo Bitrate CalculatorSeed Germination Rate CalculatorFertilizer Calculator (NPK)Raised Bed Soil CalculatorFrost Date CalculatorLawn Fertilizer CalculatorCompost Calculator (C:N Ratio)Solar Panel CalculatorSolar ROI CalculatorHome Energy Audit CalculatorAppliance Energy Cost CalculatorWater Usage CalculatorElectricity Generation Cost CalculatorHeat Loss CalculatorFlight Distance CalculatorTravel Budget CalculatorJet Lag CalculatorPacking List GeneratorTip Splitter (Advanced)Lease vs Buy CalculatorHourly Rate Calculator (Freelancer)Invoice Late Fee CalculatorESPP CalculatorStock Split CalculatorOptions Probability CalculatorDollar to Gold ConverterBeam Load CalculatorPipe Flow CalculatorBolt Torque CalculatorSteel Weight CalculatorGravel, Sand & Topsoil CalculatorRandom Sentence GeneratorRandom Paragraph GeneratorRandom Math Problem GeneratorRandom Bible Verse GeneratorRandom Cat/Dog Name GeneratorRandom Debate Topic GeneratorBody Recomposition CalculatorAlcohol Calorie CalculatorMedication Dosage CalculatorPace to Calories CalculatorHydration CalculatorTrain Meeting Problem SolverAge Word Problem SolverMixture Problem SolverWork Rate Problem SolverDistance-Speed-Time Triangle CalculatorCoin Word Problem SolverNumber Bonds GeneratorCarry and Borrow VisualizerTimes Tables QuizMental Math TrainerRoman Numeral Math SolverEgyptian Multiplication CalculatorVedic Math Tricks CalculatorRussian Peasant MultiplicationSoroban Abacus SimulatorAnnuity Payout CalculatorReverse Mortgage CalculatorVariable Annuity CalculatorFixed Indexed Annuity CalculatorBond Convexity CalculatorBond Duration Calculator (Macaulay & Modified)Forward Rate CalculatorMortgage Recast CalculatorTreasury Inflation-Protected Securities (TIPS) CalculatorStock Beta Calculator