Methodology

How we compute distance

The shortest path between two points on Earth is a geodesic — the ellipsoidal cousin of a straight line. Treating Earth as a sphere (the Haversine formula) gets you within roughly 0.5 % of the true distance, fine for most rough navigation but inadequate for aviation flight planning. We use Thaddeus Vincenty's 1975 iterative inverse formula on the WGS-84 ellipsoid because it converges to sub-millimetre precision in standard double-precision arithmetic.

The great-circle path between JFK and HKG measures about 12,983 km, while the rhumb-line course you would steer by holding a single magnetic heading runs roughly 15,200 km — a 17 % detour on the same trip. That 2,200-km gap is the whole reason every long-haul jet uses geodesic navigation rather than a constant compass bearing. The bigger the latitude swing, the bigger the penalty for steering a straight line on a Mercator map.

1. 1
   Reduce the latitudes

   Convert geographic latitudes φ₁, φ₂ to reduced latitudes U₁, U₂ via tan U = (1 − f) tan φ. This step collapses the latitude problem onto an auxiliary sphere of radius b/a so the rest of the algorithm can use spherical trigonometry.

2. 2
   Iterate λ until convergence

   Starting with λ = L (the longitude difference), compute σ, sin α, and cos 2σm, then update λ from those quantities. Vincenty's inner loop contains six trigonometric terms; we run it for up to 100 iterations with a 10⁻¹² rad convergence tolerance — typical real-world pairs converge in 4–8 passes.

3. 3
   Resolve fallback for near-antipodes

   For points within about half a degree of being antipodal the inverse problem may not converge — Vincenty himself flagged this in the original paper. We fall back to the Haversine formula, which always returns a finite value and is accurate to a few hundred metres at antipodal scale.

4. 4
   Apply the final ellipsoid correction

   Compute u² from cos²α and the squared semi-axes, derive the series coefficients A and B (Vincenty equations 3 and 4), then return the surface distance s = b·A·(σ − Δσ) in metres. We then convert to km, statute miles (× 0.621371), and nautical miles (× 0.539957).

The chart above plots the residual between successive λ values on the London → Sydney route — a 17,016-km flight that is geometrically aggressive but well-behaved for Vincenty. The residual halves through the first two iterations and then drops six orders of magnitude per step once σ stabilises. The 10⁻¹² rad tolerance corresponds to roughly 6 micrometres of position error at Earth scale, well below the precision of any GNSS receiver.

Earth is not a sphere — its 24-hour rotation flattens it by 21.4 km between equatorial and polar radii. Using the sphere approximation on a London → Tokyo route produces an error of about 40 km; Vincenty's ellipsoid solution drops that to under a millimetre. That difference is the entire reason aviation flight plans, ETOPS clearance, and oceanic track allocation depend on geodesic math rather than spherical shortcuts.

How we estimate flight time

A modern narrow-body cruises at Mach 0.78 — about 833 km/h true airspeed at FL370 — while a long-haul wide-body holds Mach 0.85 (≈ 903 km/h). We use 850 km/h as a single cruise reference because it sits midway between those two operating points and matches the block-time arithmetic published by most airline planning teams. Then we add ground time for taxi, climb-out, descent, and arrival taxi.

Ground time scales with distance because long-haul flights typically depart from larger airports with longer taxi-out queues and have more elaborate descent procedures. We use 30 minutes for routes under 1,500 km, 40 minutes for 1,500–4,000 km, and 50 minutes beyond 4,000 km. The total is rounded to the nearest minute and split into hours-and-minutes for display.

How we calculate CO₂

The base emission factor comes from the UK Government's annual greenhouse-gas reporting tables, published by the Department for Energy Security and Net Zero (DESNZ, the body that took over from DEFRA's GHG inventory work). The 2024 tables give kg CO₂ per passenger-kilometre for three distance bands; the cabin-class multipliers reflect how much aircraft floor area each ticket buys; and a 1.9 × radiative-forcing uplift converts CO₂ to CO₂-equivalent for the warming effect of contrails, NOₓ, and water vapour at altitude.

For a return economy flight London → New York our calculator returns roughly 1,668 kg CO₂e — more than the per-capita 2-tonne annual carbon target that the IPCC's 1.5 °C scenarios require by 2030, and about 1.6 months of the average UK resident's full personal carbon budget. That arithmetic is the point of showing the number prominently: it lets you compare a trip against your annual footprint rather than reading an abstract figure with no anchor.

Time-zone and jet-lag estimation

We read both airports' IANA time-zone strings (sourced from OpenFlights) and let the browser's Intl.DateTimeFormat resolve the current UTC offset, including daylight-saving transitions. The hour difference becomes a jet-lag severity band — none (≤ 2 h), mild (3–5 h), moderate (6–9 h), and severe (10 h or more). Recovery days follow the well-documented circadian asymmetry: westward travel realigns at about 92 minutes per day, eastward at about 57 minutes.

Airport, airline, and route data

OpenFlights is our base data layer — about 7,698 airport rows of which ~3,000 carry IATA codes, ~6,162 airline rows, and 67,663 route rows captured before the third-party route feed stopped supplying updates in June 2014. We treat the route table as a topology hint (which carriers historically flew which pairs), never as a current schedule. Coordinates, IATA codes, and time-zone strings are kept because they describe physical attributes that do not expire.

Limitations and disclaimers

These figures are decision-support estimates, not flight plans or compliance documents. Actual aircraft paths bend around restricted airspace, oceanic tracks rotate daily with the jet stream, and DESNZ emission factors are fleet-wide averages across many aircraft and load factors. We surface the underlying constants so you can substitute your own when a more precise number is available.