Distance between coordinates: the great-circle line
The straight-line distance between two cities on a globe is not a straight line on a map: it follows the curvature of the Earth along the shortest path, called the great-circle route. The Haversine formula computes this distance from the cities' latitude and longitude coordinates. A distance calculator applies it to major city pairs instantly, in kilometers or miles.
TL;DR
- Each city is represented by its latitude and longitude
- Haversine Formula: d = 2R × arcsin(√( sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2) ))
- Example 1: Rome to Milan
How it works
Each city is represented by its latitude and longitude. The calculator converts the coordinate differences into radians and applies the Haversine formula, which accounts for the spherical geometry of the Earth with a mean radius of about 6,371 km.
The math
Convert the latitudes and longitudes to radians, compute the differences, apply the Haversine formula to obtain the central angle, and multiply by the Earth mean radius to get the great-circle distance in kilometers.
R is the Earth mean radius (6,371 km); Δlat and Δlon are the coordinate differences in radians. The formula returns the shortest path distance over the sphere.
Examples
Example 1: Rome to Milan
- Rome: 41.9028° N, 12.4964° E
- Milan: 45.4642° N, 9.1900° E
- Great-circle calculation
- Distance ≈ 477 km (296 miles) as the crow flies
Example 2: London to New York
- London: 51.5074° N, 0.1278° W
- New York: 40.7128° N, 74.0060° W
- Great-circle calculation
- Distance ≈ 5,570 km (3,461 miles)
When to use it
✦ Travel Planning
Travelers estimate the air distance between cities to compare flight options or the straight-line gap for radio and signal planning.
✦ Geographic Reference
Students and journalists cite accurate straight-line distances between major cities for articles and educational material.
⚠ Common Distance Calculation Misconceptions
- Confusing Straight Line with Road Distance: The great-circle distance ignores roads, terrain, and rail; driving routes are typically 20-40% longer.
- Forgetting the Earth Is Not a Perfect Sphere: The 6,371 km mean radius approximation introduces errors below 1% for most city pairs.
- Mixing Degrees and Radians: Applying trig functions to degrees without conversion corrupts the result completely.
FAQ Calculation (6)
What is a great-circle distance?
It is the shortest path between two points on a sphere, which for Earth appears as a curved arc on flat maps.
Why is driving distance longer?
Roads follow terrain, rivers, and urban layouts, so the road network distance always exceeds the straight-line distance.
Is my data kept private when I use these everyday tools?
Yes. Whether it's a word count or a time-between-dates check, nothing is sent to a server. The page does the counting locally — you can paste a draft, get 1,242 words and 6 min reading time, and close it without a trace.
Do I need internet after the first load?
Not really. Once cached, word-counter, hours, fuel-cost and the rest work offline. Handy if you're drafting on a train or counting hours on site without signal — load once, use anywhere.
How reliable are the results for work?
They follow documented rules — reading time at 200-250 wpm, hours as decimal, etc. — and are tested automatically. For casual use they're spot-on; for payroll with overtime rules or legal word-count filings, do a final check against your HR or editorial guide.
What's the fastest way to share a result?
'Share Link' does it. It encodes your inputs in the address bar, so the other person sees the exact same hours (e.g. 09:15 to 17:45 = 8h 30m) without you retyping.