As the Crow Flies Distance Calculator & Formula

An as-the-crow-flies distance calculator finds the straight-line distance between two points using their latitude and longitude. Enter the coordinates of the start and destination, and it returns the approximate distance over Earth’s surface—not the distance along roads or a route you can travel.

Formula

The calculator uses the haversine formula, which estimates the shortest surface distance between two points on a spherical Earth. It accounts for the fact that longitude lines converge toward the poles, so a degree of longitude does not represent the same ground distance everywhere.

a = sin²(Δφ/2) + cos(φ₁) × cos(φ₂) × sin²(Δλ/2)
c = 2 × atan2(√a, √(1 − a))
d = R × c

• φ₁ and φ₂ are the start and destination latitudes, converted from degrees to radians for the calculation.
• λ₁ and λ₂ are their longitudes, likewise converted to radians.
• Δφ is φ₂ − φ₁; Δλ is λ₂ − λ₁.
• c is the central angle between the points, in radians.
• R is the assumed Earth radius, 6,371 km (about 3,959 miles).
• d is the resulting great-circle distance, reported here in kilometres and converted to miles.

The calculator’s first result is the distance in kilometres. Its second result converts that answer using 1 mile = 1.609344 kilometres. The spherical-Earth assumption is useful for ordinary distance comparisons, though it is not a survey-grade geodesic calculation.

Worked Example

Using the default coordinates, the starting point is 40.7128° N, 74.0060° W, and the destination is 34.0522° N, 118.2437° W. These coordinates represent New York City and Los Angeles, respectively. The calculator interprets west longitudes as negative values.

1. Convert the coordinate differences to radians: Δφ = (34.0522 − 40.7128) × π/180 ≈ −0.11625; Δλ = (−118.2437 − (−74.0060)) × π/180 ≈ −0.77209.
2. Substitute those differences and the two latitudes into the haversine expression. This gives a central angle of approximately 0.618 radians.
3. Multiply by Earth’s assumed radius: 6,371 × 0.618 ≈ 3,936.38 km.
4. Convert to miles: 3,936.38 ÷ 1.609344 ≈ 2,446.81 mi.

Small differences in the last decimal can occur when intermediate values are rounded for display; the calculator retains the formula’s precision until it displays the result.

How to Enter Coordinates

Latitude says how far north or south a point is from the equator; longitude says how far east or west it is from the prime meridian. Enter decimal degrees, not degrees-minutes-seconds. Valid latitude runs from −90° to 90°; valid longitude runs from −180° to 180°.

• Use a positive latitude for north and a negative latitude for south.
• Use a positive longitude for east and a negative longitude for west.
• For example, 40.7128° N, 74.0060° W becomes latitude 40.7128 and longitude −74.0060.
• Copy both values from the same coordinate reading. Reversing latitude and longitude can point to a completely different location.

Many mapping tools display coordinates when you select a location or inspect a map point. Check the coordinate format and signs before entering them. A value written as degrees, minutes, and seconds must first be converted to decimal degrees: degrees + minutes/60 + seconds/3600, with the sign applied for south or west.

When This Distance Is Useful

Straight-line distance is useful when you want a geographic comparison independent of roads: estimating how far apart two cities are, comparing locations, describing the distance between a site and a landmark, or checking whether a destination is nearby in broad terms. It is also called “as the crow flies” distance because it imagines a direct path rather than a path constrained by streets.

It is not a travel-time calculator. A 50 km straight-line separation does not mean a 50 km drive, flight, hike, or boat trip. Terrain, waterways, road layouts, access restrictions, air routes, and the mode of travel all affect the actual route. For planning a journey, use routing information that matches how you will travel.

Accuracy, Units, and Common Mistakes

The formula models Earth as a sphere with a mean radius. Earth is slightly flattened at the poles, so more precise geodesic methods use an ellipsoid and can yield a somewhat different answer, especially over long distances or when high accuracy matters. For general comparisons, the spherical result is usually a practical approximation; for surveying, navigation, or technical work, use a suitable geodetic tool and datum.

• Mixing coordinate formats: Decimal-degree fields cannot be given values such as 40° 42′ 46″ without conversion.
• Dropping a minus sign: Treating a western longitude as positive can place a point on the other side of the globe.
• Swapping latitude and longitude: Latitude must be entered in the first field and longitude in the second.
• Confusing distance with route length: A direct line normally cannot follow every road or accessible path.
• Overreading decimals: The displayed precision is not a promise that the coordinates or Earth model are accurate to that many decimal places.

Distances are shown in kilometres and miles. To convert kilometres to miles, divide by 1.609344; to convert miles to kilometres, multiply by that factor. The output rounds to two decimal places, which is suitable for readability but not a substitute for measurement precision.

Frequently Asked Questions

What does “as the crow flies” mean?
It means the direct, straight-line distance between two points, without following roads, trails, or other routes. On Earth, the shortest surface path is an arc of a great circle.

How do I calculate straight-line distance from latitude and longitude?
Use the haversine formula: calculate the central angle between the coordinates, then multiply it by Earth’s radius. This calculator performs the degree-to-radian conversion and calculation for you.

Is as-the-crow-flies distance the same as driving distance?
No. Driving distance follows available roads and can be much longer—or occasionally differ less—depending on the route, terrain, and local geography. A routing map is needed for road distance.

Can I use coordinates in degrees, minutes, and seconds?
Convert them to decimal degrees first. For example, 40° 30′ 0″ is 40.5°. Remember to make south and west coordinates negative.

Why does my result differ from another calculator?
Tools may use different Earth models, coordinate data, or rounding precision. Differences can also come from swapped coordinates, omitted negative signs, or comparing a straight-line distance with a route distance.

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in lat1 | Start latitude | ° | 40.7128 | -90 | 90
in lon1 | Start longitude | ° | -74.0060 | -180 | 180
in lat2 | Destination latitude | ° | 34.0522 | -90 | 90
in lon2 | Destination longitude | ° | -118.2437 | -180 | 180
out distance | Straight-line distance | km | 6371 * 2 * atan2(sqrt((sin((lat2-lat1)*pi/180/2))^2 + cos(lat1*pi/180)*cos(lat2*pi/180)*(sin((lon2-lon1)*pi/180/2))^2), sqrt(1-((sin((lat2-lat1)*pi/180/2))^2 + cos(lat1*pi/180)*cos(lat2*pi/180)*(sin((lon2-lon1)*pi/180/2))^2))) | 2
out miles | Straight-line distance | mi | distance / 1.609344 | 2