Bounding Box Area Calculator
A bounding box is a rectangle on the map set by its southwest and northeast corners. Its true surface area is not width times height, because a degree of longitude covers less ground as you move toward the poles. This calculator uses the exact spherical formula, the Earth radius squared times the longitude span in radians times the difference of the sines of the corner latitudes, on a sphere of mean radius 6,371,008.8 meters. Enter the four corner coordinates in decimal degrees and it returns the area in square kilometers, square miles, acres and hectares.
Bounding box area formula
Area = R^2 * (lonE - lonW in radians) * (sin(latN) - sin(latS))
R = 6,371,008.8 m
1 km^2 = 0.386102 mi^2; 1 km^2 = 247.105 acres = 100 hectares
This is the exact area of a spherical zone band clipped to the longitude span. The sine difference captures the convergence of meridians toward the poles.
Bounding box context
- Corners are decimal degrees, north and east positive.
- North latitude must exceed south latitude; east longitude must exceed west.
- Width-times-height overstates area away from the equator; this formula corrects that.
- Bounding boxes drive map queries, tiling and data clipping.
- Area uses the IUGG mean Earth radius and exact unit conversions.
Bounding box area: frequently asked questions
What is a bounding box?
A bounding box is a rectangle defined by a southwest corner and a northeast corner in latitude and longitude. It is the simplest way to describe a rectangular extent on a map, used in tiling, search queries, and data clipping.
How is the area of a lat-long box computed on a sphere?
The exact spherical area of a box between latitudes and longitudes equals the Earth radius squared times the longitude span in radians times the difference of the sines of the two latitudes. This accounts for the convergence of meridians toward the poles.
Why not just multiply width by height?
Because a degree of longitude shrinks toward the poles. A box one degree wide covers less ground at 60 degrees latitude than at the equator. The sine-of-latitude term handles this convergence so the area is correct everywhere.
What corners do I enter?
Enter the south latitude and west longitude (the southwest corner) and the north latitude and east longitude (the northeast corner), all in decimal degrees with north and east positive. The north latitude must exceed the south latitude.
What Earth radius and units are used?
The mean spherical radius of 6,371,008.8 meters is used. Area is reported in square kilometers, square miles, acres and hectares using exact unit conversions, so you can pick whichever fits your task.
Official sources
- U.S. Geological Survey: U.S. Geological Survey.
- NIST: Fundamental physical constants and units.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.