Bounding Box Area Calculator
Calculate the surface area of a latitude/longitude bounding box on the Earth’s sphere.
How it works
A = R² · |sin φ₂ − sin φ₁| · Δλ(rad)
A latitude/longitude box is a spherical rectangle, and its exact surface area on a sphere is R² times the difference in the sines of the two latitudes times the longitude span in radians. Using the sine of latitude correctly accounts for meridians converging toward the poles, so a box near the equator is far larger than the same degree-box near a pole.
Worked example
A box around New York from 40.4774°N to 40.9176°N and −74.2591° to −73.7004°: A = 6371² × |sin 40.918° − sin 40.477°| × (0.5587° in rad) ≈ 2,340 km².
Sources: Spherical geometry — Wikipedia
Frequently asked questions
Why not just multiply width by height?
Because lines of longitude converge toward the poles, a degree of longitude is narrower at high latitudes. The sine-of-latitude formula gives the exact spherical area.
Does this work across the date line?
The calculator takes the shorter longitude span, so a box crossing ±180° is handled as long as its width is under 180°.
Is this the ellipsoidal area?
No, it uses a sphere of radius 6,371 km. The true WGS84 ellipsoidal area differs by well under 1%.
Related calculators
Educational estimate. Uses a spherical-Earth model; results differ slightly from ellipsoidal (WGS84) calculations.