ST_DISTANCE_SPHERE

Compute the great-circle distance between two points on a spherical Earth using the spherical law of cosines.

Category: geospatialReturns: DOUBLEDialect: Standard

Syntax

ST_DISTANCE_SPHERE(lat1, lng1, lat2, lng2)

Description

## Overview Returns the great-circle distance in meters between two points on a spherical Earth model, calculated using the spherical law of cosines. The formula is numerically simpler than Haversine and produces nearly identical results for most real-world distances. It is intended as an interchangeable alternative where a specific formula is required by tooling or for cross-engine compatibility. Use ST_DISTANCE_SPHERE whenever you want a fast, dependency-free distance between latitude/longitude pairs and you are not worried about the very small precision loss that the law of cosines exhibits at extremely short distances. ## When to use ST_DISTANCE_SPHERE vs. alternatives - **ST_DISTANCE_SPHERE** (this function): spherical Earth, law-of-cosines formulation. Accurate to roughly 0.3 percent across most of the globe. Drop-in alternative to Haversine. - **ST_DISTANCE_HAVERSINE**: spherical Earth, Haversine formulation. Preferred default because it is numerically stable for very short distances (under about 1 meter). - **ST_DISTANCE_VINCENTY**: ellipsoidal (WGS 84) distance. Survey-grade accuracy; slower and can fail to converge at near-antipodal points. - **ST_DISTANCE**: planar distance in CRS units; use only on projected data. ## Behavior - Returns a DOUBLE in meters. - Uses a spherical Earth with mean radius 6,371,008.8 meters, matching the other spherical distance functions. - Arguments are ordered (lat, lng), not (lng, lat), mirroring ST_DISTANCE_HAVERSINE and the other great-circle functions. - Symmetric: swapping the two points returns the same value. - Returns 0 for identical points. - Returns NULL if any argument is NULL. - Handles the antimeridian correctly; longitudes do not need to be pre-normalized. - Inputs outside valid latitude/longitude ranges are not rejected; they produce numerically defined but geographically meaningless results. ## Accuracy and performance - Accuracy: approximately 0.3 percent for distances up to a few thousand kilometers, increasing slightly on trans-global paths. - The law of cosines can lose precision on sub-meter distances due to floating-point cancellation in arccos; prefer ST_DISTANCE_HAVERSINE when working at very short ranges. - Performance is comparable to Haversine; both are constant-cost per call. - Combine with H3 cell prefiltering (see H3_LATLNG_TO_CELL) to avoid cross-product scans on large tables. ## Compatibility - Matches the spherical-law-of-cosines distance convention used by most SQL geospatial engines that expose a dedicated sphere function. - Inputs are always WGS 84 decimal degrees. No SRID argument is required or accepted.

Parameters

Name	Type	Description
`lat1`		Specifies the WGS 84 latitude of the first point in decimal degrees, in the range -90 to 90.
`lng1`		Specifies the WGS 84 longitude of the first point in decimal degrees, in the range -180 to 180.
`lat2`		Specifies the WGS 84 latitude of the second point in decimal degrees, in the range -90 to 90.
`lng2`		Specifies the WGS 84 longitude of the second point in decimal degrees, in the range -180 to 180.

Examples

-- Great-circle distance in meters.
-- Expected result: approximately 1,181,000 meters.
SELECT ST_DISTANCE_SPHERE(52.5200, 13.4050, 41.9028, 12.4964) AS distance_m;

-- Divide by 1000 for kilometers.
SELECT ST_DISTANCE_SPHERE(51.5074, -0.1278, 48.8566, 2.3522) / 1000.0 AS distance_km;

-- Keep stores within 10 km of a reference location.
SELECT store_id, store_name
FROM retail.catalog.stores
WHERE ST_DISTANCE_SPHERE(latitude, longitude, 51.5074, -0.1278) <= 10000;

-- Haversine and spherical-law-of-cosines agree to within floating-point noise for most inputs.
SELECT
  ST_DISTANCE_HAVERSINE(51.5074, -0.1278, 40.7128, -74.0060) AS haversine_m,
  ST_DISTANCE_SPHERE(51.5074, -0.1278, 40.7128, -74.0060) AS sphere_m,
  ST_DISTANCE_SPHERE(51.5074, -0.1278, 40.7128, -74.0060) -
    ST_DISTANCE_HAVERSINE(51.5074, -0.1278, 40.7128, -74.0060) AS delta_m;

-- Spot the sub-percent differences between spherical and ellipsoidal models.
SELECT
  ST_DISTANCE_SPHERE(51.5074, -0.1278, 48.8566, 2.3522) AS sphere_m,
  ST_DISTANCE_HAVERSINE(51.5074, -0.1278, 48.8566, 2.3522) AS haversine_m,
  ST_DISTANCE_VINCENTY(51.5074, -0.1278, 48.8566, 2.3522) AS vincenty_m;

-- Return the 5 closest stations to a given point.
SELECT station_id,
       ST_DISTANCE_SPHERE(lat, lng, 35.6762, 139.6503) AS distance_m
FROM transit.catalog.stations
ORDER BY distance_m
LIMIT 5;

Pitfalls

Arguments are ordered (lat, lng), not (lng, lat). Reversing them silently produces wrong distances because latitude and longitude share overlapping numeric ranges.
The law of cosines loses precision for sub-meter distances due to floating-point cancellation. If you need accurate very-short distances, prefer ST_DISTANCE_HAVERSINE.
The function assumes a spherical Earth. For survey-grade work where sub-meter accuracy matters, switch to ST_DISTANCE_VINCENTY.
The result is in meters, not kilometers or miles. Convert explicitly at the call site when comparing against literal thresholds.
Out-of-range coordinates are not rejected. Validate inputs against [-90, 90] and [-180, 180] upstream or the function can return numerically valid nonsense.