Understanding Geohashing: A Comprehensive Guide

What is Geohashing?

Geohashing is a method for encoding geographic coordinates (latitude and longitude) into a short string of letters and digits. This encoded string, called a geohash, offers a compact, human-readable way to represent geographic locations. Developed by Gustavo Niemeyer in 2008, geohashing is widely used in geographic information systems (GIS), spatial databases, and location-based services.

Why is Geohashing Required?

Advantages of Geohashing

  1. Compact Representation:
    • Geohashes condense geographic coordinates into a short string
    • This makes them easier to store and communicate
  2. Spatial Locality:
    • Geohashes maintain spatial locality, meaning that points close to each other geographically will have similar geohashes
    • This is crucial for efficient spatial querying and indexing
  3. Hierarchical Structure:
    • Geohashes provide a hierarchical structure where each additional character increases the precision of the location
    • This allows for variable levels of granularity in spatial data representation
  4. Efficient Querying:
    • Geohashes enable efficient spatial queries, such as finding all points within a certain area or bounding box
    • This is especially useful for applications like geocoding, mapping, and location-based services

Understanding Geohash Precision

Precision in geohashing refers to the accuracy of the geographic location represented by the geohash.

The length of the geohash string determines its precision: longer geohashes correspond to smaller areas, thus representing locations more accurately.

Here is a table showing the precision of geohashes based on their length:

Geohash Precision Table

Geohash Length Latitude Bits Longitude Bits Cell Width Cell Height
1 2 3 ≤ 5,000 km ≤ 5,000 km
2 5 5 1,250 km 625 km
3 7 8 156 km 156 km
4 10 10 39.1 km 19.5 km
5 12 13 4.89 km 4.89 km
6 15 15 1.22 km 0.61 km
7 17 18 153 m 153 m
8 20 20 38.2 m 19.1 m
9 22 23 4.77 m 4.77 m
10 25 25 1.19 m 0.596 m
11 27 28 149 mm 149 mm
12 30 30 37.2 mm 18.6 mm

alt text

How is Geohash Calculated?

Step-by-Step Calculation Using a 4-Character Geohash

Let’s derive a 4-character (precision) geohash for Google’s headquarters located at approximately latitude 37.422 and longitude -122.084

We’ll break down the process into detailed steps.

1. Convert Latitude and Longitude to Binary

Latitude Conversion

Latitude ranges from -90 to +90.

Step Range Midpoint 37.422 Comparison Binary New Range
1 [-90, 90] 0 37.422 > 0 1 [0, 90]
2 [0, 90] 45 37.422 < 45 10 [0, 45]
3 [0, 45] 22.5 37.422 > 22.5 101 [22.5, 45]
4 [22.5, 45] 33.75 37.422 > 33.75 1011 [33.75, 45]
5 [33.75, 45] 39.375 37.422 < 39.375 10110 [33.75, 39.375]
6 [33.75, 39.375] 36.5625 37.422 > 36.5625 101101 [36.5625, 39.375]
7 [36.5625, 39.375] 37.96875 37.422 < 37.96875 1011010 [36.5625, 37.96875]
8 [36.5625, 37.96875] 37.265625 37.422 > 37.265625 10110101 [37.265625, 37.96875]
9 [37.265625, 37.96875] 37.6171875 37.422 < 37.6171875 101101010 [37.265625, 37.6171875]
10 [37.265625, 37.6171875] 37.44140625 37.422 < 37.44140625 1011010100 [37.265625, 37.44140625]

Latitude binary: 1011010100

Longitude Conversion (-122.084)

Longitude ranges from -180 to +180.

Step Range Midpoint -122.084 Comparison Binary New Range
1 [-180, 180] 0 -122.084 < 0 0 [-180, 0]
2 [-180, 0] -90 -122.084 < -90 00 [-180, -90]
3 [-180, -90] -135 -122.084 > -135 001 [-135, -90]
4 [-135, -90] -112.5 -122.084 < -112.5 0010 [-135, -112.5]
5 [-135, -112.5] -123.75 -122.084 > -123.75 00101 [-123.75, -112.5]
6 [-123.75, -112.5] -118.125 -122.084 < -118.125 001010 [-123.75, -118.125]
7 [-123.75, -118.125] -120.9375 -122.084 < -120.9375 0010100 [-123.75, -120.9375]
8 [-123.75, -120.9375] -122.34375 -122.084 > -122.34375 00101001 [-122.34375, -120.9375]
9 [-122.34375, -120.9375] -121.640625 -122.084 < -121.640625 001010010 [-122.34375, -121.640625]
10 [-122.34375, -121.640625] -121.9921875 -122.084 < -121.9921875 0010100100 [-122.34375, -121.9921875]

Longitude binary: 0010100100

2. Interleave the Bits

Interleave the bits of longitude and latitude to create a single binary string.

(Longitude, Latitude) -> (01)

Step Latitude Longitude Interleaved
1 1 0 01
2 0 0 0100
3 1 1 010011
4 1 0 01001101
5 0 1 0100110110
6 1 0 010011011001
7 0 0 01001101100100
8 1 1 0100110110010011
9 0 0 010011011001001100
10 0 0 01001101100100110000

Interleaved binary: 01001101100100110000

3. Convert Interleaved Binary to Base32

The binary string 01001101100100110000 needs to be converted to base32.

  1. Pad the binary string to make its length a multiple of 5: The length of 01000110100100110000 is 20, which is already a multiple of 5, so no padding is needed.

  2. Divide the binary string into 5-bit groups:

    01001 10110 01001 10000
  3. Convert each 5-bit group to its decimal equivalent:
    • 01001 = 9
    • 10110 = 28
    • 01001 = 9
    • 10000 = 16
  4. Map each decimal value to the corresponding base32 character: Base32 alphabet: 0123456789bcdefghjkmnpqrstuvwxyz
    • 9 -> 9
    • 28 -> u
    • 9 -> 9
    • 16 -> h

Therefore, the binary string 01000110100100110000 converts to the base32 string 9u9h.

Resulting Geohash

The 4-character geohash for Google’s headquarters (latitude 37.422, longitude -122.084) is 9u9h.

Benefits of Interleaving

  1. Spatial Locality:
    • Interleaving ensures that geohashes for nearby locations are similar, preserving spatial locality. This is critical for spatial queries and indexing.
  2. Efficient Range Queries:
    • Interleaved geohashes allow for efficient bounding box queries, which are common in geographic searches. This makes it easier to query all points within a certain area.
  3. Balanced Precision:
    • By interleaving, both latitude and longitude contribute equally to the precision of the geohash. This avoids skewed precision that could occur if one coordinate is given more bits than the other.
  4. Hierarchical Subdivision:
    • Interleaving provides a hierarchical structure where each additional character refines the location, allowing for varying levels of granularity.

References