SEXAGESIMAL

What is Sexagesimal?

The sexagesimal system, also known as base-60, is a numeral system with sixty as its base. In the context of geographic coordinates, it is used to express latitude and longitude in degrees (°), minutes (′), and seconds (″) — a format dating back to Babylonian mathematics.

Each coordinate is structured as a sum of degrees, minutes, and seconds:

This means that one degree is divided into 60 minutes, and one minute into 60 seconds. For example:

Coordinates in this format are typically followed by directional indicators:

• N or S for latitude (North/South)
• E or W for longitude (East/West)

For instance, the coordinate: 60° 23′ 45″N, 10° 37′ 12″E represents a point 60.39583° north of the Equator and 10.62000° east of the Greenwich Meridian.

When to Use Sexagesimal Instead of Other Coordinate Systems

The sexagesimal format, commonly expressed as degrees, minutes, and seconds (DMS), is a traditional way of describing geographic coordinates using angular units. It remains widely used in navigation, official documents, and fields where human interpretation or formal standards are important.

Sexagesimal is recommended when:

• You are reading or referencing legacy maps and nautical charts — Many topographic and nautical charts express positions in DMS format.
• You are engaged in maritime, aeronautical, or outdoor navigation — Compass-based systems and navigation equipment often default to DMS for clarity and tradition.
• You are communicating coordinates verbally or formally — The DMS format is highly structured and avoids decimal confusion (e.g., 34°12′30″N is more visually distinct than 34.2083°).
• You are following regulatory or legal conventions — Property boundaries, land descriptions, and environmental regulations often use sexagesimal notation.
• You want to ensure interpretability by a non-technical audience — DMS is often perceived as more familiar and less abstract than decimal degrees.

Use alternatives to Sexagesimal when:

• You are performing calculations or spatial analysis — Decimal degrees are better suited for programming, mathematical operations, and GIS tools.
• You need meter-based coordinates — Use UTM or MGRS when working with distances, areas, or metric units.
• You are building web-based or digital map applications — Decimal formats integrate better with APIs, geospatial databases, and web mapping services like Google Maps.
• You are working with modern sensors or GNSS devices — Most devices output data in decimal degrees for computational efficiency.

In summary, sexagesimal coordinates are best suited for traditional navigation, legal descriptions, and contexts where human readability or established convention takes precedence over computational efficiency.

Historical Background

The sexagesimal system has its roots in ancient Sumerian civilisation and was later adopted and refined by the Babylonians around 2000 BCE. Their choice of base-60 was likely influenced by its mathematical versatility — 60 is divisible by 2, 3, 4, 5, and 6 — making it highly practical for fractional arithmetic.

This system laid the groundwork for developments in astronomy, geometry, and map-making. It was further developed by Greek scholars such as Hipparchus and Ptolemy, who used sexagesimal notation to catalogue the stars and describe planetary motion in works like the Almagest.

During the Islamic Golden Age, scholars preserved and enhanced this knowledge, translating Greek texts and expanding upon mathematical and astronomical principles — often using sexagesimal arithmetic.

The legacy of this system endured into the European Renaissance and beyond, ultimately shaping how we measure time (60 minutes per hour, 60 seconds per minute) and angles (360 degrees in a circle, with 60 minutes per degree).

Today, sexagesimal notation continues to serve as a vital link between ancient wisdom and modern spatial systems — a numerical heritage that remains embedded in our maps, clocks, and navigation tools.

The Future of the Sexagesimal System

The sexagesimal system, though ancient in origin, continues to play a role in modern geographic, navigational, and timekeeping practices. However, its future is shaped by the increasing dominance of digital computation and global data standards.

In contemporary geospatial and technological systems, formats such as decimal degrees are favoured for their computational simplicity, ease of integration with software applications, and compatibility with GIS platforms, APIs, and real-time processing pipelines.

Despite this, the sexagesimal format is far from obsolete. It remains an important standard in:

• Maritime and aeronautical navigation, where degrees–minutes–seconds are part of operational protocols.
• Surveying, cartography, and legal land descriptions, where the DMS format is embedded in formal documentation.
• Education and public maps, where the format is more intuitively readable for general audiences.

The likely trajectory for sexagesimal use is a model of coexistence with decimal formats. Digital tools increasingly support bidirectional conversion between representations, making it possible to store and compute in decimal while displaying and communicating in sexagesimal.

In this way, the sexagesimal system will continue to serve as a human-friendly bridge between ancient tradition and modern technology — a legacy of Babylonian thought that still guides orientation, measurement, and global movement.