Convert Degrees (°) to Minutes (')

What Is a Degree?

The degree (°) is a non-SI unit of plane angle defined as exactly 1/360 of a full rotation. It is accepted for use with the SI due to its importance in navigation, surveying, engineering, and astronomy.

The 360-degree circle dates back to Babylonian astronomy over 3,000 years ago. In the DMS (Degrees-Minutes-Seconds) system, each degree is subdivided into 60 arcminutes, inheriting the sexagesimal (base-60) system from the same Babylonian tradition.

Key equivalences: 1° = π/180 rad = 60′ = 3,600″.

What Is an Arcminute?

The arcminute (′), also called minute of arc, is exactly 1/60 of a degree. Its exact relationship to the radian is 1′ = π/10,800 rad.

Arcminutes provide angular precision between whole degrees and arcseconds. They are the standard subdivision in DMS notation for geographic coordinates, celestial positions, and survey bearings. One arcminute of latitude equals one nautical mile (1,852 m) — a relationship that made arcminutes fundamental to maritime navigation.

Key equivalences: 60′ = 1°; 1′ = 60″; 21,600′ = 360°.

Degrees to Arcminutes Formula

The conversion factor is exact:

arcminutes = degrees × 60

This is a definition, not an approximation. One degree is subdivided into exactly 60 arcminutes, following the sexagesimal system inherited from Babylon.

Worked Example

Convert the coordinate 40.4461° (latitude of New York City) to DMS:

1. Whole degrees: 40°
2. Remaining: 0.4461 × 60 = 26.766′
3. Remaining: 0.766 × 60 = 46″

Result: 40° 26′ 46″ N — the standard DMS notation for NYC's latitude.

Quick Estimation

For mental math, multiply degrees by 60 — there is no shortcut since the factor is already a round number. For the reverse (arcminutes to degrees), divide by 60. Example: 150′ ÷ 60 = 2.5°. Each 0.1° = exactly 6′.

Common Conversions at a Glance

Which Is Bigger: Degree or Arcminute?

A degree is exactly 60 times larger than an arcminute. One degree covers about the width of your little finger held at arm's length. One arcminute — 1/60 of that — is roughly the angular diameter of the Moon as seen from Earth (~31′). The human eye can barely resolve details at the 1-arcminute scale.

When You Need This Conversion

• Navigation and GPS: Nautical charts express positions in degrees and arcminutes (e.g., 51° 30.5′ N). One arcminute of latitude = 1 nautical mile (1,852 m), making arcminutes the natural unit for maritime and aviation distance.
• Astronomy: Telescopes specify field of view and object separations in arcminutes. The Moon's diameter is about 31′, Jupiter's disk about 0.8′, and the Andromeda galaxy spans 190′.
• Surveying and geodesy: Land surveys record bearings in DMS notation (e.g., N 45° 30′ E). Converting to decimal degrees for GIS software requires the ×60 factor.
• Optometry: Visual acuity is defined in arcminutes — 20/20 vision means the eye resolves details subtending 1 arcminute at 20 feet.