Gradian to Arcminute Converter

Result

54
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Conversion Formula

=grad×360×60400\mathrm{\prime} = \mathrm{grad} \times \frac{360 \times 60}{400}

Unit Description

Gradian (grad)

Definition

A gradian (grad), also called a gon, is a unit of angular measurement where a full rotation is divided into 400 gradians. One gradian equals 1/400 of a complete circle, making a right angle equal to 100 gradians.

History

The gradian was introduced during the French Revolution as part of the metric system around 1795. It was designed to decimalize angle measurement, making calculations easier by using base-10 arithmetic. The system was promoted alongside other metric reforms but never achieved widespread adoption outside of surveying.

Current Use

Gradians are primarily used in surveying and some European engineering applications. They're particularly common in land surveying in France, Germany, and other parts of Europe. Some surveying instruments and software support gradian measurements, though degrees remain more common globally.

Arcminute (′)

Definition

An arcminute (′) is a unit of angular measurement equal to 1/60 of a degree. It provides finer precision than degrees for measuring small angles, particularly useful in astronomy and navigation.

History

Arcminutes developed from the Babylonian base-60 system, where each degree was subdivided into 60 minutes. The term 'minute' comes from the Latin 'pars minuta prima' meaning 'first small part'. This subdivision system has been used in astronomy and navigation for over 2,000 years.

Current Use

Arcminutes are extensively used in astronomy for measuring celestial object positions and separations, in surveying for precise land measurements, and in navigation for GPS coordinates. They're also used in optics for measuring angular resolution and in artillery for targeting calculations.

Conversion Table

Gradian(grad)
Arcminute()
1
54
2
108
3
162
4
216
5
270
6
324
7
378
8
432
9
486
10
540
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Conversion Examples

Convert 1 Gradian to Arcminute

  1. Conversion Formula: ′ = grad × (360 × 60)/400
  2. Calculation: 1grad × (360 × 60)/400 = 54′

Convert 10 Gradian to Arcminute

  1. Conversion Formula: ′ = grad × (360 × 60)/400
  2. Calculation: 10grad × (360 × 60)/400 = 540′

Convert 100 Gradian to Arcminute

  1. Conversion Formula: ′ = grad × (360 × 60)/400
  2. Calculation: 100grad × (360 × 60)/400 = 5,400′

Convert 1,000 Gradian to Arcminute

  1. Conversion Formula: ′ = grad × (360 × 60)/400
  2. Calculation: 1,000grad × (360 × 60)/400 = 54,000′
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