Gradians to Seconds of Arc Converter

Enter the angle in gradians below to convert it to seconds of arc.

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Result in Seconds of Arc:

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1g = 3,240 arcsec

Do you want to convert seconds of arc to gradians?

How to Convert Gradians to Seconds of Arc

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To convert a measurement in gradians to a measurement in seconds of arc, multiply the angle by the following conversion ratio: 3,240 seconds of arc/gradian.

Since one gradian is equal to 3,240 seconds of arc, you can use this simple formula to convert:

seconds of arc = gradians × 3,240

The angle in seconds of arc is equal to the angle in gradians multiplied by 3,240.

For example, here's how to convert 5 gradians to seconds of arc using the formula above.
seconds of arc = (5g × 3,240) = 16,200"

How Many Seconds of Arc Are in a Gradian?

There are 3,240 seconds of arc in a gradian, which is why we use this value in the formula above.

1g = 3,240"

Gradians and seconds of arc are both units used to measure angle. Keep reading to learn more about each unit of measure.

What Is a Gradian?

A gradian is equal to 1/400 of a revolution or circle, or 9/10°. The grad, or gon, is more precisely defined as π/200, or 1.570796 × 10-2 radians.[1]

This unit simplifies the measurements of right angles, as 90° is equal to 100 gradians.

Right angles in gradians
GradiansDegrees
0 grad0°
100 grad90°
200 grad180°
300 grad270°
400 grad360°

A gradian is sometimes also referred to as a grad, gon, or grade. Gradians can be abbreviated as g, and are also sometimes abbreviated as gr or grd. For example, 1 gradian can be written as 1g, 1 gr, or 1 grd.

In the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.

Learn more about gradians.

What Is a Second of Arc?

The second of arc is a unit of angle equal to 1/60th of one minute of arc or 1/3,600 of one degree.

A second of arc is sometimes also referred to as an arc second or arcsecond. Seconds of arc can be abbreviated as arcsec, and are also sometimes abbreviated as asec. For example, 1 second of arc can be written as 1 arcsec or 1 asec.

The second of arc is most commonly expressed using a double prime (″), though a double quote is often used as well. For example, 1 second of arc is most often written as 1″.

Learn more about seconds of arc.

Gradian to Second of Arc Conversion Table

Table showing various gradian measurements converted to seconds of arc.
Gradians Seconds Of Arc
0.001g 3.24"
0.002g 6.48"
0.003g 9.72"
0.004g 12.96"
0.005g 16.2"
0.006g 19.44"
0.007g 22.68"
0.008g 25.92"
0.009g 29.16"
0.01g 32.4"
0.02g 64.8"
0.03g 97.2"
0.04g 129.6"
0.05g 162"
0.06g 194.4"
0.07g 226.8"
0.08g 259.2"
0.09g 291.6"
0.1g 324"
0.2g 648"
0.3g 972"
0.4g 1,296"
0.5g 1,620"
0.6g 1,944"
0.7g 2,268"
0.8g 2,592"
0.9g 2,916"
1g 3,240"

References

  1. Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), National Institute of Standards and Technology, https://physics.nist.gov/cuu/pdf/sp811.pdf

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