Convert Gradian (grad) to Minute of Arc (′) instantly. Enter any value and get the result immediately.
grad → ′ Converter
| Gradian (grad) | Minute of Arc (′) |
|---|---|
| 0.1 grad | 5.399892 ′ |
| 0.5 grad | 26.99946001 ′ |
| 1 grad | 53.99892002 ′ |
| 2 grad | 107.99784004 ′ |
| 5 grad | 269.99460011 ′ |
| 10 grad | 539.98920022 ′ |
| 20 grad | 1079.97840043 ′ |
| 50 grad | 2699.94600108 ′ |
| 100 grad | 5399.89200216 ′ |
| 200 grad | 10,799.784 ′ |
| 500 grad | 26,999.46 ′ |
| 1000 grad | 53,998.92 ′ |
| 5000 grad | 269,994.6001 ′ |
| 10000 grad | 539,989.2002 ′ |
Converting gradians to minutes of arc bridges two very different angular traditions — the decimal metric gradian system used in European professional surveying and the classical sexagesimal arcminute system embedded in navigation, astronomy, and geographic coordinates. One gradian equals 0.9 degrees, and since one degree contains 60 arcminutes, one gradian equals exactly 54 arcminutes. To convert, multiply the gradian value by 54. Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 10 grad to minutes of arc:
Step-by-step example — Convert 100 grad to minutes of arc:
Step-by-step example — Convert 5 grad to minutes of arc:
Gradian (grad), also known as a gon or grade, is a metric angular unit that divides a full circle into exactly 400 equal parts. Developed during the French Revolution as part of the decimalization of measurement, the gradian was designed so that a right angle equals a clean 100 grad — making calculations involving perpendicular lines and quarter-circle geometry particularly convenient in a decimal arithmetic framework. Gradians remain the standard unit on professional surveying instruments — theodolites, total stations, and electronic levels — across much of continental Europe, including France, Germany, the Netherlands, Switzerland, and Scandinavia. One gradian equals exactly 0.9 degrees or 54 arcminutes.
Minute of Arc (′), also called an arcminute, is a subdivision of the degree equal to exactly 1/60th of one degree. Its name comes from the Latin pars minuta prima — "first small part" — reflecting the ancient Babylonian base-60 subdivision of the circle that has been in use for over two thousand years. One arcminute corresponds to approximately 1.852 kilometers on Earth's surface along a meridian — a relationship that defines the nautical mile and underpins all maritime and aviation distance measurement. Arcminutes appear in geographic coordinates (the middle value in Degrees, Minutes, Seconds notation), in astronomy for describing the apparent sizes of celestial objects, in optometry for defining visual acuity, and in precision shooting as the Minute of Angle (MOA) used for scope adjustments. A full circle contains 21,600 arcminutes (360° × 60′), while the 400-gradian circle contains 21,600 arcminutes as well — both systems describe the same physical circle, just divided differently.
| Gradians (grad) | Minutes of Arc (′) | Common Reference |
|---|---|---|
| 0 grad | 0′ | No rotation |
| 1 grad | 54′ | Basic gradian step = 0°54′ |
| 5 grad | 270′ | 4°30′ in DMS notation |
| 10 grad | 540′ | 9° exactly |
| 50 grad | 2,700′ | 45° — half a right angle |
| 100 grad | 5,400′ | 90° — right angle |
| 133.33 grad | 7,200′ | 120° — equilateral triangle angle |
| 200 grad | 10,800′ | 180° — straight angle |
| 300 grad | 16,200′ | 270° — three-quarter rotation |
| 400 grad | 21,600′ | 360° — full circle |
There are exactly 54 minutes of arc in one gradian. This comes from the chain: 1 grad = 0.9° and 1° = 60′, so 1 grad = 0.9 × 60 = 54′. This is the exact conversion factor — no approximation needed.
The formula is: ′ = grad × 54. Multiply any gradian value by 54 to get the equivalent angle in arcminutes. For the reverse, divide arcminutes by 54 to get gradians.
100 grad = 5,400′. Since 100 gradians equals a right angle (90°), and 90° = 90 × 60 = 5,400 arcminutes, this is a useful benchmark confirming that the two systems describe the same physical angle consistently.
400 grad = 21,600′. A full circle of 400 gradians equals 21,600 arcminutes — which also equals 360° × 60′ = 21,600′. Both systems divide the same circle, just using different primary units.
1 grad = 0.9° = 0°54′0″ in DMS notation. Since 0.9° = 0° plus 0.9 × 60′ = 54′ exactly, one gradian converts to a clean whole number of arcminutes — a fortunate property of the 9/10 relationship between gradians and degrees.
Because 1 grad = 9/10 of a degree, and 1 degree = 60 arcminutes: multiplying 9/10 × 60 = 54. The clean integer result — no fractional arcminutes — occurs because 60 is divisible by 10, allowing the decimal gradian-to-degree ratio to produce a whole number of arcminutes. This makes grad-to-arcminute conversion one of the tidier cross-system conversions in angular measurement.
One gradian (54′) is larger than one arcminute. A gradian is 54 times the size of an arcminute. Conversely, one arcminute is approximately 0.01852 gradians. Gradians are a coarser unit than arcminutes — suitable for instrument readouts in field surveying — while arcminutes are used when finer angular subdivision is needed, such as in geographic coordinates and astronomical measurements.
Yes — and the conversion is clean. Since 1 grad = 0°54′0″ exactly, multiply the gradian value by 0.9 to get decimal degrees, then convert to DMS: the integer part is degrees, multiply the decimal remainder by 60 for minutes, and multiply the remaining decimal by 60 for seconds. For example, 7.5 grad = 6.75° = 6°45′0″. Because 1 grad always produces a whole number of arcminutes (54′), gradian values that are multiples of simple fractions often convert to clean DMS values — a feature appreciated by surveyors working across both systems.