Convert Gradians to Milliradians
1 gradian is 15.71 mrad. One gradian is exactly 15.7079632679 milliradians.
One gradian is 15.707963 milliradians. To convert gradians to milliradians, multiply by 15.707963; to go the other way, divide by 15.707963 or multiply by 0.063661977. The relation is exact but the figure is not: it is a rounding of a number that does not terminate, and it follows from NIST Special Publication 811. A 400th of a turn, so a right angle is exactly 100.
Factor checked against the defining standard · How we check
- Gradians × 15.707963
1 * 15.70796315.708 mrad
1 gradian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.01570796327 rad | × 0.0157079632679 |
| degrees | 0.9 ° | × 0.9 |
| gradians (as entered) | 1 gon | — |
| arcminutes | 54 ′ | × 54 |
| arcseconds | 3,240 ″ | × 3,240 |
| turns | 0.0025 turn | × 0.0025 |
| milliradians | 15.70796327 mrad | × 15.7079632679 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert gradians to milliradians? The converter and the working
- 1.Take the measurement in gradians.
- 2.Multiply by 15.707963 — that is how many milliradians fit in one gradian.
- 3.To go back the other way, divide by 15.707963, or multiply by 0.063661977.
Worked example: 25 gradians to milliradians
- Formula
- gon × 15.707963 = mrad
- Arithmetic
- 25 × 15.707963 = 392.7 mrad
- Answer
- 25 gon = 392.7 mrad
The factor is rounded for display; the figure above is computed from the full value.
Gradians to milliradians conversion table
| Gradians | Milliradians |
|---|---|
| 1 gon | 15.71 mrad |
| 2 gon | 31.42 mrad |
| 3 gon | 47.12 mrad |
| 4 gon | 62.83 mrad |
| 5 gon | 78.54 mrad |
| 6 gon | 94.25 mrad |
| 7 gon | 109.96 mrad |
| 8 gon | 125.66 mrad |
| 9 gon | 141.37 mrad |
| 10 gon | 157.08 mrad |
| 12 gon | 188.5 mrad |
| 15 gon | 235.62 mrad |
| 20 gon | 314.16 mrad |
| 25 gon | 392.7 mrad |
| 50 gon | 785.4 mrad |
| 100 gon | 1,570.8 mrad |
| 200 gon | 3,141.59 mrad |
| 300 gon | 4,712.39 mrad |
| 500 gon | 7,853.98 mrad |
| 1000 gon | 15,707.96 mrad |
| 2000 gon | 31,415.93 mrad |
| 5000 gon | 78,539.82 mrad |
| 10000 gon | 157,079.63 mrad |
What is a gradian?
A 400th of a turn, so a right angle is exactly 100. Invented with the metric system and still used in European surveying and on calculators with a GRAD mode nobody means to press.
What is a milliradian?
A thousandth of a radian, and the unit rifle scopes adjust in: at 100 meters one milliradian moves the point of impact by 10 cm. The military "mil" is a different thing — 6,400 to a turn rather than the true 6,283.
How many milliradians are in a gradian?
One gradian is 15.707963 milliradians. Going the other way, one milliradian is 0.063661977 gradians. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to a gradian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Gradians to milliradians. Rule Calculator. https://rulecalculators.com/convert/gradian-to-milliradian
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- Chicago
- Rule Calculator. "Convert Gradians to milliradians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/gradian-to-milliradian.
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Questions people actually ask
- How many milliradians are in a gradian?
- 15.707963. A thousandth of a radian, and the unit rifle scopes adjust in: at 100 meters one milliradian moves the point of impact by 10 cm. The military "mil" is a different thing — 6,400 to a turn rather than the true 6,283.
- How do I convert milliradians back to gradians?
- Divide by 15.707963, or multiply by 0.063661977 — they are the same operation.
Other angle conversions
Milliradians to gradians — the same conversion the other way.