Convert Radians to Mils - Angle Converter
This converter transforms angles expressed in gradians (also called gons) into mils. Gradians divide a full circle into 400 units; many mil definitions divide a circle into either 6400, 6000, or use the milliradian definition (≈6283.185 mrad per circle).
By default this tool maps gradians to the common NATO-style mil (1 circle = 6400 mils). The page also explains other mil conventions and gives guidance on choosing precision based on surveying, navigation, or ballistics use-cases.
Interactive Converter
Convert between gradian and mil with precision rounding.
Quick reference table
| Gradian | Mil |
|---|---|
| 1 grad | 16 mil |
| 5 grad | 80 mil |
| 10 grad | 160 mil |
| 25 grad | 400 mil |
| 50 grad | 800 mil |
| 100 grad | 1,600 mil |
Methodology
Conversions are performed by converting each unit to the same circle fraction and then computing the ratio. For example, 1 gradian = 1/400 of a full circle. A NATO mil = 1/6400 of a full circle. Therefore 1 gradian = 6400/400 = 16 NATO mils.
Where multiple mil definitions exist (NATO 6400, metric milliradian ≈6283.185, or older 6000-based systems), the page lists the alternative factors and explains when each is commonly used so you can verify results against instrument markings or regulatory guidance.
Worked examples
Example 1: Convert 2.5 gradians to NATO mils → 2.5 × 16 = 40 mils.
Example 2: Convert 100 gradians to Soviet-style mils (6000-per-circle) → 100 × 15 = 1500 mils.
Example 3: Convert 1 gradian to milliradians (mrad) → 1 × 15.707963267948966 ≈ 15.70796 mrad (useful when working directly in radians).
Expert Q&A
Which definition of a mil does this converter use by default?
By default the converter uses the common NATO-style definition where 1 circle = 6400 mils (so 1 gradian = 16 mils). If you need a different mil standard, see the alternate-factors explanation and adjust results accordingly.
Why are there different mil values and which should I use?
Different regions and communities historically adopted different mil systems: NATO (6400), Soviet/Scandinavian (6000), and the milliradian-based system (derived from radians, ≈6283.185 mrad per circle). Choose the one that matches your instrument markings, survey standard, or military doctrine. Always verify against the documentation for the equipment you use.
How accurate is the conversion and how should I round?
The mathematical relationships are exact given the chosen definitions (for example, 1 gradian = exactly 16 NATO mils). Practical rounding should reflect instrument precision and application: surveying often uses 0.1 mil or 0.01 gon depending on instruments; ballistics may require finer resolution but must consider sighting error and range estimation.
How do I convert back from mils to gradians?
Invert the same ratio. For NATO mils: gradians = mils × (1/16). For other mil conventions, use the appropriate divisor (for 6000-per-circle mils, gradians = mils × (1/15)).
Are these conversions suitable for high-precision lab work or legal metrology?
The arithmetic conversions are exact given a chosen unit definition, but for legal metrology or traceable laboratory measurements use calibrated equipment and reference standards. Consult national metrology guidance such as NIST and the BIPM SI brochure for formal requirements on traceability and uncertainty reporting.
How do instrument limitations affect conversions?
Most angular instruments report limited resolution and have measurement uncertainty. Converting a reported value does not improve its underlying uncertainty; always propagate the instrument's stated uncertainty through conversions and round results appropriately.
Sources & citations
- NIST — The International System of Units (SI) — https://www.nist.gov/pml/weights-and-measures/si-units
- BIPM — SI Brochure (overview of angle, radian, and SI conventions) — https://www.bipm.org/en/publications/si-brochure
- NOAA Ocean Service — Radians and degrees explained — https://oceanservice.noaa.gov/facts/radians.html