deg to mrad Converter
Convert degree angles into precise milliradians
Degrees to milliradians FAQ
How do you convert degrees to milliradians exactly?
A milliradian (mrad) is one thousandth of a radian: 1 mrad = 0.001 rad. A full circle is 360° = 2π rad, so 1° = π/180 rad. Combining these gives 1° = (π/180) × 1000 mrad ≈ 17.45329252 mrad. To convert from degrees to milliradians, you multiply the degree value by (1000π/180). For example, 1° ≈ 17.45 mrad and 0.5° ≈ 8.73 mrad. The calculator uses this exact relationship and handles all the rounding for you.
Is this the same as “mil” values used on scopes?
Many modern rifle scopes use milliradian-based click values, where 1 mrad corresponds to about 10 cm at 100 meters. In that context, 1 mrad is defined exactly as 0.001 rad, matching the math definition used here. Some artillery and older systems use different “mil” systems (like 6400 or 6000 mils in a circle), which are very close but not identical. This converter sticks to true mathematical mrads so your results line up with standard radian-based formulas and most mrad scopes.
What’s 1 degree in milliradians?
Using the exact factor, 1° = 17.45329252 mrad. In practice, shooters and engineers usually round this to 17.45 mrad or even 17.5 mrad for quick estimates. The converter keeps the full precision in the background but presents a nicely formatted number that you can copy into tables, ballistic calculators or field notes.
Why use milliradians instead of degrees for scopes and targeting?
Milliradians are convenient because they link angle directly to linear corrections at distance. One mrad spans 1 unit at 1000 units of range (for example, 1 meter at 1000 meters). That makes it easy to map spotter corrections or group sizes in the target to clicks on a turret. Degrees are more familiar, but much less convenient when you want to think in “how many clicks” instead of pure angle.
Can I use this for artillery, surveying and engineering?
Yes. The deg to mrad converter is suitable for any context where angles are recorded or commanded in degrees but calculations or sights are in milliradians. You can enter bearing changes, elevation angles or instrument readings in degrees, convert to mrads, and then feed the results into fire control tables, surveying software or targeting systems that prefer radian-based units.
Is there a quick mental shortcut for degrees to mrads?
A simple rule of thumb is to multiply degrees by 17.5. Because the exact factor is about 17.45, using 17.5 gets you very close. For example, 2° × 17.5 ≈ 35 mrad (exact ≈ 34.91 mrad), 5° × 17.5 ≈ 87.5 mrad (exact ≈ 87.27 mrad). The calculator uses the precise (1000π/180) factor every time, so you can check your mental estimate against an accurate result before writing anything into a dope card or log.
From intuitive degree angles to milliradian precision
This deg to mrad converter bridges the gap between the everyday world of degrees and the precision world of milliradians. Many people think in degrees when they picture angles, but scopes, fire-control software, some surveying instruments and many engineering formulas work internally in radians or mrads. Instead of rebuilding formulas or punching numbers into a calculator every time, you type a degree value, press convert and get a clear line such as “1.2° = 20.94 mrad”.
1. Single-box interface for quick angle conversions
The layout stays deliberately simple: one field for degrees, one result card. It works well for very small angles, like 0.1° of elevation change, and larger angles, such as 10° of traverse. You can enter decimal degrees from CAD, GIS or ballistics software (for example, 3.75°), and the converter uses the exact 1° ≈ 17.4533 mrad relationship to give a clean numerical result. There is nothing to configure and no unit dropdowns to manage: this page is dedicated to degrees-to-mrad only.
When you need to reverse the conversion, the “Swap Units” button jumps straight to the mrad-to-deg tool. That makes it easy to move back and forth between degrees and milliradians without changing settings on a scientific calculator or building a custom spreadsheet.
2. Exact relationship: 1° ≈ 17.4533 mrad
The converter is grounded in the same definitions used in mathematics and standard ballistics references. A full revolution is 2π rad, and one radian corresponds to 1000 milliradians. Because 180° = π rad, we get:
- 1° = π/180 rad
- 1 rad = 1000 mrad
- 1° = (π/180) × 1000 mrad ≈ 17.4533 mrad
Using this exact chain keeps your degrees to milliradians conversions aligned with the radian-based formulas you see in physics, optics and engineering. Whether you’re building a ballistics table, checking a scope manual or sanity-checking a simulator, the underlying numbers will match.
If you later need to mix in other angle units such as pure radians, gradians or full turns, you can step up to the full angle conversion calculator, which keeps the same clean result style while handling more combinations.
3. Common degrees to milliradians values at a glance
Here are some useful reference points, especially for scope adjustments, target offsets and instrument calibration. They match what the calculator produces:
| Degrees (°) | Milliradians (mrad) |
|---|---|
| 0.1° | ≈ 1.745 mrad |
| 0.25° | ≈ 4.363 mrad |
| 0.5° | ≈ 8.727 mrad |
| 1° | ≈ 17.45 mrad |
| 2° | ≈ 34.91 mrad |
| 5° | ≈ 87.27 mrad |
| 10° | ≈ 174.53 mrad |
| 15° | ≈ 261.80 mrad |
| 30° | ≈ 523.60 mrad |
A handy mental check is to multiply by 17.5 and accept the tiny rounding difference. If your angle is 3°, you expect roughly 52.5 mrad, and the precise value is about 52.36 mrad. The converter hides all the heavy lifting and gives you the exact figure for when those small differences matter in practice.
4. Where the deg to mrad converter shines
You will often reach for this tool when you:
- Dial or read rifle scopes — translate intuitive degree offsets or angular errors into the mrad clicks your turrets use.
- Prepare ballistic tables — convert trajectory, wind or lead angles from degrees into mrads for consistent firing solutions.
- Work with artillery or fire control — move between degree-based fire plans and milliradian-based sight or computer inputs.
- Handle surveying and alignment tasks — express small angular deviations and instrument readings in mrads for high precision.
- Design and calibrate optical systems — connect beam divergence or field-of-view in degrees to radian-based design equations.
Because the underlying conversion is fixed by the definition of the radian and milliradian, this degrees to milliradians converter will give the same answer every time you enter a value. It becomes a dependable bridge between human-friendly degree angles and the mrad numbers that modern optics, ballistics tools and engineering formulas prefer.
References and further reading on degrees, radians and mrads
These references explain how degrees, radians and milliradians are defined and why radian-based units are popular in engineering and ballistics:
- Radian — describes the radian as the standard mathematical unit of angle and shows how it relates to the circle.
- Milliradian — explains the milliradian, its use in scopes, gunnery and surveying, and the relationship to degrees and minutes of angle.
- Degree (angle) — covers the degree as a unit of plane angle and its common applications.
For formal fire-control tables, safety-critical work or standards-based surveying, always follow the exact angle definitions and rounding rules specified by your manuals, procedures or governing body.