Milliradian Calculator

Accurately convert between Milliradians, Degrees, and Minutes of Angle (MOA).

Unit	Value (for 1 mrad input)	Represents at 100m Distance
Milliradians (mrad)	1.000	10 cm
Degrees (°)	0.0573	~0.999 cm
Minutes of Angle (MOA)	3.438	~29.08 cm

Table Note: The "Represents at 100m Distance" column shows the linear distance covered by 1 unit of the respective angle at a range of 100 meters. For example, 1 mrad subtends approximately 10 cm at 100m.

What is Milliradian (mrad)?

A milliradian (mrad), often shortened to mil or milrad, is a unit of angular measurement. It is defined as one-thousandth of a radian. A full circle, which contains 360 degrees or 2π radians, contains exactly 6283.185 milliradians. In practical terms, a milliradian is a very small angle. For most practical applications, particularly in fields like long-range shooting, ballistics, and optical alignment, the milliradian system offers a convenient and precise way to measure and calculate angles and distances. A key advantage of the milliradian system is its direct relationship with distance at a given range. One milliradian at 1000 units of distance (like meters or yards) subtends one unit of linear distance (like a meter or yard). This 1:1000 ratio simplifies many calculations compared to degrees or minutes of angle.

Who should use it? This milliradian calculator is invaluable for:

• Long-range shooters and competitive marksmen: To estimate windage and elevation corrections, understand scope reticles, and calculate bullet drop.
• Hunters: For estimating range and making necessary adjustments in the field.
• Optical engineers and technicians: For precise alignment of lenses, mirrors, and other optical components.
• Surveyors and cartographers: For measuring angles and distances in geographical mapping.
• Anyone working with small angular measurements in engineering or physics requiring conversion between different angular units.

Common misconceptions: A frequent misunderstanding is the exact value of a milliradian relative to a degree. While often approximated as 1 mrad ≈ 0.057 degrees, the precise value is closer to 0.0572958 degrees. Another misconception is confusing "mils" in the context of angular measurement with "milli" as a prefix for thousandths (like in millimeters). While related, the term "mil" in angular measurement specifically refers to milliradians. Also, the "1 mil = 1 yard at 1000 yards" rule is an approximation; the precise ratio is 1 mrad = 1 meter at 1000 meters.

Milliradian (mrad) Formula and Mathematical Explanation

The conversion between milliradians, degrees, and minutes of angle relies on the fundamental relationships between these units and the radian.

Radians to Milliradians: Since 1 radian = 1000 milliradians: Milliradians = Radians × 1000

Degrees to Milliradians: We know that 180° = π radians. Therefore, 1° = (π / 180) radians. Converting this to milliradians: 1° = (π / 180) × 1000 milliradians 1° ≈ 0.017453 × 1000 milliradians 1° ≈ 17.453 milliradians Thus, to convert degrees to milliradians: Milliradians = Degrees × (1000π / 180) Or, using the approximate factor: Milliradians ≈ Degrees × 17.453

Milliradians to Degrees: From the above, we derive the inverse conversion: Degrees = Milliradians × (180 / 1000π) Or, using the approximate factor: Degrees ≈ Milliradians × 0.0573

Minutes of Angle (MOA) to Milliradians: 1 MOA is defined as 1/60th of a degree. 1 MOA = (1/60)° We know 1° ≈ 17.453 mrad. So, 1 MOA ≈ (1/60) × 17.453 mrad 1 MOA ≈ 0.29088 mrad Thus, to convert MOA to milliradians: Milliradians = MOA × 0.29088

Milliradians to MOA: The inverse conversion: MOA = Milliradians / 0.29088 Or, more commonly expressed using the 100-yard rule (1 MOA ≈ 1 inch at 100 yards): 1 mrad subtends 1 yard at 1000 yards. 1 MOA subtends 1 inch at 100 yards. Since 1 yard = 36 inches, 1000 yards = 3600 inches. So, 1 mrad at 1000 yards covers 1 yard (36 inches). At 100 yards, 1 mrad covers 0.1 yards (3.6 inches). 1 MOA at 100 yards covers 1 inch. Therefore, 1 mrad at 100 yards covers 3.6 MOA. This gives the approximation: MOA ≈ Milliradians × 3.6

Summary Table of Variables:

Variable	Meaning	Unit	Typical Range / Value
mrad	Milliradian	Angle	e.g., 0.1, 1, 3.5
deg	Degrees	Angle	e.g., 0.0573, 1, 5
MOA	Minutes of Angle	Angle	e.g., 0.29, 1, 10
π (pi)	Mathematical constant	Dimensionless	≈ 3.14159
Distance	Range to target	Meters, Yards, etc.	e.g., 100m, 500yds
Linear Subtension	Actual distance covered by angle at range	Meters, Yards, Inches, cm	Calculated value

Practical Examples (Real-World Use Cases)

Let's illustrate the utility of milliradian calculations with practical examples.

Example 1: Estimating Bullet Drop Correction

A marksman is shooting at a target 800 meters away. Their rifle scope has a reticle with 0.1 mrad (1 cm at 100m) subtensions, and their ballistic data indicates a required elevation adjustment of 2.5 milliradians for the current wind and distance.

• Input: Angle = 2.5 mrad, Unit = Milliradians (mrad)
• Calculation: Using the calculator (or manual conversion):
  • Milliradians: 2.5 mrad
  • Degrees: 2.5 * 0.0573 ≈ 0.143°
  • MOA: 2.5 / 0.29088 ≈ 8.6 MOA
• Result Interpretation: The marksman needs to dial in 2.5 milliradians of elevation. If their scope turrets are also marked in mrad and each click represents 0.1 mrad, they would need to adjust 25 clicks (2.5 / 0.1 = 25). Alternatively, if their scope uses MOA turrets, they would need to adjust approximately 8.6 MOA. This milliradian calculator helps ensure the correct adjustment is made, regardless of the unit system used on the scope or reticle.

Example 2: Measuring Target Size at Distance

An observer is using a spotting scope with a reticle marked in milliradians to estimate the size of a target 500 meters away. They measure the target's width as 4 mrad on their reticle.

• Input: Angle = 4 mrad, Unit = Milliradians (mrad)
• Calculation: To find the linear width of the target: Linear Subtension = Angle (in mrad) × Distance (in km) Linear Subtension = 4 mrad × (500m / 1000m/km) Linear Subtension = 4 × 0.5 km = 2 km… Wait, this is wrong. Correct calculation: Linear Subtension = Angle (in mrad) * Distance (in meters) / 1000 Linear Subtension = 4 mrad * 500 meters / 1000 Linear Subtension = 2 meters.
• Result Interpretation: The target is estimated to be approximately 2 meters wide. This demonstrates the direct utility of the 1:1000 ratio in milliradians for range estimation and size assessment. The calculator confirms this value and allows conversion to other units if needed for comparison with different equipment or standards.

How to Use This Milliradian Calculator

Using our milliradian calculator is straightforward. Follow these simple steps to get accurate conversions:

1. Enter the Angle Value: In the "Angle Value" input field, type the numerical value of the angle you wish to convert.
2. Select the Input Unit: Use the "From Unit" dropdown menu to choose the unit of the angle you just entered (Milliradians, Degrees, or Minutes of Angle).
3. Click Calculate: Press the "Calculate" button.
4. View Results: The calculator will instantly display the equivalent angle in all three units (Milliradians, Degrees, and MOA). The primary result (the converted value of your input) will be highlighted.
5. Understand Intermediate Values: The displayed intermediate values show the exact conversions, helping you cross-reference or use them in further calculations.
6. Interpret the Chart and Table: The dynamic chart visually compares the units, and the table provides specific values, like the linear distance subtended at 100m, which is crucial for practical applications.
7. Reset or Copy: Use the "Reset" button to clear the fields and start over with default values. Click "Copy Results" to copy the calculated values and key assumptions to your clipboard for easy pasting elsewhere.

Decision-making guidance: This tool helps you make informed decisions by providing a unified view of angular measurements. Whether you're adjusting a scope, calculating bullet drop, or aligning an optical system, having consistent and accurate conversions ensures precision and eliminates errors. For example, if your rifle scope reticle is in mrad but your turret adjustments are in MOA, this calculator bridges that gap.

Key Factors That Affect Milliradian Results

While the milliradian conversion itself is a direct mathematical relationship, the *application* of these conversions in real-world scenarios involves several critical factors:

• Accuracy of Input Measurement: The precision of the initial angle measurement is paramount. If you misread your scope reticle or your angle-measuring device is inaccurate, the converted results will also be inaccurate. Garbage in, garbage out.
• Range to Target (Distance): Milliradians have a direct relationship with linear distance (1 mrad = 1 unit of distance at 1000 units of distance). Therefore, an accurate determination of the range to the target is crucial for calculating actual corrections (e.g., bullet drop, windage holds). Small errors in range estimation can lead to significant misses at longer distances.
• Environmental Conditions (Wind): Especially critical for shooting applications. While the calculator converts angular units, it doesn't account for the complex effects of wind. Wind speed, direction, and even atmospheric density significantly impact projectile trajectory, requiring additional angular adjustments (windage) that are often estimated using the same mrad or MOA system.
• Ballistic Coefficient (BC) of Projectile: For shooting, the BC of the bullet determines how efficiently it overcomes air resistance. A higher BC means less drop and drift. Ballistic calculators, which often use mrad or MOA for output, factor in BC, velocity, and drag models. Our calculator provides the angular units needed to input into such systems or interpret their output.
• Equipment Calibration and Zeroing: Your firearm, scope, and any other measurement tools must be properly zeroed. A scope zeroed at 100 yards will yield different results if used at 500 yards without proper adjustments. The calculator assumes your equipment is set up correctly. Understanding your scope's "per click" value (e.g., 0.1 mrad/click) is also vital.
• Atmospheric Factors (Temperature, Pressure, Humidity): These conditions affect air density, which in turn influences bullet flight. While less impactful than range or wind for many applications, at extreme ranges, these factors can necessitate fine-tuning of adjustments, often expressed in mrad or MOA.
• Optical Distortion and Magnification: The apparent size of an object can be affected by optical magnification and potential distortion in the scope or other optical devices. Ensure you understand how your reticle's subtensions are calibrated at different magnifications (e.g., First Focal Plane vs. Second Focal Plane scopes).

Frequently Asked Questions (FAQ)

Q1: What is the difference between mrad and MOA?

Both mrad (milliradian) and MOA (Minute of Angle) are units used to measure small angles, primarily in shooting and optics. A milliradian is approximately 3.6 MOA. The key difference lies in their mathematical basis and practical application: mrad has a direct 1:1000 relationship with distance (1 mrad = 1 unit of distance at 1000 units of distance), while MOA relates to inches at yards (1 MOA ≈ 1 inch at 100 yards). Many modern scopes use mrad reticles and turrets due to the simpler decimal-based calculations.

Q2: Is 1 milliradian equal to 1 yard at 1000 yards?

This is a common and useful approximation. The precise relationship is 1 milliradian subtends 1 meter at 1000 meters. Since 1 yard is approximately 0.9144 meters, 1 mrad at 1000 yards subtends about 0.9144 yards, which is roughly 32.9 inches. 1 yard is 36 inches. So, the approximation is close but not exact. For most practical shooting, 1 mrad ≈ 3.6 inches at 100 yards, and 1 yard at 1000 yards is a good rule of thumb.

Q3: How do I convert degrees to milliradians?

To convert degrees to milliradians, you can use the formula: Milliradians = Degrees × 17.453. Alternatively, use the exact conversion factor: Milliradians = Degrees × (1000π / 180). Our calculator handles this conversion automatically when you select 'Degrees' as your input unit.

Q4: What does a scope with an MRAD reticle mean?

An MRAD (milliradian) reticle means the markings or subtensions on the crosshairs are based on milliradians. For example, a marking might represent 1 mrad, 0.5 mrad, or 0.2 mrad. If the scope also has MRAD turrets, each "click" typically adjusts the point of impact by 0.1 mrad. This setup allows for direct measurement of range and correction for bullet drop or windage using the reticle and turrets in a consistent unit system.

Q5: Can I use this calculator for astronomical measurements?

Yes, absolutely. Milliradians are used in astronomy to measure very small angular separations between celestial objects. While astronomers might use specialized software, this calculator provides the fundamental unit conversions needed for basic calculations or understanding data from astronomical instruments.

Q6: How accurate is the "1 mrad = 10 cm at 100m" rule?

This rule is derived from the definition of a milliradian (1/1000th of a radian) and the relationship between radians and arc length. Arc Length = Radius × Angle (in radians). 1 mrad = 0.001 radians. So, at a radius of 100 meters, the arc length is 100m * 0.001 = 0.1 meters, which is exactly 10 centimeters. This relationship is mathematically exact and forms the basis for using milliradians in range estimation and correction.

Q7: Does the calculator account for bullet drop?

No, this calculator converts angular measurements between units (mrad, degrees, MOA). It does not calculate bullet drop, wind drift, or other ballistic trajectories. Bullet drop is dependent on many factors like the specific ammunition, firearm, environmental conditions, and ballistic coefficient of the projectile. However, the angular values this calculator provides (like the required elevation or windage adjustments in mrad or MOA) are the direct output needed for external ballistic calculators or for making manual scope adjustments.

Q8: What is the difference between a mil-dot reticle and an MRAD reticle?

While often used interchangeably, there can be subtle differences. A true MRAD reticle has markings that accurately represent milliradians at a specific magnification (usually on a Second Focal Plane scope). A traditional "mil-dot" reticle was designed such that the dots were spaced 1 mil apart at 10x magnification on some scopes. Modern scopes increasingly use MRAD for clearer, decimal-based markings and calculations, and they often feature more complex reticle patterns than simple mil-dots. Always check the manufacturer's specifications for your specific scope.