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Understanding Mrad (Milliradian) Calculations
The Mrad Calculator is an essential tool for long-range shooters, snipers, and hunters utilizing optics with milliradian-based reticles. Unlike generic unit converters, this tool focuses specifically on the trigonometry of ballistics: range estimation ("milling") and sight correction.
What is a Milliradian?
A milliradian (often called a "mil" or "mrad") is an angular unit of measurement. It is defined as 1/1000th of a radian. Because there are $2\pi$ radians in a circle (approximately 6.283), there are approximately 6,283 milliradians in a circle.
The beauty of the metric system and milliradians is the simplicity of the ratio:
1 Mrad subtends exactly 10 cm at 100 meters.
1 Mrad subtends exactly 1 meter at 1000 meters.
For imperial users, 1 Mrad is approximately 3.6 inches at 100 yards.
Part 1: The Range Estimation Formula
Range estimation, often called "milling a target," involves measuring the height or width of a target of known size using the hash marks in your scope's reticle. The calculator uses the standard milling formula:
Range (meters) = (Target Size in mm) / Mils Read
Or, if you are working in mixed units (Inches and Yards):
Range (yards) = (Target Size in Inches × 27.778) / Mils Read
Example Scenario: You see a standard IPSC target torso (approximately 30 inches tall). In your scope, it measures 2.5 Mils.
Calculation: $(30 \times 27.778) / 2.5 = 333.3$ yards.
Part 2: Calculating Scope Adjustments
Once you know your range and where your bullet is impacting (or where it will drop), you need to adjust your turrets. Most modern tactical scopes have turrets calibrated in 0.1 Mrad clicks.
The formula for adjustment is:
Correction (Mrads) = (Deviation / Distance) × 1000
Note: Ensure deviation and distance are converted to the same unit (e.g., both in meters) before dividing.
Using the Calculator for Zeroing
If you are at the range and your shot hits 4 inches low at 100 yards:
- Select Distance: 100 Yards
- Select Deviation: 4 Inches
- The calculator determines the angular difference required to move the point of impact to the center.
- Dial the resulting number of clicks on your elevation turret (UP).
function calculateRange() {
var size = parseFloat(document.getElementById("targetSize").value);
var unit = document.getElementById("sizeUnit").value;
var mils = parseFloat(document.getElementById("mradReading").value);
var resBox = document.getElementById("rangeResult");
if (isNaN(size) || isNaN(mils) || mils === 0) {
// Do not show result if inputs are invalid
resBox.style.display = "none";
return;
}
// Convert target size to Meters for calculation base
var sizeInMeters = 0;
if (unit === "cm") {
sizeInMeters = size / 100;
} else if (unit === "m") {
sizeInMeters = size;
} else if (unit === "in") {
sizeInMeters = size * 0.0254;
} else if (unit === "yd") {
sizeInMeters = size * 0.9144;
}
// Basic Formula: Range (m) = (Size (m) * 1000) / Mils
var rangeMeters = (sizeInMeters * 1000) / mils;
var rangeYards = rangeMeters * 1.09361;
document.getElementById("resMeters").innerText = rangeMeters.toFixed(1) + " m";
document.getElementById("resYards").innerText = rangeYards.toFixed(1) + " yds";
resBox.style.display = "block";
}
function calculateAdjustment() {
var dist = parseFloat(document.getElementById("distance").value);
var distUnit = document.getElementById("distUnit").value;
var dev = parseFloat(document.getElementById("deviation").value);
var devUnit = document.getElementById("devUnit").value;
var clickVal = parseFloat(document.getElementById("clickValue").value);
var adjBox = document.getElementById("adjResult");
if (isNaN(dist) || isNaN(dev) || dist === 0) {
adjBox.style.display = "none";
return;
}
// Normalize Distance to Meters
var distMeters = (distUnit === "yd") ? dist * 0.9144 : dist;
// Normalize Deviation to Meters
var devMeters = 0;
if (devUnit === "cm") {
devMeters = dev / 100;
} else if (devUnit === "mm") {
devMeters = dev / 1000;
} else if (devUnit === "in") {
devMeters = dev * 0.0254;
}
// Formula: Mrad = (Deviation / Distance) * 1000 (Small angle approximation)
// Since both are in meters, the ratio is radians. * 1000 gives milliradians.
var mradNeeded = (devMeters / distMeters) * 1000;
// Calculate clicks
var clicks = mradNeeded / clickVal;
document.getElementById("resMradAdj").innerText = mradNeeded.toFixed(2) + " MRAD";
document.getElementById("resClicks").innerText = Math.round(clicks) + " Clicks";
adjBox.style.display = "block";
}