Use this calculator to determine bullet drop, windage, and other ballistic data for your rifle and ammunition combination. Understanding these factors is crucial for accurate long-range shooting.
Ammunition & Rifle Data
Range & Environmental Factors
12 (Headwind)
1
2
3 (Right to Left)
4
5
6 (Tailwind)
7
8
9 (Left to Right)
10
11
Ballistic Results
Bullet Drop:— inches
Windage Adjustment:— inches
Time of Flight:— seconds
Impact Velocity:— fps
Impact Energy:— ft-lbs
Understanding Your Ballistic Trajectory
A ballistic calculator is an essential tool for any shooter, especially when engaging targets at varying distances or in challenging environmental conditions. It predicts how a bullet will travel through the air, accounting for gravity, air resistance, and wind.
Key Input Parameters Explained:
Muzzle Velocity (fps): The speed at which the bullet leaves the barrel. This is a primary factor in determining trajectory and energy.
Bullet Weight (grains): The mass of the bullet. Heavier bullets generally retain more energy and are less affected by wind, but may have a lower muzzle velocity.
Ballistic Coefficient (G1): A measure of a bullet's ability to overcome air resistance. A higher BC indicates less drag and a flatter trajectory. The G1 model is a common standard.
Bullet Diameter (inches): The diameter of the bullet, used to calculate its frontal area for drag computations.
Sight Height (inches): The vertical distance from the center of the rifle's bore to the center of the scope's reticle. This is critical for accurate zeroing.
Zero Range (yards): The distance at which your rifle is sighted in, meaning the bullet should impact exactly where the crosshairs are aimed.
Target Range (yards): The actual distance to your target. The calculator will determine bullet behavior at this specific range.
Wind Speed (mph) & Direction (o'clock): Wind is a major factor in bullet drift. Direction is typically given in "o'clock" format, where 12 is a headwind, 3 is a wind from the right, 6 is a tailwind, and 9 is a wind from the left.
Temperature (Fahrenheit) & Altitude (feet): These environmental factors affect air density, which in turn influences air resistance (drag) on the bullet. Denser air (lower temperature, lower altitude) means more drag.
Understanding the Results:
Bullet Drop (inches): The vertical distance the bullet falls below your line of sight at the target range, relative to your zero. A negative value indicates drop.
Windage Adjustment (inches): The horizontal distance the bullet drifts due to wind at the target range. A positive value typically indicates drift to the right (for a left-to-right wind).
Time of Flight (seconds): The time it takes for the bullet to travel from the muzzle to the target.
Impact Velocity (fps): The speed of the bullet when it reaches the target.
Impact Energy (ft-lbs): The kinetic energy of the bullet upon impact, indicating its potential to transfer energy to the target.
How it Works (Simplified):
This calculator uses a numerical integration method, often called a "point mass" model, to simulate the bullet's path. It breaks the trajectory into many small time steps. In each step, it calculates the forces acting on the bullet (gravity, drag, wind) and updates its position and velocity. The G1 ballistic coefficient and a standard G1 drag function are used to model air resistance. An iterative process is used to find the correct launch angle for your specified zero range.
Example Calculation:
Let's say you're shooting a .308 Winchester with a 168-grain bullet (BC 0.475) at 2800 fps muzzle velocity. Your scope is 1.5 inches above the bore, and you're zeroed at 100 yards. You spot a target at 500 yards, with a 10 mph wind coming from 3 o'clock (right to left). The temperature is 59°F at sea level (0 feet altitude).
Inputting these values into the calculator would yield results similar to:
Bullet Drop: Approximately -48 to -52 inches (meaning it drops 48-52 inches below your line of sight).
Windage Adjustment: Approximately 10 to 12 inches to the left (due to the right-to-left wind).
Time of Flight: Around 0.7 seconds.
Impact Velocity: Roughly 1900-2000 fps.
Impact Energy: Around 1300-1500 ft-lbs.
These results tell you that to hit the 500-yard target, you'd need to aim about 50 inches high and 10-12 inches into the wind (to the right of the target) to compensate for the bullet's movement.
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// Constants
var G = 32.174; // Acceleration due to gravity in ft/s^2
var PI = Math.PI;
var TIME_STEP = 0.001; // seconds for simulation steps
// G1 Drag Coefficient Table (Velocity in fps, Cd_G1) – Piecewise linear approximation
var G1_DRAG_TABLE = [
[0, 0.2], [500, 0.2], [1000, 0.2], [1100, 0.22], [1200, 0.25], [1300, 0.28], [1400, 0.3],
[1500, 0.32], [1600, 0.34], [1700, 0.36], [1800, 0.38], [1900, 0.4], [2000, 0.42],
[2500, 0.4], [3000, 0.38], [3500, 0.36], [4000, 0.34], [5000, 0.32] // Extended for higher velocities
];
// Unit Conversion Functions
function yardsToFeet(y) { return y * 3; }
function inchesToFeet(i) { return i / 12; }
function grainsToSlugs(g) { return g / 7000 / G; } // 1 slug = G lbs, 1 lb = 7000 grains
function mphToFps(m) { return m * 5280 / 3600; }
function fahrenheitToRankine(f) { return f + 459.67; }
// Linear interpolation for G1 Drag Coefficient
function getG1Cd(velocityFps) {
if (velocityFps G1_DRAG_TABLE[G1_DRAG_TABLE.length – 1][0]) return G1_DRAG_TABLE[G1_DRAG_TABLE.length – 1][1];
for (var i = 0; i = p1[0] && velocityFps <= p2[0]) {
var slope = (p2[1] – p1[1]) / (p2[0] – p1[0]);
return p1[1] + slope * (velocityFps – p1[0]);
}
}
return G1_DRAG_TABLE[G1_DRAG_TABLE.length – 1][1]; // Should not be reached
}
// Calculate Air Density (Standard Atmosphere Model)
function calculateAirDensity(tempF, altitudeFt) {
var T0 = 518.67; // Standard temperature at sea level (Rankine)
var P0 = 2116.216; // Standard pressure at sea level (psf)
var L = 0.003566; // Lapse rate (R/ft)
var R_air = 1716; // Gas constant for air (ft-lb/(slug-R))
var tempR = fahrenheitToRankine(tempF);
// Adjust temperature and pressure for altitude
var T_alt = T0 – L * altitudeFt;
var P_alt = P0 * Math.pow(T_alt / T0, G / (L * R_air));
// Adjust pressure for actual temperature at altitude (non-standard temp)
// This is a simplification, a full ICAO model would be more complex.
// For practical purposes, we'll use the calculated P_alt and the input tempR
var rho = P_alt / (R_air * tempR); // Air density in slugs/ft^3
return rho;
}
// Simulate Trajectory
function simulateTrajectory(initialVelocity, launchAngleRad, bulletMassSlugs, bulletAreaSqFt, BC_G1, airDensity, windCrossSpeedFps, sightHeightFt, maxRangeFt) {
var x = 0; // Horizontal distance (feet)
var y = 0; // Vertical distance (feet)
var z = 0; // Lateral distance (feet) – for windage
var vx = initialVelocity * Math.cos(launchAngleRad); // Horizontal velocity (fps)
var vy = initialVelocity * Math.sin(launchAngleRad); // Vertical velocity (fps)
var vz = 0; // Lateral velocity (fps) – for windage
var time = 0;
var path = []; // Stores [x, y, z, velocity, time]
// Ensure BC_G1 is not zero to prevent division by zero
if (BC_G1 <= 0) BC_G1 = 0.001;
while (x = -sightHeightFt) { // Stop if bullet hits ground or exceeds max range
var currentVelocity = Math.sqrt(vx * vx + vy * vy + vz * vz);
if (currentVelocity < 1) currentVelocity = 1; // Prevent division by zero for very low velocities
var Cd_G1 = getG1Cd(currentVelocity);
// Cd_bullet = (Mass / (BC * Area)) * Cd_G1_standard
var Cd_bullet = (bulletMassSlugs / (BC_G1 * bulletAreaSqFt)) * Cd_G1;
// Drag force calculation
var dragForceMagnitude = 0.5 * airDensity * currentVelocity * currentVelocity * bulletAreaSqFt * Cd_bullet;
// Accelerations due to drag
var ax_drag = -dragForceMagnitude * (vx / currentVelocity) / bulletMassSlugs;
var ay_drag = -dragForceMagnitude * (vy / currentVelocity) / bulletMassSlugs;
var az_drag = -dragForceMagnitude * (vz / currentVelocity) / bulletMassSlugs;
// Accelerations due to gravity
var ay_gravity = -G;
// Accelerations due to wind (lateral only for simplicity)
// Relative wind velocity for lateral drift
var relativeWindVelZ = windCrossSpeedFps – vz;
var az_wind = 0.5 * airDensity * relativeWindVelZ * Math.abs(relativeWindVelZ) * bulletAreaSqFt * Cd_bullet / bulletMassSlugs;
// Update velocities
vx += (ax_drag) * TIME_STEP;
vy += (ay_drag + ay_gravity) * TIME_STEP;
vz += (az_drag + az_wind) * TIME_STEP;
// Update positions
x += vx * TIME_STEP;
y += vy * TIME_STEP;
z += vz * TIME_STEP;
time += TIME_STEP;
path.push([x, y, z, currentVelocity, time]);
}
return path;
}
// Find the launch angle required to hit the zero range at sight height
function findZeroAngle(muzzleVelocity, bulletMassSlugs, bulletAreaSqFt, BC_G1, airDensity, zeroRangeFt, sightHeightFt) {
var lowAngle = 0; // radians
var highAngle = 10 * PI / 180; // 10 degrees, a generous upper bound
var iterations = 100; // Number of iterations for bisection method
for (var i = 0; i < iterations; i++) {
var midAngle = (lowAngle + highAngle) / 2;
var path = simulateTrajectory(muzzleVelocity, midAngle, bulletMassSlugs, bulletAreaSqFt, BC_G1, airDensity, 0, sightHeightFt, zeroRangeFt + 10); // Simulate slightly past zero range, no wind for zeroing
var y_at_zero = -sightHeightFt; // Default if bullet doesn't reach zero range
var foundZeroPoint = false;
for (var j = 0; j = zeroRangeFt) {
// Interpolate y at exactly zeroRangeFt
if (j > 0) {
var p1 = path[j-1];
var p2 = path[j];
var ratio = (zeroRangeFt – p1[0]) / (p2[0] – p1[0]);
y_at_zero = p1[1] + ratio * (p2[1] – p1[1]);
} else {
y_at_zero = path[j][1];
}
foundZeroPoint = true;
break;
}
}
if (!foundZeroPoint) { // Bullet fell before zero range
lowAngle = midAngle; // Need more angle
} else if (y_at_zero > 0) { // Bullet hit above sight line at zero range
highAngle = midAngle;
} else { // Bullet hit below sight line at zero range
lowAngle = midAngle;
}
}
return (lowAngle + highAngle) / 2;
}
function calculateBallistics() {
var errorDiv = document.getElementById("ballisticError");
errorDiv.style.display = "none";
errorDiv.innerHTML = "";
// Get input values
var muzzleVelocity = parseFloat(document.getElementById("muzzleVelocity").value);
var bulletWeight = parseFloat(document.getElementById("bulletWeight").value);
var ballisticCoefficient = parseFloat(document.getElementById("ballisticCoefficient").value);
var bulletDiameter = parseFloat(document.getElementById("bulletDiameter").value);
var zeroRange = parseFloat(document.getElementById("zeroRange").value);
var targetRange = parseFloat(document.getElementById("targetRange").value);
var sightHeight = parseFloat(document.getElementById("sightHeight").value);
var windSpeed = parseFloat(document.getElementById("windSpeed").value);
var windDirection = parseFloat(document.getElementById("windDirection").value);
var temperature = parseFloat(document.getElementById("temperature").value);
var altitude = parseFloat(document.getElementById("altitude").value);
// Input validation
if (isNaN(muzzleVelocity) || muzzleVelocity <= 0) { errorDiv.innerHTML = "Please enter a valid Muzzle Velocity."; errorDiv.style.display = "block"; return; }
if (isNaN(bulletWeight) || bulletWeight <= 0) { errorDiv.innerHTML = "Please enter a valid Bullet Weight."; errorDiv.style.display = "block"; return; }
if (isNaN(ballisticCoefficient) || ballisticCoefficient <= 0) { errorDiv.innerHTML = "Please enter a valid Ballistic Coefficient (G1)."; errorDiv.style.display = "block"; return; }
if (isNaN(bulletDiameter) || bulletDiameter <= 0) { errorDiv.innerHTML = "Please enter a valid Bullet Diameter."; errorDiv.style.display = "block"; return; }
if (isNaN(zeroRange) || zeroRange <= 0) { errorDiv.innerHTML = "Please enter a valid Zero Range."; errorDiv.style.display = "block"; return; }
if (isNaN(targetRange) || targetRange <= 0) { errorDiv.innerHTML = "Please enter a valid Target Range."; errorDiv.style.display = "block"; return; }
if (targetRange < zeroRange) { errorDiv.innerHTML = "Target Range should ideally be greater than or equal to Zero Range for meaningful drop calculations."; errorDiv.style.display = "block"; }
if (isNaN(sightHeight) || sightHeight < 0) { errorDiv.innerHTML = "Please enter a valid Sight Height."; errorDiv.style.display = "block"; return; }
if (isNaN(windSpeed) || windSpeed < 0) { errorDiv.innerHTML = "Please enter a valid Wind Speed."; errorDiv.style.display = "block"; return; }
if (isNaN(temperature)) { errorDiv.innerHTML = "Please enter a valid Temperature."; errorDiv.style.display = "block"; return; }
if (isNaN(altitude)) { errorDiv.innerHTML = "Please enter a valid Altitude."; errorDiv.style.display = "block"; return; }
// Convert units to feet, slugs, seconds
var muzzleVelocityFps = muzzleVelocity;
var bulletMassSlugs = grainsToSlugs(bulletWeight);
var bulletDiameterInches = bulletDiameter;
var bulletAreaSqFt = PI * Math.pow(inchesToFeet(bulletDiameterInches) / 2, 2);
var zeroRangeFt = yardsToFeet(zeroRange);
var targetRangeFt = yardsToFeet(targetRange);
var sightHeightFt = inchesToFeet(sightHeight);
var windSpeedFps = mphToFps(windSpeed);
// Calculate air density
var airDensity = calculateAirDensity(temperature, altitude);
// Calculate crosswind component
// 3 o'clock is 0 rad (90 deg from bullet path), 9 o'clock is PI rad (270 deg)
// 12 o'clock is -PI/2, 6 o'clock is PI/2
// (windDirection – 3) * PI / 6 converts o'clock to angle relative to 3 o'clock (0 rad)
var windAngleRad = (windDirection – 3) * PI / 6;
var windCrossSpeedFps = windSpeedFps * Math.sin(windAngleRad); // Positive for left-to-right wind
// 1. Find the initial launch angle for zeroing
var zeroAngleRad = findZeroAngle(muzzleVelocityFps, bulletMassSlugs, bulletAreaSqFt, ballisticCoefficient, airDensity, zeroRangeFt, sightHeightFt);
// 2. Simulate the full trajectory to the target range with the determined zero angle and wind
var fullTrajectory = simulateTrajectory(muzzleVelocityFps, zeroAngleRad, bulletMassSlugs, bulletAreaSqFt, ballisticCoefficient, airDensity, windCrossSpeedFps, sightHeightFt, targetRangeFt + 10); // Simulate slightly past target range
// Find results at target range
var bulletDropInches = 0;
var windageAdjustmentInches = 0;
var timeOfFlight = 0;
var impactVelocity = 0;
var impactEnergy = 0;
var foundTargetPoint = false;
for (var i = 0; i = targetRangeFt) {
// Interpolate values at exactly targetRangeFt
if (i > 0) {
var p1 = fullTrajectory[i-1];
var p2 = fullTrajectory[i];
var ratio = (targetRangeFt – p1[0]) / (p2[0] – p1[0]);
var y_at_target = p1[1] + ratio * (p2[1] – p1[1]);
var z_at_target = p1[2] + ratio * (p2[2] – p1[2]);
var v_at_target = p1[3] + ratio * (p2[3] – p1[3]);
var t_at_target = p1[4] + ratio * (p2[4] – p1[4]);
bulletDropInches = (y_at_target – sightHeightFt) * 12;
windageAdjustmentInches = z_at_target * 12;
timeOfFlight = t_at_target;
impactVelocity = v_at_target;
impactEnergy = 0.5 * bulletMassSlugs * impactVelocity * impactVelocity;
} else { // Target range is very close to muzzle
bulletDropInches = (fullTrajectory[i][1] – sightHeightFt) * 12;
windageAdjustmentInches = fullTrajectory[i][2] * 12;
timeOfFlight = fullTrajectory[i][4];
impactVelocity = fullTrajectory[i][3];
impactEnergy = 0.5 * bulletMassSlugs * impactVelocity * impactVelocity;
}
foundTargetPoint = true;
break;
}
}
if (!foundTargetPoint) {
errorDiv.innerHTML = "Bullet did not reach target range. Consider increasing muzzle velocity or reducing target range.";
errorDiv.style.display = "block";
// Display last known values or zeros
var lastPoint = fullTrajectory[fullTrajectory.length – 1];
if (lastPoint) {
bulletDropInches = (lastPoint[1] – sightHeightFt) * 12;
windageAdjustmentInches = lastPoint[2] * 12;
timeOfFlight = lastPoint[4];
impactVelocity = lastPoint[3];
impactEnergy = 0.5 * bulletMassSlugs * impactVelocity * impactVelocity;
} else {
bulletDropInches = 0; windageAdjustmentInches = 0; timeOfFlight = 0; impactVelocity = 0; impactEnergy = 0;
}
}
// Display results
document.getElementById("bulletDrop").innerHTML = bulletDropInches.toFixed(2);
document.getElementById("windageAdjustment").innerHTML = windageAdjustmentInches.toFixed(2);
document.getElementById("timeOfFlight").innerHTML = timeOfFlight.toFixed(3);
document.getElementById("impactVelocity").innerHTML = impactVelocity.toFixed(0);
document.getElementById("impactEnergy").innerHTML = impactEnergy.toFixed(0);
}