How The Calculator Works

Overview

This calculator uses a point-mass trajectory model (also called a 3-DOF model) to simulate bullet flight. This is the industry-standard approach used by most ballistics software, including JBM Ballistics and many commercial solutions.

For each calculation, it computes: bullet drop (inches, MOA, MIL), wind drift (inches, MOA, MIL), remaining velocity, kinetic energy, and time of flight at each range increment.

Ballistic Model

Point-Mass Trajectory Simulation

The calculator models the bullet as a point mass moving through the atmosphere, subject to gravitational acceleration (32.194 ft/s²) and aerodynamic drag. The simulation steps through time, updating velocity and position at each increment until the bullet reaches the target range.

Drag Functions (G1 through G8)

The calculator supports the standard G1 through G8 drag models. Each drag function represents a different standard projectile shape:

• G1 — Flat-base bullets, most common for commercial ammunition data
• G7 — Boat-tail bullets, preferred for long-range match projectiles
• G2, G5, G6, G8 — Specialized shapes (less commonly used)

Most manufacturers publish G1 ballistic coefficients. For precision long-range shooting with boat-tail bullets, G7 often provides better accuracy at extended ranges. See real-world examples of how drag functions affect different calibers on our 308 Winchester, 6.5 Creedmoor, 6.5 PRC, and 223 Remington caliber pages.

Atmospheric Corrections

Air density significantly affects bullet drag. The calculator corrects the ballistic coefficient based on four atmospheric factors:

• Altitude — Higher altitude = thinner air = less drag
• Barometric pressure — Lower pressure = less drag
• Temperature — Higher temperature = thinner air = less drag
• Humidity — Higher humidity = slightly less drag (water vapor is lighter than air)

Standard conditions are: sea level altitude, 29.53 inHg pressure, 59°F temperature, and 78% relative humidity. The calculator adjusts your ballistic coefficient from these standards to match your actual shooting conditions.

Numerical Methods

Integration Approach

I use trapezoidal integration with dynamic time steps to compute the trajectory. The time step automatically adjusts based on current velocity (approximately 0.5 ÷ velocity seconds), providing finer resolution during the critical early flight phase when the bullet is moving fastest.

Zero Angle Calculation

To determine the bore angle required for your zero range, the calculator uses an iterative bisection method that converges to within 0.01 MOA tolerance. This ensures your calculated drop values are accurate relative to your specified zero distance.

Forces Modeled

Known Limitations

I believe in transparency about what this calculator can and cannot do:

• Coriolis effect — Not modeled. This becomes relevant beyond approximately 1,000 yards, especially for north/south shots. Expect 3-4 inches of drift at 1,000 yards at mid-latitudes.
• Spin drift — Not modeled. For right-hand twist barrels, bullets drift slightly right. This can reach 8-10 inches at 1,000 yards for typical rifle cartridges.
• BC variation with velocity — The calculator uses a single BC value. In reality, BC changes slightly as the bullet slows through different velocity regimes.
• Transonic instability — As bullets slow through the transonic zone (~1,340-890 fps), accuracy predictions become less reliable.

Practical guidance: For most hunting and target shooting under 1,000 yards, these effects are small compared to wind-reading errors and shooter variability. This calculator is well suited for typical precision rifle applications.

Validation

I have cross-validated this calculator against JBM Ballistics, a widely respected reference in the shooting community. The results typically agree within ±0.2 MOA across multiple calibers and conditions.

I continuously spot-check the outputs against published data and welcome feedback from users who compare the results to their real-world observations.

Attribution & References

This calculator is built on the GNU Exterior Ballistics Library by Derek Yates, released under the GNU General Public License. I have enhanced the original library with:

• MIL support for elevation and windage (in addition to MOA)
• Kinetic energy calculations using bullet weight
• Configurable range intervals and maximum distances
• Input validation and error handling
• Modern JavaScript implementation for web browsers

The drag coefficient curves used in G1-G8 functions are industry-standard values derived from decades of ballistic research and testing.