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 (32.174 ft/s²) and aerodynamic drag. The trajectory is integrated step by step until the bullet passes your maximum range.

Drag Models

The calculator supports the G1, G2, G5, G6, G7, and G8 drag models, using the standard drag tables published by McCoy. Each 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)

G3 and G4 are not offered: no drag data has been published for them.

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 computes it from four atmospheric factors:

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

The reference is the International Standard Atmosphere (ICAO): sea level, 29.92 inHg, 59°F, and 0% humidity. Most modern published BCs are referenced to it. Some older G1 BCs were published against the Army Standard Metro atmosphere (29.53 inHg, 78% humidity) instead; used here, those read about 1.8% optimistic, or three to five inches of drop at 1,000 yards.

Barometric vs. Station Pressure

Pressure can be entered two ways. Barometric pressure is the number in a weather report. It has been corrected to sea level, so the calculator converts it back to the pressure at your altitude. Station pressure is the actual pressure where you stand, which is what a Kestrel reads when its reference altitude is set to 0. It is used as entered, and altitude has no further effect. Mixing them up matters: at 5,000 feet, entering a weather-report reading as station pressure moves a 308 Winchester's elevation at 1,000 yards by about 4.5 MOA.

Numerical Methods

Integration Approach

The trajectory is integrated with a fourth-order Runge–Kutta (RK4) method. Each row of the table is then interpolated onto the exact distance you asked for, measured along your line of sight, which is what a rangefinder reads. Uphill and downhill tables land on 100, 200, 300 yards rather than near them.

Zero Angle Calculation

The bore angle for your zero range is found iteratively, until the bullet crosses the line of sight at the zero distance to within 0.00006 inches. The zero is always solved on a level shot, because it describes how your rifle was zeroed, not the shot you are taking. An angled shot uses the same zero as a flat one.

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 verify this calculator against a reference set of 21 trajectories (242 table rows) generated by py-ballisticcalc, a widely used open-source ballistics library. The set covers six drag models, three muzzle velocities, five wind directions, three temperatures, three zero ranges, and a transonic 1,500-yard shot. The calculator reproduces every row to within the rounding of its table: 0.005 inches and 0.5 fps.

That reference set is itself cross-checked against an independent implementation of McCoy's MCTRAJ trajectory program. The two agree to about 0.1 inch at 1,000 yards. These checks run automatically on every proposed change to the site.

Agreement with reference software is not the same as agreement with your rifle. The ballistic coefficient, muzzle velocity, and conditions you enter matter more than any of this, so confirm your data at the range. I welcome feedback from users who compare the results to their real-world observations.

Attribution & References

The trajectory engine is js-ballistics by o-murphy, released under the ISC license. It is part of the Ballistics Lab project, whose C++ core also powers py-ballisticcalc. On top of it, this calculator adds:

• MOA and MIL (true milliradian) output for elevation and windage
• Barometric-to-station pressure conversion
• Exact line-of-sight table rows for uphill and downhill shots
• Printable tables and side-by-side load comparison
• Input validation and error handling

The drag tables are the standard G-model tables published by McCoy. Earlier versions of this calculator were built on the GNU Exterior Ballistics Library by Derek Yates, and I'm grateful for that foundation.