About

Ballistic coefficient (BC) quantifies a projectile's ability to overcome air resistance in flight. A miscalculated BC propagates errors through every downstream prediction: drop tables, wind drift, time of flight, and retained energy at range. For long-range shooting beyond 400 m, a 5% error in BC can shift point of impact by several MOA. This calculator computes BC from projectile mass m, caliber d, and drag coefficient C_d against both G1 (flat-base reference) and G7 (boat-tail reference) standard projectile models. It also derives sectional density SD and form factor i.

Limitations: this tool assumes standard ICAO atmosphere (15 °C, 1013.25 hPa, 0% humidity). Real-world BC varies with Mach number and is not truly constant across the velocity envelope. G7 models approximate boat-tail projectiles more accurately above 1.2 Mach. For subsonic flight or unconventional shapes, empirical drag functions or CFD analysis are required. Pro tip: manufacturer-published BC values are often optimistic; independent Doppler radar measurements (e.g., Litz methodology) tend to be 3 - 8% lower.

Formulas

The ballistic coefficient relates a projectile's mass, cross-sectional area, and aerodynamic drag to a reference standard projectile. The fundamental definition:

BC = SDi

Where sectional density SD is computed in imperial units as:

SD = m7000 × d²

Where m is mass in grains and d is caliber in inches. The divisor 7000 converts grains to pounds. The form factor i is the ratio of the projectile's drag coefficient to the reference standard's drag coefficient:

i = C_d (projectile)C_d (reference)

Alternatively, BC can be computed directly from first principles using the physical cross-sectional area:

BC = mC_d × A

Where A = π × (d ÷ 2)² is the cross-sectional area. This yields BC in kg/m² when SI units are used. The G1 reference projectile has C_d ≈ 0.5191 at Mach 1.0. The G7 reference has C_d ≈ 0.2720 at Mach 1.0.

Reference Data

Projectile	Caliber	Mass (gr)	Diameter (in)	SD	BC G1	BC G7	Type
5.56×45 M855	.224	62	0.224	0.177	0.304	0.151	FMJ BT
6.5 Creedmoor 140gr	.264	140	0.264	0.287	0.625	0.315	HPBT Match
7.62×51 M80	.308	147	0.308	0.221	0.393	0.197	FMJ BT
.308 Win 175gr SMK	.308	175	0.308	0.264	0.505	0.259	HPBT Match
.308 Win 168gr SMK	.308	168	0.308	0.253	0.462	0.230	HPBT Match
.30-06 M2 Ball	.308	150	0.308	0.226	0.408	0.205	FMJ FB
.338 Lapua 250gr	.338	250	0.338	0.313	0.670	0.340	HPBT Match
.338 Lapua 300gr	.338	300	0.338	0.375	0.810	0.410	Hybrid Match
.50 BMG M33 Ball	.510	647	0.510	0.356	0.670	0.337	FMJ BT
.50 BMG A-MAX 750gr	.510	750	0.510	0.412	1.050	0.530	Polymer Tip
7mm Rem Mag 168gr	.284	168	0.284	0.298	0.640	0.326	VLD Match
.223 Rem 77gr SMK	.224	77	0.224	0.220	0.372	0.190	HPBT Match
6mm Creedmoor 105gr	.243	105	0.243	0.254	0.550	0.275	Hybrid
.300 Win Mag 190gr	.308	190	0.308	0.286	0.533	0.275	HPBT Match
.375 CheyTac 350gr	.375	350	0.375	0.356	0.840	0.425	Lathe-turned Solid
9mm Luger 124gr	.355	124	0.355	0.141	0.145	0.073	FMJ RN
.45 ACP 230gr	.452	230	0.452	0.162	0.195	0.098	FMJ RN
6.5 PRC 147gr	.264	147	0.264	0.301	0.660	0.333	ELD Match

Frequently Asked Questions

G7 is the better reference model for modern boat-tail and VLD (Very Low Drag) projectiles because the G7 standard projectile shape closely matches these designs. G1 is derived from a flat-base, blunt-ogive shape typical of older military projectiles. Using G1 for a sleek boat-tail bullet forces the solver to apply a form factor i that varies significantly across the Mach range, reducing prediction accuracy. G7 keeps i nearly constant across supersonic velocities, yielding more consistent trajectory predictions beyond 600 m.

Manufacturers often publish BC values measured at a single high muzzle velocity (typically 2800 - 3000 ft/s). Since drag coefficient C_d is Mach-dependent, the effective BC decreases as the projectile decelerates. Independent testers like Bryan Litz use Doppler radar to measure BC across the entire flight envelope and typically report values 3 - 8% lower than manufacturer claims. This calculator uses a single-point C_d input, so your result corresponds to that specific velocity regime.

Sectional density SD measures mass concentration per unit cross-sectional area. Higher SD generally correlates with deeper penetration because the projectile carries more momentum per unit of frontal resistance. For hunting applications, SD above 0.250 is commonly recommended for medium game, and above 0.300 for large or dangerous game. However, SD alone does not account for bullet construction, expansion, or fragmentation behavior.

Divide your projectile's measured C_d by the reference standard's C_d at the same Mach number. For G1 at Mach 1.0, the reference C_d is approximately 0.5191. For G7 at Mach 1.0, it is approximately 0.2720. Typical form factors for modern match bullets range from 0.85 to 1.10 against G7, and 0.40 to 0.65 against G1. A form factor below 1.0 means the projectile is more aerodynamic than the reference standard.

BC itself is a property of the projectile, not the atmosphere. However, the effective drag force depends on air density ρ, which decreases with altitude and increases with lower temperature. At 1500 m elevation, air density drops roughly 15% compared to sea level, reducing drag proportionally. Ballistic solvers account for this by adjusting the drag equation rather than changing BC. This calculator assumes standard ICAO atmosphere: 15 °C, 1013.25 hPa, sea level.

Yes. The formula is universal for any projectile in ballistic flight. For arrows, mass is typically 300 - 600 grains with diameters around 0.245 - 0.350 in. Air rifle pellets range from 7 - 16 grains at 0.177 - 0.22 in. Note that G1/G7 references were designed for supersonic bullets. At subsonic velocities (arrows, pellets), the drag curve shape differs substantially from either reference, so the resulting BC may not predict trajectories accurately without a custom drag model.