How this instrument works
Ballistic coefficient packs three things a projectile is fighting against — its own mass, its frontal area, and how bluntly that area meets the air — into one number that predicts how fast drag steals its velocity. Divide mass by the product of drag coefficient and frontal area, BC = m ⁄ (Cd·π(d ⁄ 2)²), and a heavy, narrow, streamlined body returns a large BC; a light, wide, blunt one returns a small one. The units, kilograms per square metre, are exactly what falls out of dividing a mass by an area once the dimensionless drag coefficient cancels its own units away.
The shape of the formula comes straight from the drag force itself: F = ½·ρ·v²·Cd·A. Divide by mass to get deceleration, a = F ⁄ m = ½·ρ·v² ⁄ (m ⁄ (Cd·A)), and that denominator, m ⁄ (Cd·A), is exactly the ballistic coefficient. A body with a large BC needs a bigger push from the air to lose the same fraction of speed, which is why long-range shooters, artillery designers, and anyone modelling a falling object's terminal speed reach for this single figure instead of recomputing mass, area, and drag coefficient every time.
The formula assumes Cd stays fixed, which only holds over a narrow speed range — drag coefficient rises sharply as a projectile crosses the transonic zone near the speed of sound, so a BC measured at rifle-muzzle velocity is not the same number that applies once the same round slows past Mach 1. That is why serious long-range ballistics tables quote BC against a reference drag curve, the G1 or G7 standard, rather than one constant Cd, and why this instrument's result is best read as a snapshot at the drag coefficient you supplied, not a fixed property stamped on the object forever.
- Enter the projectile's mass into Projectile mass — grams by default, with kilograms and grains also on the unit menu.
- Enter its widest point into Diameter — millimetres by default, or switch to centimetres or inches.
- Enter the Drag coefficient, Cd — a dimensionless number, roughly 0.1–0.2 for a sleek boat-tail bullet and closer to 1 for a flat-nosed cylinder.
- Read Ballistic coefficient, in kg ⁄ m² — the higher the number, the flatter and faster the projectile carries downrange.
Worked example — a 10 g, 8 mm projectile at Cd 0.3
Set Projectile mass to 10 g, Diameter to 8 mm, and Drag coefficient to 0.3 — a plausible profile for a small-calibre rifle bullet with a moderately pointed nose. The instrument converts to SI before computing: 10 g becomes 0.01 kg and 8 mm becomes 0.008 m, so the frontal area works out to π×(0.008 ⁄ 2)² = π×0.004² = 0.0000502655 m². Dividing gives BC = 0.01 ⁄ (0.3 × 0.0000502655) = 663.145596216 kg/m².
That figure, 663.1 kg/m², sits well above a typical handgun round, which often lands under 150 kg/m², and it signals a projectile that sheds velocity slowly: over the first few hundred metres it drops less and drifts less in a crosswind than a blunter or lighter body fired at the same speed, which is precisely the property long-range shooters chase when they pick ammunition.
Questions
What does a high ballistic coefficient actually mean?
It means the projectile loses velocity to drag more slowly than one with a lower BC, so it retains more energy, drops less over distance, and drifts less in wind. A varmint bullet might sit near 200 kg/m², while a streamlined long-range boat-tail bullet can exceed 800 kg/m² — the difference comes from being heavier for its frontal area and shaped to keep Cd low.
Why does diameter appear squared in the formula?
Because the projectile fights drag over its frontal area, not its diameter directly, and a circle's area scales with the square of its radius: A = π(d ⁄ 2)². Doubling the diameter quadruples the area the air pushes against, so the ballistic coefficient falls to roughly a quarter of its value for the same mass and drag coefficient.
Is the drag coefficient the same at every speed?
No. Cd stays fairly flat at low subsonic speeds, climbs sharply as the projectile nears the speed of sound around Mach 0.8 to 1.2, then eases off again supersonically. A ballistic coefficient built from a muzzle-velocity Cd describes behaviour near that speed, not across the whole flight, which is why long-range shooters use velocity-banded BC tables instead of one fixed figure.
How is ballistic coefficient different from sectional density?
Sectional density is just mass divided by frontal area, or by diameter squared in the traditional inches-and-pounds form, and it ignores shape entirely. Ballistic coefficient divides that same mass by frontal area and drag coefficient together, so it also captures how bluntly or sharply the projectile is shaped — two bullets with identical sectional density but different nose profiles end up with different BCs.
Does a bigger ballistic coefficient always mean a better bullet?
Not necessarily. It means the bullet resists drag better, which flattens trajectory and cuts wind drift at range, but a high BC does nothing for terminal performance, accuracy, or recoil. Hunters and target shooters routinely trade some BC for expansion behaviour or manufacturing tolerances that matter more at their working distances.
What happens to the ballistic coefficient if I double the mass?
It doubles too, since BC is directly proportional to mass once diameter and drag coefficient are fixed. Take the mass in the worked example from 10 g to 20 g and BC rises from 663.1 kg/m² to 1,326.3 kg/m² — exactly double — which is the arithmetic reason heavier-for-caliber projectiles are prized for retained velocity.
Can this formula apply to anything besides bullets?
Yes. Any body moving through air with a roughly circular cross-section — a hailstone, an artillery shell, a meteoroid fragment, a re-entry capsule — has a ballistic coefficient defined the same way, mass over drag-times-area. Meteorologists use this same ratio to model hailstone terminal velocity, and aerospace engineers use it to estimate how fast a capsule decelerates on atmospheric entry.