Bullet Drop and External Ballistics Calculator

External Ballistics External ballistics covers the flight of a projectile after it leaves the barrel. Gravity constantly accelerates the bullet downward at 9.81 m/s². The bullet drops below the line of bore, not the line of sight. A scope sits above the bore, so the bullet crosses the line of sight twice: once close in, once at the far zero.

Simplified Drop Formula (no air resistance) Drop (vacuum) = ½ × g × t² Where t = time of flight = range / muzzle_velocity (approximation without drag). In reality, air drag slows the bullet and increases time of flight, increasing drop.

G1 Ballistic Coefficient The BC (G1) measures how efficiently a bullet retains velocity against drag. Higher BC = less drag = less drop. Typical G1 BCs: .22 LR: 0.13–0.16 | .308 168gr: 0.475 | 6.5 Creedmoor 147gr: 0.697 .338 Lapua 250gr: 0.587 | .50 BMG 750gr: 0.950

Approximate Trajectory with Drag (Pejsa model) This calculator uses a simplified atmospheric drag model for practical field use. For precision long-range work, use Hornady 4DOF or Applied Ballistics software.

What this model is good at, and what it is not

Worth being specific, because a trajectory table that looks precise invites more trust than a simplified model has earned.

The drop column comes from a numerical integration whose drag constant is fitted against published G1 trajectories. It tracks real data within about an inch at 300 yards and a couple of inches at 500. Past roughly 600 yards it starts reading short, and by 1000 it is optimistic by a good margin. Treat the long rows as a rough guide to how much elevation you will need, not as dope.

The velocity and time of flight columns come from Pejsa’s supersonic retained-velocity form, which is a different piece of arithmetic:

V(x) = (√V₀ − x / 2F)², with F proportional to the ballistic coefficient

That form matches published G1 velocity tables inside 1% for a .308 168gr and a 6.5 Creedmoor 147gr from the muzzle out to 500 yards, and within a few percent for a .338 Lapua. Its time of flight follows from the same algebra: t = x / √(V₀ × V), the geometric mean of the start and end velocities.

Two columns, two models. They are reported side by side because each is the better tool for its own job, and it is more honest to say so than to derive both from one fit that only really serves one of them.

The velocity form is built for supersonic flight. Below about Mach 1.2 it stops being reliable, which is also the point where the bullet itself stops being reliable, so the table flags it.

Scope Adjustment MOA (Minute of Angle): 1 MOA ≈ 1.047 inches at 100 yards (close enough to 1 inch). MRAD (Mil-radian): 1 mil = 10 cm at 100 m = 3.6 inches at 100 yards. Convert drop to MOA: MOA = drop_inches / (range_yards / 100) Convert drop to mils: mils = drop_cm / (range_m / 10)

Zero Range A typical 100-yard zero means the bullet is at the same height as the crosshair at 100 yards.

At 50 yards with that zero the bullet is essentially on the crosshair, a shade low, because it has only just climbed up through the line of sight. It is not an inch and a half high. That figure gets quoted a lot and it is the scope height above the bore, not a point on the trajectory. Run a 100-yard zero through the table above and the 50-yard row confirms it.

Where you do see the bullet an inch or two high at mid range is with a 200-yard zero, which is why long-range and hunting shooters favour it: the whole trajectory stays inside a few inches of the crosshair from the muzzle out past 250 yards, so there is nothing to think about on a close shot.