Ballistic Coefficient Calculator

Ballistic Coefficient Calculator estimates the G1 or G7 BC of a bullet from its weight, diameter and form factor. It also measures BC from two chronograph speeds a set range apart.

Ballistic Coefficient Calculator: Estimate or Measure

A ballistic coefficient, or BC, says how well a bullet holds its speed against air drag. Bryan Litz of Berger Bullets defines it as the ability of a bullet to maintain velocity in comparison to a standard projectile. A higher number means less speed lost over the same distance.

The Ballistic Coefficient Calculator reaches that number in two ways. The first estimates BC from the bullet’s weight, diameter and shape, with no shots fired. The second measures it from the speed of a real bullet at two points along its path. Both report the result against the G1 and G7 standards that bullet makers use, and a GA standard covers airgun pellets.

Ballistic Coefficient Formula

A bullet’s BC is its sectional density divided by its form factor. Sectional density is the weight in pounds over the diameter in inches squared. The form factor is the bullet’s drag divided by the drag of the standard bullet at the same speed.

$$SD = \frac{w}{7000 \, d^2}$$

$$BC = \frac{SD}{i}$$

The default entries in the Ballistic Coefficient Calculator repeat the worked example in Litz’s article on form factors. A 175 grain bullet of 0.308 in diameter has a sectional density of 175 / 7000 / 0.308², which is 0.264. Its measured G7 form factor is 1.006, so the G7 BC is 0.264 / 1.006, or 0.262.

The form factor presets come from the same article, where each value belongs to a pictured bullet profile. The table shows how much the shape alone changes the result when weight and diameter stay the same.

Should You Use G1 or G7?

The G in both names stands for the Gâvre Commission of the French naval artillery, which ran drag firings in the late 1800s. Sporting Shooter magazine gives that history in its piece on bullet ballistic coefficients.

The G1 standard is a flat-based projectile with a short, blunt nose. The G7 standard has a long pointed nose and a boat tail.

Litz’s advice in A Better Ballistic Coefficient is to use G7 for boat-tail bullets and G1 for flat-based bullets. A modern long-range bullet does not lose drag the way the G1 shape does. Its G1 BC therefore changes with speed, while its G7 BC stays nearly constant.

The two numbers are not interchangeable. A G7 BC is always the lower figure for the same bullet, because the G7 standard has less drag to be compared with.

Entering a G7 value into a program set to G1 gives a badly wrong trajectory. In the Ballistic Coefficient Calculator the standard is set under Drag Model, and the form factor you enter is read against that standard.

Converting a G7 BC to G1

There is no single conversion factor. The ratio between the two depends on how fast the bullet is going, because the two standard drag curves have different shapes. The Ballistic Coefficient Calculator does the conversion at the muzzle velocity you enter and shows it on the first card.

Above about 1,800 fps the G1 figure is close to twice the G7 figure. Litz’s own example fits that, with a G1 BC of 0.550 matching a G7 BC near 0.282. Below 1,800 fps the ratio falls fast, which is the velocity dependence that makes G1 a poor fit for long-range bullets.

Ballistic Coefficient From Two Velocities

Set Method to Two measured velocities to measure a BC. Enter the speed at a near chronograph, the speed at a far one and the distance between them. The calculator finds the BC that makes the standard bullet lose exactly that much speed over that distance in the air you entered.

$$BC = \frac{\pi \rho \, \Delta x}{8 \int_{v_2}^{v_1} \frac{dv}{v \, C_{ref}(M)}}$$

The symbol rho is the air density and delta x is the distance between the screens. The speeds at the near and far screens are v1 and v2. C ref is the drag coefficient of the G1 or G7 standard at each Mach number M.

The result comes out in kg/m² and is shown in lb/in². The default readings of 2,580 fps and 2,092 fps over 300 yd return a G7 BC of 0.262.

The distance between the screens decides how good the answer is. The table shows the same bullet measured over different spacings, with the change in BC caused by a 1 fps error at the far screen.

The message under the results reports this figure for your own readings and warns when it passes 2%. Published tests use long spacings for this reason. A study by Courtney and Courtney placed the second chronograph 300 ft downrange and found several makers’ advertised BCs too high.

The Physics Form of the Coefficient

Outside the shooting world, the ballistic coefficient is the mass divided by the drag coefficient times the frontal area. It is measured in kg/m² and needs no standard bullet. Choose one of the two Cd options under Drag Model to work in this form.

$$BC = \frac{m}{C_d \, A}$$

Take a 50 g ball of 13 mm diameter with a drag coefficient of 0.51. Its frontal area is 1.327 cm², so its coefficient is 738.6 kg/m², which is 1.051 lb/in². The drag coefficient is held constant in this form, which suits slow, blunt objects better than bullets.

The two forms do not give the same number for one bullet. The default bullet has a G7 BC of 0.262 lb/in², which is 184.2 kg/m², but its mass over drag area at the muzzle is 840.3 kg/m².

The G7 figure divides by the diameter squared and by a ratio of drags, where the physics form divides by the true area and the true drag coefficient of 0.281.

Speed Left at 500 and 1,000 Yards

A BC is only useful for what it predicts. The Ballistic Coefficient Calculator steps the bullet down range through the drag table and reports the speed, energy and time of flight at your target distance. The default bullet leaves at 2,600 fps in standard air of 59 °F and 29.92 inHg.

The bullet stays supersonic to 1,046 yd, where it slows to the 1,116 fps speed of sound. That range matters because Berger notes that stability is often a problem at transonic speed, below about 1,340 fps. This bullet drops under 1,340 fps a little past 800 yd.

Air density changes every figure in the table. At 90 °F and 25.0 inHg the air is 79% as dense as standard air. The same bullet then arrives at 500 yd with 1,960 fps, where it had 1,814 fps. Enter the temperature and pressure at your range under Velocity, Range and Air.

What Is a Good Ballistic Coefficient?

There is no single good number, because BC mixes weight with shape. A heavy bullet of ordinary shape can have the same BC as a light bullet of very low drag.

Litz judges the shape alone by the form factor, and calls a G7 form factor of 0.920 excellent for any caliber. The chart below sets published values beside the form factor each one implies.

The 9mm rows show why pistol bullets are rated against G1. Their short noses and flat bases resemble the G1 shape, so their form factors sit near 1. Entered in the Ballistic Coefficient Calculator with a G1 form factor of 1.011, the 115 grain bullet returns the 0.129 that Hornady lists. Fired at 1,150 fps, it is down to 954 fps at 100 yd.

Airgun Pellets and Round Balls

Diabolo pellets have their own standard. Choose GA, airgun pellets under Drag Model. Hard Air Magazine calls GA the best standard drag model available for diabolo pellets in its guide to drag and ballistic coefficients, and rates its whole pellet chart against it.

For a pellet, the two-velocity method is the practical one. Hard Air Magazine’s pellet BC chart lists the .177 JSB Exact at 940 fps at the muzzle and 770 fps at 30 yd, with a BC of 0.019. Enter those two speeds and 30 yd in the Ballistic Coefficient Calculator with the GA model. It returns a GA BC of 0.021 in standard air.

The gap comes from the method, and the first card shows it. Pellet charts are usually worked with a simple airgun formula, the distance in yards divided by 8,000 times the natural log of the speed ratio. That formula gives 0.019 for these readings, the chart’s own figure. The full GA drag table gives 0.021, and the same shots fitted to G1 give 0.023.

A round ball has a separate option. It uses a sphere drag table, and a form factor of 1.000 is a smooth ball. For slower projectiles still, the Arrow Speed Calculator covers arrows and bolts, and the other motion tools are on the Kinematics Calculators page.