A ballistic coefficient describes how well a projectile holds its speed against air drag, expressed as a comparison with a standard reference shape. It is not a measurement of the bullet on its own. It is a ratio: how heavy the bullet is for its frontal area, divided by how much drag its shape produces relative to a reference projectile whose drag curve was measured and published a long time ago. Both halves of that ratio matter, and the second half is where almost every misunderstanding starts.
This calculator takes the mass, the diameter and the form factor and returns the ballistic coefficient against the drag model you name, or works backwards from a published BC to the form factor it implies. Arb Digital builds these tools because the arithmetic is short and the traps are not: the single most common error in shooting-sports discussion is comparing a G1 coefficient with a G7 coefficient as though they were the same quantity. They are not, and the numbers differ by roughly a factor of two for the same bullet.
What This Ballistic Coefficient Calculator Does
It computes the standard published definition. Sectional density is the projectile's mass divided by the square of its diameter, in the customary units of pounds per square inch, which is why the grain figure is divided by 7,000. Form factor is the ratio of the bullet's drag to the reference projectile's drag on the model you chose. The ballistic coefficient is sectional density divided by form factor, exactly as set out in the technical material published by bullet makers such as Berger Bullets, whose form-factor article states the relation in that form.
Alongside the coefficient itself the results grid shows the sectional density on its own, the form factor, the coefficient converted to metric units of kilograms per square metre, and a drag-retardation ratio against a second BC you supply. That last figure is the practically useful one: at the same speed and in the same air, drag deceleration is inversely proportional to the ballistic coefficient, so a bullet with twice the BC sheds speed at half the rate.
How to Use It
- Choose the drag model first. G1 or G7. Everything downstream is referenced to that choice, and a form factor or a published BC from the other model will produce a wrong answer with no warning sign.
- Enter the bullet's real diameter. Not the cartridge name. Diameter is squared in the sectional density, so a two per cent error in diameter becomes a four per cent error in the result.
- Enter the mass. Grains or grams, as selected. The page converts internally and reports sectional density in the customary lb/in² either way.
- Supply a form factor, or switch modes. If you have the maker's published BC instead, switch the solver to form-factor mode and the page returns the form factor that BC implies for this bullet's sectional density.
- Read the retardation ratio. Set the comparison BC to whatever you are considering against it. The ratio tells you the relative rate of speed loss, which is the thing a BC actually predicts.
The Formula and How It Is Calculated
Let m be the projectile mass in grains and d its diameter in inches. Sectional density in pounds per square inch is:
SD = (m ÷ 7000) ÷ d²
And with a form factor i referenced to the chosen drag model:
BC = SD ÷ i
Worked through with the values loaded on this page: a 168-grain bullet of 0.308 in diameter has a mass of 168 ÷ 7000 = 0.024 lb, and 0.308² = 0.094864 in², giving a sectional density of 0.024 ÷ 0.094864 = 0.25299 lb/in². Divide that by a G1 form factor of 0.547 and the ballistic coefficient comes out at 0.46251. Against a comparison BC of 0.500, the retardation ratio is 0.500 ÷ 0.46251 = 1.081, meaning this bullet loses speed about eight per cent faster than the comparison at the same velocity.
The metric conversion is a unit change and nothing more. One pound per square inch of sectional density equals 703.07 kg/m², so the same coefficient reads as 325.2 kg/m². Some European ballistics literature uses that form; the physics is identical.
G1 Against G7 — Why the Model Has to Be Named
The reference projectiles are real, specified shapes whose drag was measured across a range of speeds and tabulated. The G1 standard is a short, flat-based, blunt shape from the era it was defined in. The G7 standard is a long, pointed, boat-tailed shape much closer to a modern long-range match bullet. A form factor is a ratio against one of those two curves, so it only means something once you say which.
The practical consequence is that a G1 coefficient for a modern low-drag bullet is not stable. Because the bullet's drag curve has a different shape from the G1 reference curve, the ratio between them changes as the bullet slows down, so the "BC" drifts with velocity. Makers deal with this by publishing banded G1 figures for different velocity ranges, or by publishing a G7 figure that stays much closer to constant. When a G1 and a G7 number appear side by side for the same bullet, the G7 will be roughly half the G1 value — not because the bullet is worse, but because the reference shape it is being divided by is much slipperier.
This is why a page like this refuses to convert between them. There is no fixed conversion factor; the relationship depends on the bullet's own drag curve. If you need a G7 number, take the maker's published G7 number.
Sectional Density Is Not Ballistic Coefficient
The two get used interchangeably in casual discussion and they are not the same thing. Sectional density is pure geometry and mass: how much bullet is packed behind each square inch of frontal area. It says nothing about shape. A round ball and a long boat-tail of identical mass and diameter have identical sectional density and wildly different ballistic coefficients, because the form factor between them differs enormously.
Sectional density still matters on its own. It appears in the BC as the numerator, and it is the quantity that governs how much mass has to be decelerated per unit of frontal area, which is the reason a heavier bullet of the same calibre generally carries better. But a shooter comparing two bullets on sectional density alone is ignoring the half of the equation that shape controls. Our momentum calculator and kinetic energy calculator handle the related quantities that depend on mass and speed rather than on shape.
What a Ballistic Coefficient Cannot Tell You
A BC predicts one thing: the rate at which a projectile sheds speed relative to the reference model, in the atmosphere the model was defined for. It does not predict where the bullet lands. Trajectory needs the launch velocity, the sight height, the zero distance, the air density on the day, and the wind, and those are separate inputs to a separate solver.
It also assumes the projectile is stable and flying point-forward. A bullet that is yawing because the barrel's twist rate is not fast enough for its length behaves nothing like its published BC, because its effective frontal area and drag are both wrong. Our barrel twist rate calculator covers that stability question with the published Miller and Greenhill relations, and the two pages belong together: a BC is only meaningful for a bullet that is actually stabilised.
Finally, a published BC comes from measurements in a defined standard atmosphere. Air density changes with altitude, temperature and pressure, and the effective coefficient scales with it. The air density calculator gives the density figure and the speed of sound calculator gives the local sonic velocity, which matters because drag rises sharply through the transonic region and both reference drag curves have a pronounced peak near Mach 1.
Measuring a Form Factor Rather Than Assuming One
The honest way to get a form factor for a specific bullet is to derive it from measured performance, which is what the second mode on this page supports in reverse. If a maker publishes a BC and you know the sectional density, the implied form factor falls straight out. If you want to check that published figure against your own rifle and ammunition, the standard method is to measure velocity at the muzzle and again downrange with a second chronograph or a Doppler radar, and fit the drop in speed to the model. That is a measurement exercise, not an arithmetic one, and it takes equipment.
Take muzzle velocity from your own chronograph or the ammunition manufacturer's published figure for your barrel length; our muzzle velocity calculator handles that side. The MOA calculator converts the angular corrections that follow, and the recoil energy calculator covers the momentum bookkeeping at the other end of the rifle.
Range Safety and the Law
Stated once and briefly, because it governs everything on this page. Firearms are treated as loaded at all times. The muzzle points only at something you are willing to destroy. The target and what lies beyond it are identified before the shot. Hearing and eye protection are worn on the line. Ownership, transport, and hunting are governed by law that varies enormously between countries, states and even municipalities, and it is the shooter's responsibility to know the rules that apply where they are.
This page publishes no load data, and none should be taken from any website. Powder selection, charge weights, primers, case preparation and the assembly of ammunition come from a current manufacturer's loading manual and from nowhere else. The Sporting Arms and Ammunition Manufacturers' Institute publishes the industry standards for cartridge and chamber dimensions and pressures that those manuals are written against.
Arb Digital builds free calculators like this one as search-visible entry points for specialist retailers, then turns the traffic they earn into enquiries with content and technical SEO built around the terms your customers actually type.
SEO Services Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing a G1 figure with a G7 figure. They are ratios against different reference shapes. The same bullet has two very different numbers and neither converts to the other by a fixed factor.
- Using the cartridge name as the diameter. A .38 Special uses a 0.357 in bullet and a .303 British uses 0.311 in. Diameter is squared, so the error compounds.
- Treating sectional density as a ballistic coefficient. Sectional density ignores shape entirely, which is the whole reason form factor exists.
- Assuming a BC is constant. A G1 coefficient for a modern bullet drifts with velocity. Banded figures exist precisely because of this.
- Applying a BC to an unstable bullet. If the twist rate does not stabilise it, the published coefficient describes a flight the bullet is not making.
Related Free Tools From Arb Digital
For the stability question that has to be settled before a BC means anything, use the barrel twist rate calculator. The muzzle velocity calculator and recoil energy calculator cover the launch end, and the MOA calculator converts angular sight corrections into inches at distance. On the physics side, the drag force calculator gives the general drag relation, the projectile motion calculator handles the vacuum trajectory case, and the Mach number calculator places a velocity relative to the local speed of sound. Browse the free online tools hub for the rest.
Frequently Asked Questions
It is a projectile's sectional density divided by its form factor against a named reference drag model. In plain terms, it describes how well the projectile holds its speed against air drag compared with a standard shape whose drag curve has been measured and published.
They are ratios against two different reference projectiles. G1 is a short flat-based shape and G7 is a long pointed boat-tail. For the same modern bullet the G7 figure is roughly half the G1 figure, and there is no fixed conversion between them because it depends on the bullet's own drag curve.
Divide the bullet mass in grains by 7,000 to get pounds, then divide by the square of the bullet diameter in inches. A 168-grain 0.308 in bullet gives 0.024 divided by 0.094864, which is 0.253 lb/in².
It means slower speed loss, which usually produces less drop and less wind drift over the same distance. But trajectory also depends on launch velocity, sight height, zero distance and air density, so a BC on its own does not predict where a bullet lands.
No. Sectional density is mass divided by frontal area and ignores shape completely. Ballistic coefficient divides that by a form factor, which is the part that accounts for shape. A round ball and a boat-tail of equal mass and diameter share a sectional density and have very different coefficients.
Because the bullet's real drag curve has a different shape from the reference model's curve, so the ratio between them is not constant. This is most pronounced with G1 figures for modern low-drag bullets, which is why makers publish velocity-banded values or a G7 number instead.
From a current loading manual published by a powder or bullet manufacturer, and from nowhere else. No website, including this one, publishes powder types, charge weights, primer or case data, and no calculator substitutes for a manual and a knowledgeable mentor.
Published coefficients are referenced to a defined standard atmosphere. At a different altitude, temperature or pressure the air density differs, and the drag the bullet actually experiences scales with it, so the effective retardation changes even though the published number does not.
This calculator reproduces published external-ballistics arithmetic for information only. It publishes no load data of any kind, and it makes no statement that any load, bullet, twist rate or firearm is safe. Ammunition components and charge weights come from a current manufacturer's loading manual; a qualified gunsmith and the firearm manufacturer's own data govern what may be fired in any given firearm, and ownership, transport and hunting are subject to laws that vary by jurisdiction.
