Ballistic Coefficient Calculator
Measure how well a projectile keeps its speed in air: ballistic coefficient, sectional density, form factor and speed retained over distance.
🎯 What is a Ballistic Coefficient?
The ballistic coefficient (BC) of a body measures how well it carries its momentum through the air. A projectile with a high BC loses speed slowly, because its mass is large compared with the drag force it has to push through. In physics the definition is simple: BC = m / (Cd A), the mass divided by the product of the drag coefficient and the cross-sectional area. The units are kilograms per square metre. It is closely tied to the drag equation, where the drag force is one half times air density times Cd times A times speed squared, so the deceleration from drag is rho v squared divided by 2 BC. That one number captures mass, size and shape together.
The same idea is used for very different objects. Sports scientists use it to compare how a baseball, a golf ball, a tennis ball or a dart carries through the air. Aerospace engineers use a similar mass-to-drag-area ratio for re-entry bodies and rockets. Small-arms and airgun ballistics tables use a related quantity, the G1 or G7 coefficient, which is the sectional density divided by a form factor relative to a standard reference projectile. This page covers three views: the physical coefficient from mass, diameter and drag coefficient, the G1 style coefficient from mass, caliber and form factor with the unit conversions, and the speed retained over a distance given a BC and an air density.
It is easy to mix up these quantities, so be careful. Sectional density depends only on mass and diameter. The form factor describes shape against a reference. A G1 BC is meaningful only against the G1 reference curve, and a BC quoted for one drag model cannot be used with another. The physical BC m/(Cd A) assumes a single constant drag coefficient, which is accurate over a limited speed range and breaks down near the speed of sound. The calculator converts units between lb/in2 and kg/m2 (a factor of 703.0696) but never pretends that a G1 value equals a physical one.
The speed-retained mode shows the practical meaning. For a constant drag coefficient, the speed falls exponentially with distance, v = v0 exp(minus rho x / (2 BC)), so a BC of 100 kg/m2 in sea level air halves the speed in about 113 m while a BC of 500 halves it in about 565 m. The mode also reports the time of flight, the average speed and the share of kinetic energy retained, and charts the speed and time against distance. It is a physics teaching model that leaves out gravity drop, spin and wind, and it is not a firing solution.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — BC of a Baseball
m = 0.145 kg, d = 73.7 mm, Cd = 0.35 (assumed)
Example 2 — BC of a Steel-Tip Dart
m = 20 g, d = 7 mm, Cd = 1.0 (assumed illustrative values)
Example 3 — G1 Style BC of a Target Pellet
8.44 grains, 0.177 in diameter, form factor 1.5 (assumed)
Example 4 — G1 Style BC of a Long Target Projectile
175 grains, 0.308 in diameter, form factor 0.55 (assumed)
Example 5 — Baseball Speed Over 18.44 m
BC = 97.11 kg/m², v₀ = 40 m/s, x = 18.44 m, ρ = 1.225 kg/m³
Example 6 — A Dart Over 2.37 m
BC = 519.7 kg/m², v₀ = 20 m/s, x = 2.37 m, ρ = 1.225 kg/m³
❓ Frequently Asked Questions
🔗 Related Calculators
What is a ballistic coefficient?
The ballistic coefficient measures how well a body overcomes air resistance. In its physical form BC = m / (Cd A), mass divided by drag coefficient times cross-sectional area. A higher value means less deceleration from drag, because the mass is large compared with the drag force it feels.
What is the formula for ballistic coefficient?
The physical form is BC = m / (Cd A) in kg/m2. For small-arms style G1 values, BC = SD / i, where SD = m / d squared is the sectional density and i is the form factor. This page calculates both and shows the unit conversion.
What is sectional density?
Sectional density is mass divided by the square of the diameter, SD = m / d squared. In imperial units it is weight in pounds divided by diameter in inches squared (grains divided by 7000 gives pounds). A 175 grain projectile of 0.308 in diameter has SD 0.2635 lb/in2.
What is the form factor?
The form factor i compares the drag shape of a projectile with a reference projectile. A value of 1 means the same drag per unit of sectional density as the reference, below 1 is more streamlined, above 1 is draggier. The G1 BC is the sectional density divided by this factor.
How do I convert BC from lb/in2 to kg/m2?
Multiply by 703.0696, because 1 lb/in2 equals 0.45359237 kg divided by 0.0254 m squared. A BC of 0.479 lb/in2 is therefore about 336.9 kg/m2. Remember that this converts units only: it does not turn a G1 value into a physical m / (Cd A) value.
How is speed retained over distance calculated?
With a constant drag coefficient, dv/dx = minus (rho / (2 BC)) v, so v = v0 exp(minus rho x / (2 BC)). A baseball with BC 97.11 kg/m2 thrown at 40 m/s keeps 35.61 m/s after 18.44 m at sea level air density.
What does a higher BC do to speed loss?
It reduces the exponent rho x / (2 BC), so the speed decays more slowly. Doubling the BC doubles the distance needed to lose a given fraction of the speed. A dart with BC 519.7 kg/m2 keeps 99.7 percent of its speed over 2.37 m.
Is the BC the same at all speeds?
No. The drag coefficient varies with speed, especially near the speed of sound. A single BC is a good approximation only over a limited speed range, which is why standard drag models with a speed-dependent curve (G1, G7 and others) are used for long-range work.
How do I find the BC of a ball?
Use the physical mode. Enter the mass, the diameter (the frontal area is pi d squared / 4) and a drag coefficient. A baseball of 0.145 kg, 73.7 mm and Cd 0.35 gives a BC of 97.11 kg/m2. The Cd value is an assumption and strongly affects the answer.
What air density should I use?
Sea level standard air is 1.225 kg/m3. Lower values apply at altitude or in hot weather, for example 0.909 at 3000 m. Lower density reduces drag in the same way as a higher BC does, so the projectile retains more speed.
What does this calculator not include?
It ignores gravity drop, spin, wind, and the change of drag coefficient with speed. It is a physics model of speed loss to drag in a straight path and is not a firing solution or a planning tool.